THE USE OF STRAIN-ENERGY TO QUANTIFY THE EFFECT OF RESIDUAL-STRESS ONMECHANICAL-BEHAVIOR

Residual stresses are common in engineering and biological materials, and their effect on the mechanical behavior of a body can be significa nt. In this article, the authors use the change in strain energy densi ty for deformations out of the residually stressed configuration to qu antify the contribution of a residual stress to the mechanical behavio r of an elastic body and to examine the relation between the form of t he residual stress field and the mechanical response. The change in st rain energy density at a point is a measure of the extent to which the material at that point is loaded or unloaded by a deformation. The au thors show that the strain energy density can be used in conjunction w ith the stress and strain fields to develop a clear physical interpret ation of the global mechanical behavior of a residually stressed body. These ideas are illustrated in two simple examples in which the prese nce of the residual stress field has the effect of making the body mor e compliant than an equivalent stress-free body under some deformation s and less compliant under other deformations.