Detachment of an elastic beam from a viscoelastic support: A variational approach

The paper is devoted to the analysis of failure in multi-layer composite materials. For the experimental study of the failure mechanism, the peel tests are used. The peel test is modeled as the detachment of an elastic beam attached to a rigid adherend by a viscoelastic adhesive layer. For solving this problem, we use the principle of minimum free energy and derive a new energy criterion of the detachment. We propose a model of an aging viscoelastic material describing the viscoelastic behavior in terms of elastic objects. Using this model we propose an expression for the specific potential energy of an aging viscoelastic medium and derive a new formulation of the principle of minimum free energy for a viscoelastic system. A numerical method for solving nonlinear integro-differential equations describing the detachment process is developed, and its convergence is established. We analyze numerically the dependence of the detachment on the construction and material parameters, and on the loading history. We demonstrate the existence of a limited training effect, which allows considerable reduction of the detachment zone by a special preliminary loading program ("training").