A strain-space plasticity theory and numerical implementation

Abstract

This thesis sets forth an alternate version of plasticity which closely parallels the traditional theory but interchanges the roles of stress and strain. As a result, the new formulation gives stress as a functional of strain, rather than the reverse, and is thus attuned to the needs of the dynamicist. In the case of a single loading surface, the two versions of plasticity are shown to be equivalent when the model parameters are appropriately selected. A similar though less satisfying result is obtained for formulations involving a plurality of loading surfaces. The strain-space formulation is coded for numerical solution, with provision for a variable number of loading surfaces. The numerical algorithm is tested for accuracy in the handling of perfect plasticity, and the results are compared with those given by three commonly-used stress-space algorithms. The new algorithm is then interfaced with a finite element code and used to study the response of a foundation resting on an elastoplastic half-space.