Author(s)

B. Yang

Abstract

We introduce a novel boundary-domain element method of initial stress, finite deformation and discrete cracks in multilayered solids. Because the special Green’s function of multilayers that satisfies the interfacial continuity and surface boundary conditions is employed as the integral kernel, the numerical discretization is reduced only along the crack surfaces and over the subdomains of finite deformation. Two examples are presented. First, we simulate the interfacial cohesive delamination around a through-thickness crack in a prestretched thin film on a flexible substrate. The process of interfacial crack initiation and growth following the expansion of a cohesive damage front, driven by the opening through-thickness crack, is shown. Second, we simulate the buckling of a delaminated pre-compressed thin film on a flexible substrate. It is shown that the compliance of the substrate plays a significant role in the critical behavior. If the substrate is more compliant than the film, the buckling initiates as a subcritical hard bifurcation. In contrast, if the substrate is stiffer than the film, it initiates as a supercritical soft bifurcation. Keywords: anisotropic elasticity, boundary element, post-buckling, crack, delamination, finite deformation, initial stress, multilayers, thin films. 1 Introduction Various integral-equation (IE) formulations have been developed for Kirchoff’s thin plates [1-3], Reissner’s thick plates [4-6], and mixed thin and thick plates [7]. Because only boundary integrals are involved, they have been applied to develop numerical boundary element (BE) methods to solve related boundary

Keywords

anisotropic elasticity, boundary element, post-buckling, crack, delamination, finite deformation, initial stress, multilayers, thin films