Effect of the thickness on elastic deformation and quasi-brittle fracture of plate components

Plane theory of elasticity lays a foundation for many important results in science and engineering. However, the understanding of the elastic solutions derived under plane stress or plane strain assumption, is far from complete. In particular, it is not clear how adequate the classical two-dimensional solutions of the plane theory of elasticity are when applied to the analysis of actual plate components having a finite thickness. So far there is no generally accepted criterion for identifying what thickness would qualify as plane stress or plane strain and, in general, what effect on the stress distribution the plate thickness has. In this work we review some recent analytical efforts, numerical and experimental studies in order to throw light onto how the plate thickness, which is largely ignored by the classical plane solutions of the theory of elasticity, influences the elastic deformation and quasi-brittle fracture of plate components.