A dynamic unilateral contact problem for a cracked body
Résumé
In this work we investigate a class of dynamic contact problems for cracked viscoelastic and elastic bodies, when Signorini’s
conditions between the two faces of the crack are considered. Firstly, using a penalty method we study a variational formulation
of a unilateral contact problem with nonlocal friction for a cracked viscoelastic body. Several estimates on the penalized solutions
are obtained which enable us to analyze the time and spatial discretizations of the problem. Then we consider the corresponding
elastic problem, for which a fictitious domain formulation is proposed with Lagrange multipliers representing the normal jump of the
displacements. Numerical examples, based on the fictitious domain method for solving the diffraction of elastic waves by cracks, are
presented.
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