A material momentum balance law for shells and plates with application to phase transformations and adhesion

Abstract

A balance law for material momentum in shells and plates is proposed. The implications of this balance law for the propagation of defects, phase transformations, and shocks are explored. The developments are presented using a purely mechanical theory of a Cosserat (or directed) shell and specialized to the cases of a Kirchhoff–Love shell theory and a linearly elastic plate theory. To explore connections to the literature on delamination and adhesion, the balance law is applied to the problem of blistering.