Elastic-plasticity of Isotropic Materials

The strain hardening behavior of materials is a major factor in structural response as metal working processes or plastic instability problems. A proper description of strain hardening at large plastic strains is generally imperative. For many plasticity problems, the hardening behavior of the material is simply characterized by the strain-stress curve of the material. For the proportional loading this is generally true. However, if the loading path is combined, the characterization by a simple strain-stress curve is no longer adequate.

The incremental plasticity theory is generally used in computational methods. Plasticity models are written as rate-dependent or independent. A rate-dependent model is a one in which the strain rate does affect the constitutive law. This is true for a large range of metals at low temperature relative to their melting temperature.

Most isotropic elastic-plastic material laws in Radioss use von Mises yield criteria as given in Stresses in Solids. Several kinds of models are integrated. The models involve damage for ductile or brittle failures with or without dislocation. The cumulative damage law can be used to access failure. The next few paragraphs describe theoretical bases of the integrated models.