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. - In: EUROPEAN JOURNAL OF APPLIED MATHEMATICS. - ISSN 0956-7925. - 28:1(2017), pp. 91-122. [10.1017/S0956792516000097]
A contact problem for viscoelastic bodies with inertial effects and unilateral boundary constraints
Scala Riccardo;
2017
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.File | Dimensione | Formato | |
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