Revisiting plane strain: Necessary conditions for its realization

Abstract

Abstract Without exception, every physical object is three-dimensional. However, in many stress analysis situations the analyst is justified in using simplified two-dimensional idealizations of plane stress and plane strain, reducing the complexity of the problem. By obviating the need to mesh in the third dimension, this advantage also extends to numerical studies, helping economize significantly on time and computational power requirements. In plane stress idealization the out-of-plane stresses are zero, whereas in plane strain the out-of-plane strains are zero. These idealizations have variously been linked with the out-of-plane dimension as well as the end conditions of the object under consideration. However, the exact correlation of the out-of-plane dimension with these idealizations remains ambiguous. One certain instance of plane stress is a situation where the out-of-plane dimension of the object is very small as compared to its in-plane dimensions; and additionally, the loading is purely in-plane. On the other hand, there is much disagreement found in literature regarding the necessary conditions for the realization of plane strain, which needs to be addressed. Employing finite element analysis and analytical solutions, this work aims to resolve this issue.