Constitutively admissible gradients of plastic deformation in isotropic solids.

This article focuses on the modeling of length scale effects in plastically deformed solids within the framework of gradient plasticity, emphasizing the role of inhomogeneity fields. For materially uniform crystalline solids, inhomogeneity is uniquely described by the torsion tensor or the geometrically necessary dislocation density derived from the plastic deformation gradient. In isotropic solids, inhomogeneity is characterized by the Riemann tensor induced by the plastic metric, involving the plastic deformation and its first and second gradients. The article demonstrates that constitutive functions depending on the plastic deformation and its gradients in isotropic solids can be fully expressed in terms of the Riemann tensor, establishing that inhomogeneity alone accounts for length scale effects in these materials. It further explains that, due to material symmetry and isotropy, constitutive functions must be invariant under arbitrary rotations, which restricts their dependence to the Riemann tensor or equivalently the Ricci tensor, thus refining the modeling approach for isotropic gradient plasticity.