Computational plasticity

A material is said to have deformed plastically if it doesn’t return to its original shape after the load is removed. The most common application for plasticity in nite element analysis is modeling the deformation of metals. While a great deal of research is available on the plasticity of metals at a very fundamental level, the majority of plasticity models are phenomenological and have no motivation beyond duplicating experimental data. The models discussed here are among the simpler plasticity models, and they are, indeed, completely phenomenological. While there are post hoc rationalizations of why these simple models perform as well as they do, they are still rationalizations.

The tension test

The most common mechanical test for characterizing metals is the tension test. A specimen is put in a machine which pulls it at a prescribed rate and simultaneously records the load on the specimen.

The equations for isotropic von Mises plasticity

The consistency condition

The continuum tangent matrix for plastic flow

Radial Return

The most popular method for integrating the plasticity equations for isotropic von Mises plasticity is radial return, developed by Wilkins for HEMP and Maenchen and Sack for TENSOR, two finite difference codes developed at Lawrence Livermore National Laboratory.

Generalizing the yield function

The consistent tangent matrix

In the evaluation of the tangent sti ness matrix, the material tangent matrix is required. The continuum tangent matrix was developed in a previous article, and it is frequently used in nite element calculations.

Solving problems with path dependent materials