Analytical solutions of two-layer beams with interlayer slip and bi-linear interface law

A new formulation to analyze two-layer beams with interlayer slip is proposed. Each layer is modeled as a linearly elastic Timoshenko beam. The connection between the layers is assumed to be perfect in the transverse direction while imperfect in the longitudinal one (only interlayer slips are allowed). The interface behavior in the longitudinal direction is described through a linear non proportional relationship relating tangential reactions transmitted between the two layers and slips. The problem is then solved analytically and a novel closed form solution is obtained. Explicit expressions for all static and kinematic variables are derived. This analytical solution is shown to be employed in the analysis of composite beams for different boundary and loading conditions generating interfacial tractions that induce an irreversible process of progressive debonding at the interface. Some numerical examples are considered and a parametric analysis performed to investigate the influence of the interface behavior on the response of the composite beam when the layers are still elastic.