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A mixed extended finite element formulation for the simulation of cracks in nearly incompressible materials
Author(s) -
Loehnert Stefan
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800452
Subject(s) - finite element method , discontinuity (linguistics) , compressibility , degrees of freedom (physics and chemistry) , mixed finite element method , extended finite element method , displacement (psychology) , convergence (economics) , displacement field , mechanics , stress (linguistics) , mathematics , field (mathematics) , smoothed finite element method , stress field , element (criminal law) , mathematical analysis , physics , structural engineering , engineering , boundary knot method , philosophy , psychotherapist , economic growth , linguistics , psychology , quantum mechanics , economics , law , boundary element method , political science , pure mathematics
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.