Correlation of out-of-plane dimension with simplified geometric models in stress analysis

Abstract

Everything in the world is 3D but often there is the justification of using idealized 2D simplification models: plane stress and plane strain. These models help save on time as well as computational resources. The definition of plane stress is simple enough: when the out-of-plane dimension is very small as compared to the inplane dimensions and loading is purely in-plane, then the body is in the state of plane stress (plane stress: out-of-plane stresses are zero). The definition of plane strain is clear but when it comes to the necessary conditions of the plane strain, there is a discrepancy found in the literature. It has variously been linked to the out-of-plane dimensions and/or end conditions/constraints (plane strain: out-of-plane strains are zero). “What are the true necessary conditions of plane strain?” is a question that needs to be answered unambiguously. The question breaks down into the following sub-questions: Is there any correlation with the out-of-plane dimension? Does it depend on the boundary conditions (end conditions)? These questions have been addressed in this research. Plane Stress, Plane Strain and the unconstrained long cylinder has been modelled and simulated in Abaqus. The results of the unconstrained cylinder have been compared with both simplified models and a conclusion has been made. It has been concluded that the unconstrained cylinder is in a state of plane stress. Thus there is no correlation of plane strain with the large unconstrained out-of-plane dimension in the presence of all kinds of forces like mechanical as well as body forces. Plane strain simplification is only valid when the body is constrained at the ends somehow.