Abstract
A thermodynamically admissible model of volumetric growth is presented which exploits the notion of material transplant or local structural rearrangement issued from the Epstein-Maugin theory of material inhomogeneities. The driving force appears to be the Mandel stress (a part of the Eshelby stress tensor). Anisotropy of growth is characterized by a vector field slaved to the principal directions of that tensor. The model is very much like one of viscoelasticity in finite strains. It is applicable to self-organization or adaptation. The numerical solution of specific problems is based on a finite-element formulation obtained with reference to the total Lagrangian approach. The validity of the model is thus assessed in terms of circumferential (monotomic) growth/resorption behavior, stress induction in a ring, and the dynamical effect (repeated alternate loading) on the material growth in a cantilever beam. The model proves to possess a sufficiently rich potential for a further comprehensive description of growth/adaptation phenomena.
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Maugin, G.A., Imatani, S. (2003). Material Growth in Solid-Like Materials. In: Miehe, C. (eds) IUTAM Symposium on Computational Mechanics of Solid Materials at Large Strains. Solid Mechanics and Its Applications, vol 108. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0297-3_20
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DOI: https://doi.org/10.1007/978-94-017-0297-3_20
Publisher Name: Springer, Dordrecht
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