Three-dimensional adhesive contact laws with debonding: a nonconvex energy bundle method Original Research Article

In the present paper we develop a new numerical approach to the problem of structures having two or more parts of them adhesively bonded together like e.g. in sandwich structures. The adhesive material is idealized by a nonmonotone, possibly multivalued stress–strain law, which is three-dimensional (3D) and introduces a nonconvex nonsmooth energy function in the problem. The problem is formulated as a hemivariational inequality, whose solution(s) must render the potential energy substationary. We apply here the proximal bundle method and more specifically the optimization programme NSOLIB, based on first order polyhedral approximations of the locally Lipschitz continuous objective function. This algorithm permits the determination of at least one substasionarity point, e.g. of an equilibrium problem. An example of a 3D finite element model, illustrates the effectiveness of the proposed mehod.