On the Homogeneity of Non-uniform Material Bodies

Characteristic foliations of material evolution: from remodeling to aging

“…Then, for each g ∈ Γ , A Γ true¯ g T is the vector subspace of T g Γ linearly generated by the evaluation of the admissible vector fields at g . Observe that, for all g ∈ Γ , the zero vector 0 g ∈ T g Γ is contained in the fiber of the distribution at g , namely A Γ true¯ g T (we refer to [5, 6, 16] for non-trivial examples). Furthermore, it satisfies that a vector field Θ of Γ fulfills conditions (i) and (ii) if, and only if, its local flow …”

“…Section 3 is devoted to a quick introduction to the theory of simple materials and the concept of uniformity. A first use of the characteristic distribution is given in this section following [7, 8, 16] (see also the book [5]). Finally, Section 4.1 is devoted to the introduction of the concept of material evolution in a very abstract setting.…”