Scott J. Brandenberg, UCLA
This course covers the following topics
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Python and Jupyter
1.1. Downloading Python and Jupyter
1.2. Simple tutorials -
Rate Independent One-Dimensional Elasto-Plasticity
2.1 Additive decomposition of strain rate
2.2 Elastic stress-strain relationship
2.3 Yield surface
2.4 Flow rule
2.5 Hardening law
2.6 Karush-Kuhn-Tucker conditions
2.7 Consistency condition
2.8 Return mapping
2.9 Elastic-perfectly plastic model
2.10 Kinematic and isotropic hardening models -
Nonlinear Consolidation Finite Difference Solution
3.1 Governing differential equation
3.2 Finite difference formulation
3.3 Nonlinear stress-strain relationship
3.4 Hydraulic conductivity relationship -
Three-Dimensional Stress at a Point
4.1 Cauchy stress tensor
4.2 Index notation
4.3 Principal stresses and principal stress planes
4.4 Stress paths
4.5 Invariants of Cauchy stress tensor, I1, I2, I3
4.6 Stress deviator tensor
4.7 Invariants of stress deviator tensor, J1, J2, J3
4.8 Lode angle -
Three-Dimensional Small Deformation Linear Elasticity
5.1 Hooke’s law
5.2 Field equations for isotropic homogeneous linear elasticity
5.3 Hypo-elasticity -
Small Deformation Elasto-Plasticity
6.1 Additive decomposition of strain rate tensor
6.2 Integration algorithms (forward Euler, backward Euler, midpoint rule)
6.3 Drucker-Prager yield surface
6.4 Mohr-Coulomb yield surface
6.5 Cam Clay material model
6.6 Manzari-Dafalias material models
6.7 PressureDependMultiYield and PressureIndependMultiYield material models
6.8 PM4Sand and PM4Silt material models -
Numerical Implementation of Elasto-Plastic Material Models
7.1 Introduction to modeling software (FLAC, PLAXIS, OpenSees, RS2)
7.2 Load stages and increments
7.3 Effective stress vs. total stress analysis
7.4 Pore pressure coupling via UP formulation
7.5 Strength reduction method for slope stability
7.6 Shallow foundation bearing capacity
7.7 Sheet pile stability