A size-dependent imperfect interface model for adhesively bonded joints considering strain gradient elasticity

As the size of a layered assembly is reduced, the adhesive layer thickness correspondingly decreases from macro to micro scale. The influence of micro-scale adhesive layers becomes more pronounced, significantly changing the overall performance of the composite structure. This work proposes an original imperfect interface model simulating the behavior of a thin strain gradient elastic adhesive, embedded between two strain gradient elastic bodies, through the asymptotic methods. The intermediate layer is assumed to be mechanically compliant. The contact laws, expressed in terms of the jumps and means values of the displacements, normal derivatives of the displacements, stresses, and double-stresses, represent a formal generalization of the soft elastic interface conditions. Two simple benchmark equilibrium problems (a three-layer composite micro-bar subjected to an axial load and a torsional moment) are developed to analytically/numerically assess the asymptotic model. Size effects and non-local phenomena, due to high strain concentrations at the edges, are highlighted. The example proves the efficiency of the proposed approach in designing micro-scale layered devices.