A consistent finite elastoplasticity theory combining additive and multiplicative decomposition of the stretching and the deformation gradient

A phenomenological finite deformation elastoplasticity theory is proposed b y consistently combining the additive decomposition of the stretching D and the multiplicative decomposition of the deformation gradient F. The propos ed theory is Eulerian type and suitable for both isotropic and anisotropic elastoplastic materials with general isotropic and kinematical hardening be haviour. Within the context of the proposed theory, the Eulerian rate type constitutive formulation based on the decomposition D = D-e + D-ep determin es the total stress, the total kinematical quantities as well as the elasti c part D-e and the coupled elastic-plastic part D-ep etc. Then, the two rat e quantities D-e and D-ep are related to the elastic part F-e and the plast ic part F-p in the decomposition F = (FFp)-F-e in a direct and natural mann er. It is found that the just-mentioned relationship between the two widely used decompositions, together with a suitable elastic relation defining th e elastic stretch V-e = root (FFe T)-F-e consistently and uniquely determin es the elastic deformation F-e and the plastic deformation F-p and all thei r related kinematical quantities, without recourse to the widely used ad ho c assumption about a special form of F-e. Moreover, it is shown that for ea ch process of purely elastic deformation the incorporated Eulerian rate typ e formulation intended for elastic response, which is based on the newly di scovered logarithmic rate, is exactly-integrable to deliver a general hyper elastic relation with any given type of initial material symmetry, and thus the suggested theory is subjected to no self-inconsistency difficulty in t he rate form characterization of elastic response, as encountered by other existing Eulerian rate type theories. In particular, it is proved that, to achieve the just-mentioned goal, the logarithmic rate is the only choice am ong all possible (infinitely many) objective corotational rates. Further,pr oposed theory is shown to fulfill, in a full sense, the invariance requirem ent under the change of frame or the superposed rigid body motion. Accordin gly, with the suggested theory the main fundamental discrepancies involving the decompositions of D and F disappear. (C) 2000 Elsevier Science Ltd. Al l rights reserved.