one_dimensional_plasticity_explicit.ipynb

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    "# Elastic Perfectly-Plastic - Explicit Integration\n",
    "\n",
    "## Define Model\n",
    "\n",
    "#### i. Elastic stress-strain relationship  \n",
    "$\\dot{\\sigma} = E\\left(\\dot{\\varepsilon} - \\dot{\\varepsilon}^p\\right)$  \n",
    "\n",
    "#### ii. Hardening variables  \n",
    "$\\sigma_y$ = Yield stress\n",
    "\n",
    "#### iii. Yield Surface  \n",
    "\n",
    "$f(\\sigma,\\sigma_y) = |\\sigma| - \\sigma_y$\n",
    "\n",
    "#### iv. Flow rule  \n",
    "\n",
    "$\\dot{\\varepsilon}^p = \\gamma \\cdot sign\\left(\\sigma\\right)$\n",
    "\n",
    "#### v. Hardening Law  \n",
    "\n",
    "$\\dot{\\sigma_y} = 0$\n",
    "\n",
    "#### vi. Karush-Kuhn-Tucker complementary conditions  \n",
    "\n",
    "$\\gamma \\geq 0$  \n",
    "\n",
    "$f\\left(\\sigma, \\sigma_y\\right) \\leq 0$  \n",
    "\n",
    "$\\gamma \\cdot f\\left(\\sigma, \\sigma_y\\right)=0$  \n",
    "\n",
    "#### vii. Consistency condition  \n",
    "\n",
    "$\\gamma \\cdot \\dot{f}\\left(\\sigma, \\sigma_y\\right) = 0$  "
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "## Implicit Implementation (Return Mapping)\n",
    "\n",
    "$\\sigma_{i}$ = stress value at start of current load step  \n",
    "\n",
    "$\\Delta \\varepsilon$ = strain increment  \n",
    "\n",
    "$\\sigma_{i+1}^{trial} = \\sigma_{i} + E \\cdot \\Delta \\varepsilon$  \n",
    "\n",
    "$f_{i+1}^{trial} = \\left|\\sigma_{i+1}^{trial}\\right| - \\sigma_y$  \n",
    "\n",
    "if $f_{i+1}^{trial} < 0$:\n",
    "\n",
    "> $\\sigma_{i+1} = \\sigma_{i+1}^{trial}$\n",
    "\n",
    "> $\\varepsilon^p_{i+1} = \\varepsilon^p_i$  \n",
    "\n",
    "else:\n",
    "\n",
    "> $\\Delta \\gamma = \\frac{f_{i+1}^{trial}}{E}$  \n",
    "\n",
    "> $\\sigma_{i+1} = \\sigma_{i+1}^{trial} - \\Delta \\gamma \\cdot E \\cdot sign \\left(\\sigma_{i+1}^{trial}\\right)$  \n",
    "\n",
    "> $\\varepsilon^p_{i+1} = \\varepsilon^p_i + \\Delta \\gamma \\cdot sign \\left(\\sigma_{i+1}^{trial}\\right)$"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "## Explicit Implementation\n",
    "\n",
    "initialize model at time step 0:  \n",
    "\n",
    "$\\Delta\\epsilon^p = 0.0$\n",
    "\n",
    "\n",
    "Now loop over time steps, starting from index 1, where index 0 is the initial condition of the model\n",
    "\n",
    "$\\sigma_{i+1} = \\sigma_{i} + E\\left(\\Delta_\\epsilon - \\Delta_\\epsilon^p\\right)$  \n",
    "\n",
    "$f = \\left|\\sigma_{i+1}\\right| - \\sigma_y$  \n",
    "\n",
    "if f < 0:\n",
    "\n",
    "> $\\Delta\\epsilon^p = 0.0$  \n",
    "\n",
    "else:\n",
    "\n",
    "> $\\Delta\\gamma = \\frac{f}{E}$  \n",
    "\n",
    "> $\\Delta\\epsilon_p = \\Delta\\gamma sign\\left(\\Delta \\epsilon\\right)$  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
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   "outputs": [
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       "\n",
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       "\n",
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       "    fig.send_draw_message();\n",
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       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\n",
       "                /* FIXME: We get \"Resource interpreted as Image but\n",
       "                 * transferred with MIME type text/plain:\" errors on\n",
       "                 * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "                 * to be part of the websocket stream */\n",
       "                img.type = 'image/png';\n",
       "            }\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function (e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e) {\n",
       "        e = window.event;\n",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
       "\n",
       "    return { x: x, y: y };\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    var canvas_pos = mpl.findpos(event);\n",
       "\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(data);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager) {\n",
       "        manager = IPython.keyboard_manager;\n",
       "    }\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img 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\" width=\"575.5555708025713\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x114cd97cf70>]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "E = 100\n",
    "sigmay = 1\n",
    "epsilon_y = sigmay/E\n",
    "Npts = 10000 # Number of points per cycle in sinusoidal strain history\n",
    "Ncyc = 3 # Number of cycles in sinusoidal strain history\n",
    "N = Npts*Ncyc\n",
    "time = np.arange(0,N)\n",
    "epsilon_max = 5.0*epsilon_y\n",
    "epsilon = epsilon_max*np.sin(2.0*np.pi*time/Npts)\n",
    "\n",
    "# Now define stress\n",
    "sigma = np.zeros(N)\n",
    "for i in range(1,N):\n",
    "    depsilon = epsilon[i] - epsilon[i-1]\n",
    "    sigma_trial = sigma[i-1] + E*depsilon\n",
    "    ftrial = np.abs(sigma_trial) - sigmay\n",
    "    if(ftrial<0):\n",
    "        sigma[i] = sigma_trial\n",
    "    else:\n",
    "        delta_gamma = ftrial/E\n",
    "        sigma[i] = sigma_trial - delta_gamma*E*np.sign(sigma_trial)\n",
    "        \n",
    "        \n",
    "# Implement explicit model\n",
    "sigma_ex = np.zeros(N)\n",
    "epsilon_p_ex = np.zeros(N)\n",
    "depsilon_p = 0\n",
    "for i in range(1,N):\n",
    "    depsilon = epsilon[i] - epsilon[i-1]\n",
    "    sigma_ex[i] = sigma_ex[i-1] + E*(depsilon - depsilon_p)\n",
    "    f = np.abs(sigma_ex[i-1]) - sigmay\n",
    "    if(f<0):\n",
    "        epsilon_p_ex[i] = epsilon_p_ex[i-1]\n",
    "        depsilon_p = 0.0\n",
    "    else:\n",
    "        dgamma = f/E\n",
    "        depsilon_p = dgamma*np.sign(depsilon)\n",
    "        epsilon_p_ex[i] = epsilon_p_ex[i-1] + depsilon_p\n",
    "        \n",
    "plt.plot(epsilon,sigma)\n",
    "plt.plot(epsilon,sigma_ex)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "/* global mpl */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function () {\n",
       "    if (typeof WebSocket !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof MozWebSocket !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert(\n",
       "            'Your browser does not have WebSocket support. ' +\n",
       "                'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "                'Firefox 4 and 5 are also supported but you ' +\n",
       "                'have to enable WebSockets in about:config.'\n",
       "        );\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = this.ws.binaryType !== undefined;\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById('mpl-warnings');\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent =\n",
       "                'This browser does not support binary websocket messages. ' +\n",
       "                'Performance may be slow.';\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = document.createElement('div');\n",
       "    this.root.setAttribute('style', 'display: inline-block');\n",
       "    this._root_extra_style(this.root);\n",
       "\n",
       "    parent_element.appendChild(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen = function () {\n",
       "        fig.send_message('supports_binary', { value: fig.supports_binary });\n",
       "        fig.send_message('send_image_mode', {});\n",
       "        if (fig.ratio !== 1) {\n",
       "            fig.send_message('set_dpi_ratio', { dpi_ratio: fig.ratio });\n",
       "        }\n",
       "        fig.send_message('refresh', {});\n",
       "    };\n",
       "\n",
       "    this.imageObj.onload = function () {\n",
       "        if (fig.image_mode === 'full') {\n",
       "            // Full images could contain transparency (where diff images\n",
       "            // almost always do), so we need to clear the canvas so that\n",
       "            // there is no ghosting.\n",
       "            fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "        }\n",
       "        fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "    };\n",
       "\n",
       "    this.imageObj.onunload = function () {\n",
       "        fig.ws.close();\n",
       "    };\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_header = function () {\n",
       "    var titlebar = document.createElement('div');\n",
       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
       "    var titletext = document.createElement('div');\n",
       "    titletext.classList = 'ui-dialog-title';\n",
       "    titletext.setAttribute(\n",
       "        'style',\n",
       "        'width: 100%; text-align: center; padding: 3px;'\n",
       "    );\n",
       "    titlebar.appendChild(titletext);\n",
       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = (this.canvas_div = document.createElement('div'));\n",
       "    canvas_div.setAttribute(\n",
       "        'style',\n",
       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
       "            'overflow: hidden;' +\n",
       "            'position: relative;' +\n",
       "            'resize: both;'\n",
       "    );\n",
       "\n",
       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
       "    // Apply a ponyfill if ResizeObserver is not implemented by browser.\n",
       "    if (this.ResizeObserver === undefined) {\n",
       "        if (window.ResizeObserver !== undefined) {\n",
       "            this.ResizeObserver = window.ResizeObserver;\n",
       "        } else {\n",
       "            var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n",
       "            this.ResizeObserver = obs.ResizeObserver;\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    this.resizeObserverInstance.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'dblclick',\n",
       "        on_mouse_event_closure('dblclick')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus() {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', { width: x_pixels, height: y_pixels });\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_message = function (type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function () {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch (cursor) {\n",
       "        case 0:\n",
       "            cursor = 'pointer';\n",
       "            break;\n",
       "        case 1:\n",
       "            cursor = 'default';\n",
       "            break;\n",
       "        case 2:\n",
       "            cursor = 'crosshair';\n",
       "            break;\n",
       "        case 3:\n",
       "            cursor = 'move';\n",
       "            break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\n",
       "                /* FIXME: We get \"Resource interpreted as Image but\n",
       "                 * transferred with MIME type text/plain:\" errors on\n",
       "                 * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "                 * to be part of the websocket stream */\n",
       "                img.type = 'image/png';\n",
       "            }\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function (e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e) {\n",
       "        e = window.event;\n",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
       "\n",
       "    return { x: x, y: y };\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    var canvas_pos = mpl.findpos(event);\n",
       "\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(data);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager) {\n",
       "        manager = IPython.keyboard_manager;\n",
       "    }\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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width=\"862.9630239248646\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "E = 100000\n",
    "H = 0.1*E\n",
    "sigmay = 1000\n",
    "epsilon_y = sigmay/E\n",
    "Npts = 100 # Number of points per cycle in sinusoidal strain history\n",
    "Ncyc = 3 # Number of cycles in sinusoidal strain history\n",
    "N = Npts*Ncyc\n",
    "time = np.arange(0,N)\n",
    "epsilon_max = 5.0*epsilon_y\n",
    "epsilon = epsilon_max*np.sin(2.0*np.pi*time/Npts)\n",
    "\n",
    "# Now define stress\n",
    "sigma = np.zeros(N)\n",
    "sigma_q = np.zeros(N)\n",
    "epsilon_p = np.zeros(N)\n",
    "for i in range(1,N):\n",
    "    depsilon = epsilon[i] - epsilon[i-1]\n",
    "    sigma_trial = sigma[i-1] + E*depsilon\n",
    "    sigma_qtrial = sigma_q[i-1]\n",
    "    ftrial = np.abs(sigma_trial-sigma_qtrial) - sigmay\n",
    "    if(ftrial<0):\n",
    "        sigma[i] = sigma_trial\n",
    "        sigma_q[i] = sigma_qtrial\n",
    "        epsilon_p[i] = epsilon_p[i-1]\n",
    "    else:\n",
    "        delta_gamma = ftrial/(E+H)\n",
    "        sigma[i] = sigma_trial - delta_gamma*E*np.sign(sigma_trial-sigma_qtrial)\n",
    "        sigma_q[i] = sigma_q[i-1] + delta_gamma*H*np.sign(sigma_trial-sigma_qtrial)\n",
    "        epsilon_p[i] = epsilon_p[i-1] + delta_gamma*np.sign(sigma_trial-sigma_qtrial)\n",
    "        \n",
    "        \n",
    "# Explicit implementation\n",
    "sigma_ex = np.zeros(N)\n",
    "sigma_q_ex = np.zeros(N)\n",
    "epsilon_p_ex = np.zeros(N)\n",
    "depsilon_p_ex = 0.0\n",
    "for i in range(1,N):\n",
    "    depsilon = epsilon[i] - epsilon[i-1]\n",
    "    sigma_ex[i] = sigma_ex[i-1] + E*(depsilon-depsilon_p_ex)\n",
    "    sigma_q_ex[i] = sigma_q_ex[i-1] + H*depsilon_p_ex\n",
    "    f = np.abs(sigma_ex[i] - sigma_q_ex[i]) - sigmay\n",
    "    if(f<=0):\n",
    "        depsilon_p_ex = 0.0\n",
    "        epsilon_p_ex[i] = epsilon_p_ex[i-1]\n",
    "    else:\n",
    "        dgamma = f/(E+H)\n",
    "        depsilon_p_ex = dgamma*np.sign(depsilon)\n",
    "        epsilon_p_ex[i] = epsilon_p_ex[i-1] + depsilon_p_ex\n",
    "        \n",
    "fig, ax = plt.subplots(2,2,sharex='all',sharey='all')\n",
    "ax[0,0].plot(epsilon,sigma,label='implicit')\n",
    "ax[0,1].plot(epsilon_p, sigma)\n",
    "ax[1,0].plot(epsilon,sigma_q)\n",
    "ax[1,1].plot(epsilon_p,sigma_q)\n",
    "ax[0,0].plot(epsilon,sigma_ex,label='explicit')\n",
    "ax[0,1].plot(epsilon_p_ex, sigma_ex)\n",
    "ax[1,0].plot(epsilon,sigma_q_ex)\n",
    "ax[1,1].plot(epsilon_p_ex,sigma_q_ex)\n",
    "ax[1,0].set_xlabel(r'$\\epsilon$')\n",
    "ax[0,0].set_ylabel(r'$\\sigma$')\n",
    "ax[1,0].set_ylabel(r'$\\sigma_q$')\n",
    "ax[1,1].set_xlabel(r'$\\epsilon_p$')\n",
    "ax[0,0].legend()\n",
    "plt.tight_layout()"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}