Bangert, Kira and Dolzmann, Georg (2023) Stress-modulated growth in the presence of nutrients-Existence and uniqueness in one spatial dimension. ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 103 (10): e202200558. ISSN 0044-2267, 1521-4001
Full text not available from this repository. (Request a copy)Abstract
Existence and uniqueness of solutions for a class of models for stress-modulated growth is proven in one spatial dimension. The model features the multiplicative decomposition of the deformation gradient F into an elastic part Fe$F_e$ and a growth-related part G. After the transformation due to the growth process, governed by G, an elastic deformation described by Fe$F_e$ is applied in order to restore the Dirichlet boundary conditions and, therefore, the current configuration might be stressed with a stress tensor S. The growth of the material at each point in the reference configuration is given by an ordinary differential equation for which the right-hand side may depend on the stress S and the pull-back of a nutrient concentration in the current configuration, leading to a coupled system of ordinary differential equations.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | MODELS; MECHANICS; SOLIDS |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Georg Dolzmann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 05 Mar 2024 12:16 |
| Last Modified: | 05 Mar 2024 12:16 |
| URI: | https://pred.uni-regensburg.de/id/eprint/59317 |
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