A Beam in Adhesive Contact

A quasistatic process of contact with adhesion between an elastic beam and a foundation is considered. The contact is modeled with the Signorini condition when the foundation is rigid, and with normal compliance when it is deformable. The adhesion is modeled by introducing the bonding function β, the evolution of which is described by an ordinary differential equation. The existence and uniqueness of the weak solution for each of the problems is established. A fully-discrete scheme for numerical solutions of the problem with normal compliance is described.