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We consider a viscoelastic body occupying a smooth bounded domain of $R^3$under the effects of volumic traction forces. Inertial effects are considered:hence, the equation describing the evolution of displacements is of the secondorder in time. On a part of the boundary of the domain, the body is anchored toa support and no displacement may occur; on a second part, the body can movefreely; on a third portion of the boundary, the body is in adhesive contactwith a solid support. The boundary forces acting there as a byproduct ofelastic stresses are responsible for delamination, i.e., progressive failure ofadhesive bonds. This phenomenon is mathematically represented by a boundaryvariable that represents the local fraction of active bonds and is assumed tosatisfy a doubly nonlinear ODE. Following the lines of a new approach based onduality methods in Sobolev-Bochner spaces, we define a suitable concept of weaksolution to the resulting system of equations. Correspondingly, we prove anexistence result on finite time intervals of arbitrary length.

A contact problem for viscoelastic bodies with inertial effects and unilateral boundary constraints