Analytical and numerical studies on simple shear of a bimaterial strip by using elastic micromorphic theory

The mechanical behavior of a bimaterial strip subjected to simple shear is investigated by using elastic micromorphic model as analytical and numerical treatments respectively. First, the analytical solutions are carried out under micro-clamping and couple traction free boundary conditions, which indicate that the boundary layer effects are triggered by the microscopic constraint or material non-uniformity. Then the effects of length scale, material modulus and thickness ratio on the macroscopic performance are discussed. The results show that the strain jump at the bimaterial interface increases with the increasing thickness ratio. Furthermore, the finite element implementation is developed for the micromorphic model and the simulation results agree well with the analytical solutions. The analysis shows that the coupling factor acts as a penalty parameter, so the numerical method could be used to solve the problem of the second gradient theory with such internal constraint.

► Bimaterial strip under simple shear is systematically investigated. ► We discuss two different higher order boundary conditions. ► Microscopic constraint and material non-uniformity cause boundary effects. ► Strain jump increases with the increasing thickness ratio. ► We model the micromorphic and second gradient theories.