Treatment of Inelastic Response in Solids Mechanics using Virtual Elements
Director of the Institute of Continuum Mechanics in the Faculty of Mechanical Engineering at the Leibniz Universität Hannover, Germany
Peter Wriggers is Director of the Institute of Continuum Mechanics in the Faculty of Mechanical Engineering at the Leibniz Universität Hannover, Germany. He is a member of the “Braunschweigische Wissenschaftliche Gesellschaft”, the Academy of Science and Literature in Mainz, the German National Academy of Engineering “acatech” and the National Academy of Croatia. He was President of GAMM, President of GACM and Vice-President of IACM. Furthermore, he acts as Editor-in-Chief for the International Journal “Computational Mechanics” and “Computational Particle Mechanics” and is member of 15 Editorial Boards. He was awarded the Fellowship of IACM and received the “Computational Mechanics Award” of IACM, the “Euler Medal” of ECCOMAS and the “IACM Award” of IACM as well as three honorary degrees from the Universities of Poznan, ENS Cachan and TU Darmstadt.
Virtual elements (VEM) were developed during the last decade and applied to various problems in elasticity. Due to the fact that the element shape of virtual elements can be arbitrary including even non convex shapes these elements are more flexible when the geometry of the element is considered. The success of VEM discretizations in the linear range using different polynomial orders leads directly to the question whether these elements can also be applied successfully to nonlinear situations.
This contribution is concerned with a simple low order virtual element formulations in two- and three-dimensional applications and their extension to different nonlinear problems that include inelastic material for behaviour. Especially finite strain plasticity, the effect of temperature and phase field approaches are discussed in detail. Several possible formulations and discretizations are introduced and compared by means of examples. In order to show the applicability of the virtual element method to multi-field problems, a phase field formulation for VEM is developed that allows the investigation of fracturing solids.