Deformation and fracture of plates of finite thickness

Abstract

Plane theories of elasticity are the theoretical foundation of many important developments in engineering. However, the understanding of the elastic solutions derived under plane stress or plane strain assumption, is rather far from complete. In particular, it is not clear how adequate the classical two-dimensional solutions of the plane theories of elasticity are when applied to the analysis of actual plate components made of sufficiently brittle material and having a finite thickness. So far there is no generally accepted criterion for identifying what thickness would qualify for plane-stress or plane-strain states and, in general, what effect on the stress distribution the plate thickness has. In this work we make an attempt to review some recent numerical studies and analytical efforts in order to throw light on this problem.