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Damage as \(\Gamma\)-limit of microfractures in anti-plane linearized elasticity. (English) Zbl 1157.74003

Summary: We give a homogenization result for a material having brittle inclusions arranged in a periodic structure. According to the relation between the softness parameter and the size of microstructure, three different limit models are deduced via \(\Gamma\)-convergence. In particular, damage is obtained as limit of periodically distributed microfractures.

MSC:

74A45 Theories of fracture and damage
74Q05 Homogenization in equilibrium problems of solid mechanics
74R05 Brittle damage
74B15 Equations linearized about a deformed state (small deformations superposed on large)
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