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Extended finite element method for three-dimensional crack modelling. (English) Zbl 0963.74067
Summary: We describe an extended finite element method for three-dimensional crack modelling. A discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity. This provides the domain to be modelled by finite elements with no explicit meshing of crack surfaces. In addition, we discuss computational geometry issues associated with the crack representation and the enrichment of finite element approximation. Stress intensity factors for planar three-dimensional cracks are presented, which are found to be in good agreement with benchmark solutions.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74R10 Brittle fracture
74G70 Stress concentrations, singularities in solid mechanics
Software:
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