On the debonding in multilayered composite structures. A new numerical approach

In the present paper, the behavior of multilayered structures glued by an adhesive material subjected to cleavage loading is investigated. The adhesive material is assumed to obey to a nonmonotone, multivalued reaction–displacement law in three dimensions. This kind of behavior observed as result of the development of technology, leads to a variational expression for the principle of virtual work called hemivariational inequality which is equivalent to a substationarity problem; the latter is a generalization of the principle of minimum potential energy of the multilayered composite structure taken into account the possibility of debonding along the glued interfaces. The solution of this inequality expresses the substationarity principle for the potential energy of the structure. The solution of the problem is achieved by the application of the NSOLIB algorithm, which is based on the proximal bundle method. By means of this algorithm, one at least substationarity point is obtained (e.g. at least one of the local minima or saddle points). The effectiveness of the proposed method is illustrated by means of numerical examples.