Effect of interfacial compliance on bifurcation of a layer bonded to a substrate

Abstract

The effect of interfacial compliance on the bifurcation of a layer bonded to a substrate is analyzed. The bifurcation problem is formulated for hyperelastic, layered solids in plane strain. Attention is then confined to the problem of a layer of finite thickness on a half-space. The layer and substrate are subject to plane strain compression, with the compression axis parallel to the bond line. The materials in the layer and in the half-space are taken to be incrementally linear, incompressible solids, with most results presented for Mooney-Rivlin and J2-deformation theory constitutive relations. The limiting case of an undeforming half-space is also considered. The interface between the layer and the substrate is characterized by an incrementally linear traction rate vs velocity jump relation, so that a characteristic length is introduced. A variety of bifurcation modes are possible depending on the layer thickness, on the constitutive parameters of the layer and the substrate, and on the interface compliance. These include shear band modes for the layer and the substrate, and diffuse instability modes involving deformation in the layer and the substrate. For a sufficiently compliant interface, the mode with the lowest critical stress is a long (relative to the layer thickness) wavelength plate-like bending mode for the layer.