Elements of a finite strain-gradient thermomechanical theory for material growth and remodeling

A second-gradient theory in finite strains is proposed to deal with the phenomena of material growth and remodeling, as happens in biomechanics, on account of mass transport and morphogenetic species. It involves first-order and second-order transplants (local structural rearrangements) and two material connections on the material manifold. It is shown that the evolution of these structural changes or “material inhomogeneities” is governed by Eshelby-like stress and hyperstress tensors. A thermodynamically admissible set of constitutive equations is proposed. The complexity due to the finite-strain gradient theory is a necessity in order to accommodate mass exchanges and diffusion of species.

► Proposal of a thermodynamically admissible theory of material growth. ► Remodeling based on the notion of finite strain-gradient theory of a continuum. ► Mass transport and evolution of morphogenetic species are accounted for. ► Geometrically, the model involves two material connections.