A mixed extended finite element formulation for the simulation of cracks in nearly incompressible materials. Issue 1 (17th December 2018)

• Record Type: Journal Article
• Authors: Loehnert, Stefan
• Other Names: Müller G. guestEditor.; Ulbrich M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 18:Issue 1(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-12-17
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201800452
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: A low order mixed extended finite element for the simulation of cracks in nearly incompressible materials is presented. The finite element is based on a classical Q1P0 formulation in 3D including enrichment functions and corresponding degrees of freedom to account for the discontinuity in the displacement field. In addition, in the mixed formulation the volumetric stress field is enriched as well. The additional degrees of freedom can be eliminated on element level. The superior convergence behaviour of the presented formulation especially for nearly incompressible material behaviour is demonstrated by means of examples from linear elastic fracture mechanics.