On the post-buckling behavior of laterally constrained multilayers

Material layering occurs in natural, biological, geological and synthetic load-bearing structures. The bucking and post-buckling behavior of such structures is a subject of great interest. While many studies were devoted to the case of a thin film attached to a thick substrate, little is available on the behavior of multilayers. We explore this subject using a model system consisting of 2-D, linearly elastic hard/soft multilayer under uniform edge displacement. The lateral edges of the multilayer are constrained by rigid, frictionless walls. The number of stiff layers n and layer-to-interlayer thickness and elastic moduli ratios, h and E, are systematically varied. The deformation and stresses in the multilayer are obtained with the aid a FEA. Buckling initiates in the interior layers and spreads to the outer ones. The layers adjacent to the constraining walls tend to flatten as the load is increased. For relatively large h or small E, this causes large membrane stresses that may lead to a buckling mode transition. As many as ≈ 50 stiff layers are needed in order for the multilayer to approach a laminate configuration (n ≫ 1). The multilayer as a whole displays nonlinear elastic stress–strain response. By a proper choice of the system variables n, h and E, a variety of strain hardening effects as well as large energy absorption can be achieved. The results of this study provide useful insights into the effects of b.c., material choice and load level on the response of multilayers in general.