Generalized Standard Media: An Approach using Symbolic Manipulation

The implementation of complex nonlinear material laws as finite-element-program code is extremely time-consuming. It is a source of frequent mistakes and characterized by the necessity of an expert-knowledge of this topic. But by combining a well-developed theory of continuum-mechanics with symbolic computation and numerical code, the implementation of a specific material law can be automated. One aim of this paper is to outline the systematical approach and the requirements on the symbolic tools used. In this special case the continuum-mechanical framework is established in the context of generalized standard media. In particular this is a rational theory of finite strain elasto-plasticity. This frame establishes a program-environment with the possibility to incorporate the parts prepared by symbolic computation. Note that this environment does not take into consideration the specific form of internal energy, yield function and hardening law. The symbolic computation plays a crucial role in the formulation of the parts of the program responsible for the calculation of the stress-tensor and the consistent elasto-plastic tangent. Here Mathematica is used to write down the - now exactly specified - material laws. From this foundation certain derivatives of the internal energy and the flow rule with respect to elastic and plastic strain tensors are computed.