advancedCSE.github.io

Python Constitutive Model Driver

This is a Python code to test constitutive stress updates and associated computational plasticity algorithms.

Model	Elementary	Intermediate	Difficult	Research-Grade
von Mises (isotropic hardening)	🗸
von Mises (isotropic hardening), variational update ^a				🗸
Drucker-Prager		🗸
Mohr-Coulomb		🗸
Extended Mohr-Coulomb model^b				🗸
Hardening soil model^b				🗸
Concrete damage plasticity (Feenstra and De Borst)^c				🗸
Concrete damage plasticity (Lee and Fenves)^c				🗸
Burgers model^c			🗸
Glen power law model^c			🗸

a) Based on the following papers:

Ortiz, M. and Stainier, L. “The variational formulation of viscoplastic constitutive updates.” Computer Methods in Applied Mechanics and Engineering Volume 171, Issues 3–4, 9 April 1999, Pages 419-444.
Miehe, Christian, Apel, Nikolas and Lambrecht, Matthias. “Anisotropic additive plasticity in the logarithmic strain space: modular kinematic formulation and implementation based on incremental minimization principles for standard materials.” Computer Methods in Applied Mechanics and Engineering 191.47-48 (2002): 5383-5425.

b) Simplified version with only shear hardening mechanism; no pressure dependency, no Lode angle dependency

c) Not yet available; planned for inclusion in the near future

Complementarity smoothing of the loading-unloading (or Karush-Kuhn-Tucker) condition to avoid use of active set search in models with multiple-surfaces.
Global equilibrium solvers: pseudo-inverse, least-squares to handle rank-deficient consistent tangents (e.g., due to non-smooth or multiple yield surfaces).

Adaptive time stepping - time step cuts back when there is no convergence, increases when there is convergence.
Abaqus-like input file:
- overloaded keywords *CLOAD and *BOUNDARY to specify stress and strain boundary conditions, respectively
- *AMPLITUDE keyword to specify time-varying amplitude functions
- *PARAMETER keyword to specify variables and math expressions using these variables
- *CONTROLS keyword to specify global equilibrium convergence parameters: maximum number of iterations and error tolerance

Line-by-line derivations of all equations (derivatives of yield functions, plastic potentials and residual equations) necessary for implementation are documented.

The implemented models are for educational purposes to explore advanced solution algorithms and study yield and hardening mechanisms.
Certain assumptions have been invoked to simplify implementations of certain models.
Due to the advanced algorithms considered, certain models may not interface with the solvers in commercial finite element programs.