Thermomechanics of volumetric growth in uniform bodies Marcelo Epstein a, *, GeÂrard A. Maugin b a University of Calgary, Department of Mechanical Engineering, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4 b Universite  Pierre et Marie Curie, Case 162 Laboratoire de Mode Âlisation en Me Âcanique (UMR CNRS 7607), Tour 66, 4 place Jussieu, 75252 Paris Cedex 05, France Received in ®nal revised form 16 August 1999 Abstract A theory of material growth (mass creation and resorption) is presented in which growth is viewed as a local rearrangement of material inhomogeneities described by means of ®rst- and second-order uniformity ``transplants''. An essential role is played by the balance of canonical (material) momentum where the ¯ux is none other than the so-called Eshelby material stress tensor. The corresponding irreversible thermodynamics is expanded. If the constitutive theory of basically elastic materials is only ®rst-order in gradients, diusion of mass growth cannot be accommodated, and volumetric growth then is essentially governed by the inhomogeneity velocity ``gradient'' (®rst-order transplant theory) while the driving force of irreversible growth is the Eshelby stress or, more precisely, the ``Mandel'' stress, although the possible in¯uence of ``elastic'' strain and its time rate is not ruled out. The application of various invariance requirements leads to a rather simple and reasonable evolution law for the trans- plant. In the second-order theory which allows for growth diusion, a second-order inhomo- geneity tensor needs to be introduced but a special theory can be devised where the time evolution of the second-order transplant can be entirely dictated by that of the ®rst-order one, thus avoiding insuperable complications. Dierential geometric aspects are developed where needed. # 2000 Elsevier Science Ltd. All rights reserved. Keywords: Thermomechanics; Volumetric growth; Stress tensor 1. Introduction We shall deal with the foundations of a thermomechanical theory of volumetric growth in uniform material bodies. This wording obviously requires some explanation. International Journal of Plasticity 16 (2000) 951±978 www.elsevier.com/locate/ijplas 0749-6419/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S0749-6419(99)00081-9 * Corresponding author. E-mail addresses: epstein@enme.ucalgary.ca (M. Epstein), gam@ccr.jussieu.fr (G.A. Maugin).