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On the change of energy caused by crack propagation in 3-dimensional anisotropic solids. (English) Zbl 1340.74088

Summary: Crack propagation in anisotropic materials is a persistent problem. A general concept to predict crack growth is the energy principle: A crack can only grow, if energy is released. We study the change of potential energy caused by a propagating crack in a fully three-dimensional solid consisting of an anisotropic material. Based on methods of asymptotic analysis (method of matched asymptotic expansions) we give a formula for the decrease in potential energy if a smooth inner crack grows along a small crack extension.

MSC:

74R10 Brittle fracture
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
74E10 Anisotropy in solid mechanics
35Q74 PDEs in connection with mechanics of deformable solids
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