The decomposition F = FeFp, material symmetry, and plastic irrotationality for solids that are isotropic-viscoplastic or amorphous

This study develops a general framework for discussing both isotropic-viscoplastic materials and amorphous materials. The framework, which allows for large deformations, is based on the Kröner–Lee decomposition of the deformation gradient into elastic and inelastic parts, a system of microforces consistent with its own balance, and a mechanical version of the second law that includes, via the microforces, work performed during inelastic flow. The constitutive theory allows for dependences on the elastic and inelastic parts of the deformation gradient and on the inelastic stretch-rate, but dependences on the inelastic spin are not included. The constitutive equation for the microstress Tp conjugate to inelastic flow – suitably restricted by the second law – and the microforce balance are shown to be together equivalent to a flow rule that includes a back stress due to the variation in the free energy with inelastic deformation. The introduction of a concept of material microstability reduces this flow rule to one of classical Mises-type. In a theory based on the Kröner–Lee decomposition, there are two classes of symmetry transformations available: transformations of the reference configuration and transformations of the relaxed spaces. We discuss the notion of material symmetry for a general class of materials that includes, as special cases, isotropic-viscoplastic solids, and amorphous solids. Essential to this discussion of symmetry is a general constitutive relation for the microstress Tp. The symmetry-based framework allows us to show that for typical boundary-value problems involving isotropic, viscoplastic solids or amorphous solids, if a problem has a solution, then every time- and space-dependent rotation of the relaxed spaces also yields a solution, and it is possible to choose this rotation such that the transformed solution is inelastically spin-free: Wp ≡ 0. Thus, when discussing such materials, we may, without loss in generality, restrict attention to flow rules that are inelastically irrotational.