Finite-Element Formulation for Large Strain: Large Deformation Problems in Plasticity and Viscoplasticity

摘要

A complete stress analysis of a metal-forming process is necessary to assess the onset of metal-forming such as the initiation of internal or surface cracks or the generation of residual stresses. For the study of forming with rate-independent materials, it is sufficient to use an elastic-plastic analysis. It is well known, however, that metal forming, both at room and elevated temperatures, can be rate dependent. This requires the use of a time-dependent inelastic constitutive model for material behavior. The present finite-element formulation developed through a weighted residual approach of Galerkin type, which is also equivalent to the principle of virtual work, does not rely on the existence of a homogeneous rate potential function of second degree. Thus, it can be used for time-dependent constitutive models where such a rate potential may not exist. A program to evaluate the complete stress distribution has been developed and applied to the extrusion process using an updated Lagrangian approach. The stress fields obtained for elastic-plastic materials exhibit features which are consistent with the known development of extrusion defects. (ERA citation 08:010206)