Mass transport in morphogenetic processes: A second gradient theory for volumetric growth and material remodeling

Abstract : In this work, we derive a novel thermo-mechanical theory for growth and remodeling of biological materials in morphogenetic processes. This second gradient hyperelastic theory is the first attempt to describe both volumetric growth and mass transport phenomena in a single-phase continuum model, where both stress- and shape-dependent growth regulations can be investigated. The diffusion of biochemical species (e.g. morphogens, growth factors, migration signals) inside the material is driven by configurational forces, enforced in the balance equations and in the set of constitutive relations. Mass transport is found to depend both on first- and on second-order material connections, possibly withstanding a chemotactic behavior with respect to diffusing molecules. We find that the driving forces of mass diffusion can be written in terms of covariant material derivatives reflecting, in a purely geometrical manner, the presence of a (first-order) torsion and a (second-order) curvature. Thermodynamical arguments show that the Eshelby stress and hyperstress tensors drive the rearrangement of the first- and second-order material inhomogeneities, respectively. In particular, an evolution law is proposed for the first-order transplant, extending a well-known result for inelastic materials. Moreover, we define the first stress-driven evolution law of the second-order transplant in function of the completely material Eshelby hyperstress.
Type de document :
Article dans une revue
Journal of the Mechanics and Physics of Solids, Elsevier, 2011, 60 (3), pp.432 - 450. 〈10.1016/j.jmps.2011.11.011〉
Liste complète des métadonnées

http://hal.upmc.fr/hal-01587052
Contributeur : Gestionnaire Hal-Upmc <>
Soumis le : mercredi 13 septembre 2017 - 15:44:56
Dernière modification le : jeudi 11 janvier 2018 - 06:27:14

Lien texte intégral

Identifiants

Collections

Citation

P. Ciarletta, D. Ambrosi, G.A. Maugin. Mass transport in morphogenetic processes: A second gradient theory for volumetric growth and material remodeling. Journal of the Mechanics and Physics of Solids, Elsevier, 2011, 60 (3), pp.432 - 450. 〈10.1016/j.jmps.2011.11.011〉. 〈hal-01587052〉

Partager

Métriques

Consultations de la notice

42