Buckling of an elastic layer based on implicit constitution: Incremental theory and numerical framework

Abstract

A general class of implicit bodies was proposed to describe elastic response of solids, which contains the Cauchy–Green tensor as a function of Cauchy stress. Here, we consider the buckling of solids described by such a subclass of implicit constitutive relation. We present a general linear incremental theory and carry out bifurcation analysis of a uniaxially compressed rectangular layer described by an implicit constitution. We then provide general governing equations regarding the mixed unknowns, i.e., displacement and stress fields, within the framework of finite strain deformation. Thereby, the combination of Asymptotic Numerical Method (ANM) and spectral collocation method is applied to solve the resulting nonlinear equations. We validate our numerical framework by comparing the computational results with analytical ones, and then explore effects of width-to-length ratio and material nonlinearity on the buckling and post-buckling behavior. The larger the width-to-length ratio is, the larger the critical buckling load is. The material parameter, η, has a significant impact up to 28% on the critical buckling load and influence up to 50% on the post-buckling behavior. Our model based on the implicit constitutive relation well predicts the buckling and post-buckling of Gum metal alloy.