Viscoplasticity based on additive decomposition of logarithmic strain and unified constitutive equations: Theoretical and computational considerations with reference to shell applications

In contrast to multiplicative models of finite strain plasticity and viscoplasticity, a framework of additive nature is developed in this paper. The theory is based on the additive decomposition of the logarithmic strain tensor. The stress conjugate to the logarithmic strain then plays the role of the thermodynamically driving force. The approach in this paper is motivated by the search for numerically accessible structures which can be extended to incorporate anisotropy as well. Specifically in this region, multiplicative formulations become extremely tedious. The evolution equations are of the unified type due to Bodner and Partom, and are modified so as to fit into the theoretical framework adopted. The numerical treatment of the problem is fully developed. Specifically, the algorithmic aspects of the approach are discussed and various applications to shell problems are considered. A shell theory with seven degrees of freedom, together with a four-node enhanced strain finite element formulation, is used. A central feature of the shell formulation is its eligibility to the application of a three-dimensional constitutive law.