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arXiv · 2211.13571

Stress-modulated growth in the presence of nutrients -- existence and uniqueness in one spatial dimension

Kira Bangert·Georg Dolzmann
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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 $F_e$ and a growth-related part $G$. After the transformation due to the growth process, governed by $G$, an elastic deformation described by $F_e$ 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.

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Kira Bangert, Georg Dolzmann. 2022-11-24. Stress-modulated growth in the presence of nutrients -- existence and uniqueness in one spatial dimension. https://arxiv.org/abs/2211.13571

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