The aim of this contribution is the presentation of an adaptive finite element procedure for the solution of geometrically and physically non-linear problems in structural mechanics. Within this context, the attention is mainly directed on the error estimation and hierarchical strategies for mesh refinement and coarsening in the case of finite elasto-plastic deformations. An important but sensitive aspect of adaptation approaches of the space discretization is the calculation of mechanical field variables for the modified mesh. Procedures of mesh refinement and coarsening imply the determination of strains, stresses and internal variables at the nodes and the Gauss points of new elements based on the transfer of the required data from the former mesh. In order to improve the efficiency as well as the convergence behaviour of the adaptive FE process an approach of data transfer primarily related to nodal values is presented. It is characterized by solving the initial value problem not only at the Gauss points but additionally at the nodes of the elements.
The aim of this contribution is a comparison of different mapping techniques usually applied in the field of hierarchical adaptive FE-codes. The calculation of mechanical field variables for the modified mesh is an important but sensitive aspect of adaptation approaches of the spatial discretization. Regarding non-linear boundary value problems procedures of mesh refinement and coarsening imply the determination of strains, stresses and internal variables at the nodes and the Gauss points of new elements based on the transfer of the required data from the former mesh. The kind of mapping of the field variables affects the convergence behaviour as well as the costs of an adaptive FEM-calculation in a non-negligible manner. In order to improve the stability as well as the efficiency of the adaptive process a comparison of different mapping algorithms is presented and evaluated. Within this context, the mapping methods taken into account are -an element-oriented extrapolation procedure using special shape functions, -a patch-oriented transfer approach and, -the allocation of nodal history-dependent state (field) variable data using a supplementary integration of the material law at the nodes of the elements.
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