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We consider mixed and hybrid variational formulations to the linearized
elasticity system in domains 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....
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