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Locking-free finite elements for unilateral crack problems in elasticity. (English) Zbl 1162.74039
Summary: We consider mixed and hybrid variational formulations of a linearized elasticity system in domain with cracks. Inequality-type conditions are prescribed at the crack faces which results in unilateral contact problems. The variational formulations are extended to the whole domain including the cracks which yields, for each problem, a smooth domain formulation. Mixed finite element methods such as PEERS or BDM methods are designed to avoid locking for nearly incompressible materials in plane elasticity. We study and implement discretizations based on such mixed finite element methods for the smooth domain formulations to the unilateral crack problems. We obtain convergence rates and optimal error estimates and we present some numerical experiments in agreement with the theoretical results.
74S05 Finite element methods applied to problems in solid mechanics
74R10 Brittle fracture
74B15 Equations linearized about a deformed state (small deformations superposed on large)
74G65 Energy minimization in equilibrium problems in solid mechanics
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