Project Details
Projekt
First-order system least squares finite elements for finite elasto-plasticity
Applicants
Professor Dr.-Ing. Jörg Schröder; Dr.-Ing. Alexander Schwarz; Professor Dr. Gerhard Starke
Subject Area
Mechanics
Term
from 2014 to 2019
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 255798245
The goal of the proposed research project is the development, construction and analysis of mixed finite element formulations in the field of finite elasto-plasticity on the basis of first-order systems. Since there are no simulation tools available at the moment that are capable to provide reliable solutions for such problems, the ambition of this project is to provide a new access with modern discretization techniques in this field. The least squares finite element method (LSFEM), in particular produces accurate approximations of stresses which are often of primary interest in the context of solid mechanical problems. This approach avoids the requirement of a compatibility (inf-sup) condition for the finite element spaces for stresses and displacements leading to more general combinations. Furthermore, a robust numerical behavior particularly for quasi-incompressible materials is obtained.In numerous investigations the applicants achieved a long-term joint experience basis with respect to the LSFEM and its application to solid mechanics supported by a cooperation between mathematics and mechanics. On the basis of the advances obtained within this cooperation it is now possible to jointly address problems of finite plasticity.The main tasks of the project can be divided into three steps. Firstly, the components of the method will be developed for the elastic subproblem in order to extend them to the model of finite multiplicative elasto-plasticity. After that, the resulting formulations will be validated numerically by means of the benchmark problems provided by the Priority Programme as well as by computations of real complex microheterogeneous structures as for instance of dual-phase steels. In order to improve the efficiency and robustness, these computations are guided by several investigations concerning e.g. adaptivity, choice of the approximation spaces and suitable weighting.This research project aims at setting new standards of quality in the field of non-conventional discretization methods for structural mechanical problems in the framework of finite elasto-plasticity.
DFG Programme
Priority Programmes
