Analytical solutions of three-layer beams with interlayer slip and step-wise linear interface law

A new formulation to solve the equilibrium problem of three-layer beams with interlayer slip is proposed. Each layer is modelled as a linearly elastic Euler-Bernoulli beam. Connections between layers are assumed to be perfect in the transverse direction while to have finite stiffness in the longitudinal direction (only interlayer slips are allowed). Interface behaviors in the longitudinal direction are described through linear non proportional relationships relating shear traction and slip between two layers. A novel closed form solution is then obtained and explicit expressions for all static and kinematic variables are derived. This analytical solution can be employed to simulate the response of composite beams for different boundary and loading conditions generating interfacial tractions that induce an irreversible process of progressive interfacial debonding. A numerical example is considered to investigate the influence of a post-elastic interface behavior on the global response of the composite beam when the layers are still elastic.