We consider a viscoelastic body occupying a smooth bounded domain under the effect of a volumic traction force. Inertial effects are considered; hence the equation for the macroscopic displacement contains a second order term. On a part of the boundary, the body is anchored to a support and no displacement may occur; on a second part, the body can move freely, and on a third part the body is in adhesive contact with a solid support. The boundary forces coming to the action of elastic stresses are responsible for delamination, i.e., progressive failure of adhesive bonds. 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 PDE system and correspondingly we prove an existence result on finite time intervals of arbitrary length.
A contact problem for viscoelastic bodies with inertial effects and unilateral boundary constraints
SCALA, RICCARDO;SCHIMPERNA, GIULIO FERNANDO
2017-01-01
Abstract
We consider a viscoelastic body occupying a smooth bounded domain under the effect of a volumic traction force. Inertial effects are considered; hence the equation for the macroscopic displacement contains a second order term. On a part of the boundary, the body is anchored to a support and no displacement may occur; on a second part, the body can move freely, and on a third part the body is in adhesive contact with a solid support. The boundary forces coming to the action of elastic stresses are responsible for delamination, i.e., progressive failure of adhesive bonds. 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 PDE system and correspondingly we prove an existence result on finite time intervals of arbitrary length.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
