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Finite Element Modelling of Cracks Based on the Partition of Unity Method
Author(s) -
Dumstorff P.,
Meschke G.
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310098
Subject(s) - partition of unity , finite element method , polygon mesh , jump , displacement (psychology) , representation (politics) , displacement field , extended finite element method , brittleness , structural engineering , cracking , partition (number theory) , geometry , mathematics , mathematical analysis , materials science , physics , engineering , psychology , quantum mechanics , combinatorics , politics , political science , law , composite material , psychotherapist
In this paper a finite element model for the analysis of brittle materials in the post cracking regime is presented. The model allows the representation of failure zones several times smaller than the structure itself using relatively coarse finite element meshes. The formulation is based on the partition of unity method. Discontinuous shape functions are used to enrich the continuous approximation of the displacement field where a crack has opened [2]. The magnitude of the displacement jump is determined by extra degrees of freedom at existing nodes. The crack path is completely independent of the structure of the mesh and is continuous across element boundaries. To model inelastic deformations around the crack tip a cohesive crack model is used. A representative numerical example illustrates the performance of the proposed model.