2015/07/21 by Scala, Riccardo, Schimperna, Giulio
#35L10 #46A20 #47H05 #74D10 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.1507.05837
We consider a viscoelastic body occupying a smooth bounded domain of R3 under the effects of volumic traction forces. Inertial effects are considered: hence, the equation describing the evolution of displacements is of the second order in time. On a part of the boundary of the domain, the body is anchored to a support and no displacement may occur; on a second part, the body can move freely; on a third portion of the boundary, the body is in adhesive contact with a solid support. The boundary forces acting there as a byproduct of elastic stresses are responsible for delamination, i.e., progressive failure of adhesive bonds. This phenomenon is mathematically represented by a boundary variable that represents the local fraction of active bonds and is assumed to satisfy a doubly nonlinear ODE. Following the lines of a new approach based on duality methods in Sobolev-Bochner spaces, we define a suitable concept of weak solution to the resulting system of equations. Correspondingly, we prove an existence result on finite time intervals of arbitrary length.