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Crack face contact for a hexahedral-based XFEM formulation. (English) Zbl 1312.74043

Summary: Taking into account arbitrary crack geometries, crack closure generally occurs independently of the load case. As the standard eXtended finite element method (XFEM) does not prevent unphysical crack face penetration in this case, a formulation allowing for crack face contact is proposed in terms of a penalty formulation for normal contact. The discretization is developed for non-planar cracks intersecting hexahedral elements in an arbitrary manner. Typical problems of many crack face contact implementations within the XFEM, like locking or the introduction of additional degrees of freedom, are avoided by projecting the contact contribution onto the hexahedral element nodes. The method is tested by means of suitable numerical examples, finally presenting an application in form of a multiscale setup with arbitrarily arranged micro cracks in the vicinity of a macro crack front.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
74R10 Brittle fracture
74M15 Contact in solid mechanics
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