Commutative-symmetrical elastic–plastic stretch-tensor products and their rates

Abstract

The commutative-symmetrical elastic–plastic stretch-tensor product and the multiplicative Bilby-Kröner-Lee decomposition of a deformation gradient are compared to one another in particular with respect to the corresponding time derivatives and tensor rates. It turns out that these multiplicative deformation-tensor models differ with respect to the elastic response just for a Lagrangean point of view and coincide for an Eulerian perspective. The uniqueness of the constitutive equations requires symmetric plastic-flow rules for commutative-symmetrical elastic–plastic stretch-tensor products and non-symmetric plastic-flow rules for multiplicative Bilby-Kröner-Lee formulations. Further, the author discusses whether a plastic rotation tensor—implied from a non-symmetric plastic-flow rule—is appropriate for a proper finite-plasticity formulation of polycrystalline metals and whether at all a plastic rotation is a material-dependent property in this context. A proper elasto-plasticity/-inelasticity model may be constituted for a symmetric plastic-flow rule in conjunction with a commutative-symmetrical elastic–plastic stretch-tensor product, which inherently includes even the simultaneous modeling of finite-elastic and finite-plastic/-inelastic orthotropy.