Treatment of Inelastic Response in Solids Mechanics using Virtual Elements


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 low order virtual element formulation and its extension to different nonlinear problems that include inelastic material behaviour. Especially finite strain plasticity 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 was developed that allows the investigation of fracturing solids.

Keywords: virtual element analysis, mixed methods, plasticity, finite deformations, stabilization, phase field