Strain localization analysis of layered materials with debonding interfaces by a second-order homogenization approach

The paper is focused on the multiscale modeling of shear banding in a two-phase linear elastic periodically layered material with damaging interfaces. A layered two- dimensional strip is considered under transverse shear and is assumed to have a finite length along the direction of the layers and an infinite extension along the direction perpendicular to layering. The structural system has been analysed as a second-gradient continuum in order to incorporate size effects due to the material inhomogeneities and to regularize the softening response due to the interface debonding. The multi-scale approach is based on a second- order homogenization procedure proposed by the Authors, here specialized to the simple case of layered materials. Two problems are analysed differing on the boundary conditions at the strip edges. The first case considers free warping of the edges with classical homogeneous response in the elastic regime followed by a localization process as a results of a bifurcation in analogy to Chambon’s approach. In the second model warping is inhibited at the edges and the damage propagation is obtained from the center of the specimen. In both cases the model parameters directly depend on the material microstructure so that both the extension of the shear band and the occurrence of snap-back in the post-peak phase are given in terms of the constitutive parameters and geometry of the phases.