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Thermomechanics of volumetric growth in uniform bodies. (English) Zbl 0979.74006
Authors’ summary: We present a theory of material growth (mass creation and resorption) in which growth is viewed as a local rearrangement of material inhomogeneities described by means of first- and second-order uniformity “transplants”. An essential role is played by the balance of canonical (material) momentum, where the flux is none other than the so-called Eshelby material stress tensor. The corresponding irreversible thermodynamics is developed. If the constitutive theory of basically elastic materials is only first-order in gradients, the diffusion of mass growth cannot be accommodated, and the volumetric growth is then essentially governed by inhomogeneity velocity “gradients” (first-order transplant theory). The driving force of irreversible growth is the Eshelby stress or, more precisely, the “Mandel” stress, although the possible influence of “elastic” strain and its time rate is not ruled out. We show that the application of various invariance requirements leads to a rather simple and reasonable evolution law for the transplant. In the second-order theory which allows for growth diffusion, a second-order inhomogeneity tensor needs to be introduced, but we develop a special theory where the time evolution of the second-order transplant can be entirely dictated by that of the first-order transplant, thus avoiding undesirable complications. Differential-geometric aspects are also developed where needed.

MSC:
74A15 Thermodynamics in solid mechanics
74A20 Theory of constitutive functions in solid mechanics
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