On the geometrical material structure of anelasticity

G-structures are the geometric backbone of the theory of material uniformity in continuum mechanics. Within this geometric framework, anelasticity is seen as a result of evolving distributions of inhomogeneity reflected as material nonintegrability. Constitutive principles governing the time evolution of the G-structure underlying the finite-strain theory of anelasticity (e.g., plasticity) are proposed. The material Eshelby stress tensor is shown to be the driving force behind this evolution. This should allow for a thermodynamically admissible formulation of anelasticity viewed as a G-structure evolution.