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An extended finite element method with higher-order elements for curved cracks. (English) Zbl 1038.74651
Summary: A finite element method for linear elastic fracture mechanics using enriched quadratic interpolations is presented. The quadratic finite elements are enriched with the asymptotic near tip displacement solutions and the Heaviside function so that the finite element approximation is capable of resolving the singular stress field at the crack tip as well as the jump in the displacement field across the crack face without any significant mesh refinement. The geometry of the crack is represented by a level set function which is interpolated on the same quadratic finite element discretization. Due to the higher-order approximation for the crack description we are able to represent a crack with curvature. The method is verified on several examples and comparisons are made to similar formulations using linear interpolants.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74R10 Brittle fracture
74B05 Classical linear elasticity
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