Cavities vis-à-vis Rigid Inclusions and Some Related General Results in Plane Elasticity

Abstract

There is a strange feature of plane elasticity that seems to have gone unnoticed: The stresses in a body that contains rigid inclusions and is loaded by specified surface tractions depend on the Poisson ratio of the material. If the Poisson ratio in this stress field is set equal to +1 for plane strain, or +∞ for plane stress, the rigid inclusions become cavities for elastic constants within the physical range. The paper pursues this circumstance, and in doing so also produces several useful by-products that are connected with the stretching and curvature change of a boundary.