A novel boundary-domain element method of initial stress, finite deformation and discrete cracks in multilayered anisotropic elastic solids

We introduce a novel boundary-domain element method of initial stress, finite deformation (due to large rotation) and discrete cracks in multilayered anisotropic elastic solids. Because the special Green’s function that satisfies the interfacial continuity and surface boundary conditions is employed, the numerical discretization is reduced to be along one side of the cracks and over the subdomains of finite deformation. Two examples are presented. First, the process of interfacial delamination is simulated around a growing through-thickness crack in a pre-stretched film bonded to a flexible substrate. It is shown that the progression of delamination damage is stable but the initiation of delamination crack can be a snap-back instability. This simultaneous damage and fracture process is approached by the cohesive zone model. Second, the postbuckling of a circular delaminated and pre-compressed film is simulated on a flexible substrate. It is shown that the compliance of substrate can play a significant role on the critical behavior of buckling. If the substrate is more compliant or stiffer than the film, the instability initiates as a subcritical hard or a supercritical soft bifurcation. The critical magnitude of pre-strain for the initiation of buckling increases with substrate stiffness. Also, the transition of buckling from the first to the second mode is captured in the simulation.