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Nonlinear elasticity with limiting small strain for cracks subject to non-penetration. (English) Zbl 1371.74245

Summary: A major drawback of the study of cracks within the context of the linearized theory of elasticity is the inconsistency that one obtains with regard to the strain at a crack tip, namely it becoming infinite. In this paper we consider the problem within the context of an elastic body that exhibits limiting small strain wherein we are not faced with such an inconsistency. We introduce the concept of a non-smooth viscosity solution which is described by generalized variational inequalities and coincides with the weak solution in the smooth case. The well-posedness is proved by the construction of an approximation problem using elliptic regularization and penalization techniques.

MSC:

74R10 Brittle fracture
74B15 Equations linearized about a deformed state (small deformations superposed on large)
74G25 Global existence of solutions for equilibrium problems in solid mechanics (MSC2010)
35Q74 PDEs in connection with mechanics of deformable solids
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