Abstract

The leading-order energy estimate for a thin nonlinear plate comprised of a general second-gradient elastic material is derived. A standard dimension-reduction procedure based upon a Taylor expansion of the parent energy functional in the plate thickness is utilized to this end. The equilibrium equations, edge conditions, and corner conditions emerge naturally via the principle of virtual work; the subsequent system is interpreted as a second-gradient Cosserat model. It’s novelty, induced by the second-gradient constitutive sensitivity, is that the first-order energy estimate subsumes both membrane and bending effects. This furnishes a concise, well-posed system even in the presence of compressive membrane stresses and offers a viable alternative to conventional first-gradient plate theories which require third-order regularization under such circumstances.

Keywords

Mathematical Subject Classification

Milestones

Authors