An Unified Approach to Modelling and Numerical Solution of Coupled Field Problems in Nonlinear Solid Mechanics

Abstract

Recently, two features have been observed in the field of the unified description of inelastic material behaviour. The first approach is based on the development of a general material law describing the different inelastic properties ([1]). Another approach, which is used by Bergander ([2]) consists in a unified representation of current constitutive laws. All these considerations are characterized by a pure constitutive analysis, without any reference to the field equations.

The aim of this paper is a generalization of Bergander’s standard formulation ([2]) under the aspect of a uniform treatment of both, the field equations and the constitutive relati­ons. Furthermore, this approach should allow us to develop a uniform numerical solution strategy consisting of finite element discretization, implicit time integration and a consistent linearization as a generalization of the well- known return-algorithm.