On the Use of Local Max-ent Shape Functions for the Simulation of Forming Processes

In this work we review the opportunities given by the use of local maximumentropy approximants (LME) for the simulation of forming processes. This approximation can be considered as a meshless approximation scheme, and thus presents some appealing features for the numerical simulation of forming processes in a Galerkin framework. Especially the behavior of these shape functions at the boundary is interesting. At nodes on the boundary, the functions possess a weak Kronecker-delta property, hence simplifying the prescription of boundary conditions. Shape functions at the boundary do not overlap internal nodes, nor do internal shape functions overlap nodes at the boundary. Boundary integrals can be computed easily and efficiently compared to for instance moving least-squares approximations. Furthermore, LME shapes also present a controllable degree of smoothness. To test the performance of the LME shapes, an elastic and a elasto-plastic problem was analyzed. The results were compared with a meshless method based on a moving least-squares approximation.