Free rate‐independent elastoplastic equations

Source abstract

Abstract New rate‐independent finite elastoplastic equations are proposed in unified forms applicable to all loading‐unloading cases. A departure from the classical elastoplastic equations is that these new equations are not subjected to and hence free from the usual extrinsic restrictive conditions, including the yield condition as well as the loading‐unloading conditions. Such free equations are of Eulerian rate type and assume the same smooth form for all possible stresses and for all strain rates. It is demonstrated that the essential representative features of finite elastoplastic deformations, namely, the yield behavior and the loading‐unloading behavior in the traditional sense, may be derived from and hence naturally incorporated as intrinsic physical characteristics into the free elastoplastic equations proposed in a more realistic sense and, in particular, the classical notions characterizing these features are found to exhibit novel, perhaps more profound physical meanings in the new equations. Furthermore, the strong discontinuity in tangent moduli at transition from elastic to plastic state, involved in the traditional formulation, is shown to be replaced by a smooth transition. Implications are discussed in respects of constitutive implications and numerical treatment.