Constitutive models and finite element formulations for elastic-plastic materials at large-strain deformations.

摘要

This dissertation concerns the constitutive description of elastic-plastic materials and the finite element analysis at large strains. Constitutive models are developed within the context of the finite plasticity theory of Green and Naghdi, and the algorithmic issues within the framework of the strain-driven, implicit finite element methods are discussed. The constitutive equations employed resemble those of the small strain plasticity theory, and recover the latter in the limiting cases the infinitesimal deformations. Also, the proposed constitutive structure allows for sufficient freedom to accommodate some existing experimental evidence on metal plasticity at finite strains. Selected numerical simulations are conducted, and the results indicate that the constitutive equations can adequately model the elastic-plastic response of metals or metal alloys undergoing large deformations.;Material symmetries relative to an undeformed, stress- and plastic strain-free configuration are considered, and the restriction of symmetry on the constitutive equations is discussed. Fully anisotropic constitutive equations which incorporate anisotropies in the stress response, yield criterion and flow rules are proposed and considered in the algorithmic development. A novel method for the integration of the anisotropic plastic rate equations is developed with the aid of results from anisotropic representation theory. This method generalizes the classical radial return method for isotropic case, and therefore leads to considerable reductions in the algebraic operations involved in the local integration of the plastic flow.