PP 1748: Approximation and Reconstruction of Stresses in the Deformed Configuration for Hyperelastic Material Models

Numerical simulation techniques are an essential component for the construction, design and optimisation of cutting-edge technologies as for example innovative products, new materials as well as medical-technical applications and production processes. These important developments pose great demands on quality, reliability and capability of numerical methods, which are used for the simulation of these complex problems. Challenges are for example capture of incompressibility, anisotropy and discontinuities. Existing computer-based solution methods often provide approximations which cannot guarantee substantial, absolutely necessary stability criteria respectively fulfill them. Especially in the field of geometrical and material non-linearity such uncertainties appear. Typical problems are insufficient or even pathological stress approximations due to unsuitable approximation spaces as well as weak convergence behaviour because of stiffening effects or mesh distortion. Similar problems arise in the framework of crack and contact problems. Here the resolution of the local discontinuities as well as their evolution plays a key role. The scientists of the SPP 1748 have set themselves the goal to establish a new quality in the area of non-conventional discretisation methods. Herein the work programme of the SPP is founded:

1. The evolution of modern non-conventional discretisation methods,
2. their mathematical analysis and
3. the exploration of their application limits on the basis of suitable benchmark problems.