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Analysis of three-dimensional crack initiation and propagation using the extended finite element method. (English) Zbl 1122.74498
Summary: We present a new formulation and a numerical procedure for the quasi-static analysis of three-dimensional crack propagation in brittle and quasi-brittle solids. The extended finite element method (XFEM) is combined with linear tetrahedral elements. A viscosity-regularized continuum damage constitutive model is used and coupled with the XFEM formulation resulting in a regularized crack-band version of XFEM. The evolving discontinuity surface is discretized through a $$C^0$$ surface formed by the union of the triangles and quadrilaterals that separate each cracked element in two. The element’s properties allow a closed form integration and a particularly efficient implementation allowing large-scale 3D problems to be studied. Several examples of crack propagation are shown, illustrating the good results that can be achieved.

##### MSC:
 74S05 Finite element methods applied to problems in solid mechanics 74R10 Brittle fracture
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