Finite Element Solutions of Finite-Strain Elastic-Plastic Problems, Based on a Complementary Rate Principle.

摘要

In this paper a new complementary energy theorem for the rate problem of finite strain classical (rate-independent) elasto-plasticity, and an assumed stress finite element method based on this new theorem, are presented. The presented total Lagrangean rate form of the new complementary theorem involves both the rate of unsymmetric first Piola-Kirchhoff stress tensor and the rate of rotation tensor as variables. A numerical study, using the presently developed finite element method, of the problem of necking of an initially perfect elasto-plastic bar under applied uniaxial tension is presented; and the results are compared with the solution to a similar problem by Cowper and Onat. (Author)