Appl Math Optim 53:31–66 (2006)
2005 Springer Science+Business Media, Inc.
Existence and Regularity for Dynamic Viscoelastic Adhesive
Contact with Damage
Kenneth L. Kuttler,
and Jos´e R. Fern´andez
Department of Mathematics, Brigham Young University,
Provo, UT 84602, USA
Department of Mathematics and Statistics, Oakland University,
Rochester, MI 48309, USA
Departamento de Matem´atica Aplicada,
Facultade de Matem´aticas, University of Santiago de Compostela,
15706 Santiago de Compostela, Spain
Abstract. A model for the dynamic process of frictionless adhesive contact be-
tween a viscoelastic body and a reactive foundation, which takes into account the
damage of the material resulting from tension or compression, is presented. Contact
is described by the normal compliance condition. Material damage is modelled by
the damage ﬁeld, which measures the pointwise fractional decrease in the load-
carrying capacity of the material, and its evolution is described by a differential
inclusion. The model allows for different damage rates caused by tension or com-
pression. The adhesion is modelled by the bonding ﬁeld, which measures the fraction
of active bonds on the contact surface. The existence of the unique weak solution is
established using the theory of set-valued pseudomonotone operators introduced by
Kuttler and Shillor (1999). Additional regularity of the solution is obtained when
the problem data is more regular and satisﬁes appropriate compatibility conditions.
Key Words. Existence, Regularity, Dynamic contact, Adhesion, Damage.
AMS Classiﬁcation. 74H20, 74O10, 74F99, 74H30, 74M15, 74R05.