Global material constraints and their associated reactive stresses

Abstract

The stress field in a material subject to a global material constraint is composed of a reactive stress and an active stress. The active stress is determined by the deformation while the reactive stress arises because of the constraint. The static equilibrium equations can be reduced to equations involving only the active stress. The resulting equations may then be solved to determine the deformation. Although the reactive stress is not needed in order to find the deformation, it is needed to satisfy traction boundary conditions. Rod, shell, and finite element theories can therefore be developed in an unambiguous way. As an example, one can calculate explicitly a reactive stress in a rod-like body subjected to a compressive end load.