The authors propose a general framework based on two assumptions used in most of the theories in finite plasticity. The first assumption states that the material is at any instant in some elastic range, i.e. there exists a connected subset of the configuration space, together with an elastic law, which can be expressed in terms of the Piola-Kirchhoff symmetric tensor and the intrinsic (local) configuration. The second assumption states that between two elastic ranges exists a material isomorphism, which is called the inelastic transformation. Three theorems specify the relation between material isomorphism and material symmetry. No assumptions are made on the symmetry group of the elastic law, although when we deal with solids, the symmetry group must be a subgroup of the orthogonal transformation group, as it follows from Noll’s concept.
The authors mention that the change in inelastic transformation must be determined by some evolution equation or flow rule. Hence it is necessary to add another assumptions in order to complete the theory. The elastic law with respect to the reference placement is examplified for finite elastoplasticity in the framework proposed by Lee and Green-Naghdi. In the first example the authors present the overshooting effect, and in the second one they discuss a tensile test with two single crystal speciments. Finally, some computational results are analyzed concerning the finite inelastic deformations of single crystals.
For the entire collection see [Zbl 0839.00015].