Mixed XFEM formulation for the simulation of heterogeneities including elasto‐plastic material behaviour. Issue 1 (18th November 2019)

• Record Type: Journal Article
• Authors: Löhnert, Stefan
• Other Names: Eberhardsteiner J. guestEditor.; Schöberl M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 19:Issue 1(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-11-18
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201900270
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: Metal matrix composites often show large isochoric plastic deformations within the matrix material. For dominant plastic deformations this may lead to volumetric locking effects similar to locking in incompressible materials. Lower order mixed finite element formulations can alleviate this difficulty. Complex microstructures often require extensive effort to generate a mesh suitable for finite element simulations. The eXtended Finite Element Method may improve this situation by allowing for discontinuities in the displacement and/or strain field within any finite element. In this contribution a mixed XFEM formulation is presented combining the advantages of the XFEM and mixed FEM. The formulation is applied to small deformation elasto‐plasticity with linear isotropic and linear kinematic hardening. An example demonstrates its superior convergence behaviour compared to a standard XFEM formulation.