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Mixed finite element discretization of some variational inequalities arising in elasticity problems in domains with cracks. (English) Zbl 1077.74045
Summary: We consider some mixed variational formulations of elasticity system in domains with cracks. Inequality-type conditions are prescribed at the crack faces, which results in a model of unilateral contact. Relying on a new variational formulation of these problems in the smooth domain, we study and implement various mixed finite element methods. We derive convergence rates and optimal error estimates.
MSC:
74S05 Finite element methods applied to problems in solid mechanics
74M15 Contact in solid mechanics
74B05 Classical linear elasticity
74R10 Brittle fracture
49J40 Variational inequalities
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