Stress-Strain Relations for Finite Elastoplastic Deformations

Abstract

Abstract The strains accompanying elastoplastic deformations are frequently so large that the simplified equations of the small-strain theory are invalid. Although several ways of describing finite strains are known (1), they are not readily adaptable to stress-strain analyses in elastoplastic materials. One of the difficulties arises from the failure of the laws of addition when the strains are defined in the conventional way. Another difficulty arises from the observations that the infinitesimal plastic strains, and not the finite strains, are related to the stresses. The accompanying analysis, which attempts to surmount these difficulties, is an extension of methods originally described in a paper on plastic flow in metals (2), to include elastic as well as plastic deformations.