Dynamic Adhesive Contact of a Membrane
R. S. R. MenikeOakland University, Rochester, USA
K. L. KuttlerBrigham Young University, Provo, USA
Meir ShillorOakland University, Rochester, USA
This work presents a dynamic model for adhesive contact between a stretched viscoelastic membrane and a reactive obstacle that lies beneath it. The adhesion is described by a bonding ﬁeld, and the model allows for failure, that is complete debonding in ﬁnite time. It is two-dimensional, but retains the essential mathematical structure of the full three-dimensional model. It is set as a hyperbolic equation for the vibrations of the membrane coupled with a nonlinear ordinary differential equation for the evolution of the bonding ﬁeld. Existence and uniqueness of regular solutions are established in the case of positive viscosity, and in the case of no viscosity, existence of weak solutions is obtained, while the uniqueness of the solutions remains unresolved.
Cite this article
R. S. R. Menike, K. L. Kuttler, Meir Shillor, Dynamic Adhesive Contact of a Membrane. Z. Anal. Anwend. 29 (2010), no. 1, pp. 1–20DOI 10.4171/ZAA/1395