On the Initiation of Necking Modes in Layered Plastic Solids

Abstract

The deformation of a solid consisting of alternating material layers with interface undulations is studied analytically. We assess the relative rate of growth or decay of these interface imperfections with straining. The analysis is based on a regular perturbation expansion of the finite strain, nonlinear field equations, the small parameter being the amplitude of the undulations relative to the layer thickness. Attention is focused on the influence of material and geometric parameters on imperfection growth-rates. It is found that significant connections exist between the growth of imperfections and the tendency for undulatory bifurcation modes to emerge from a perfect, layered solid.