Stress‐modulated growth in the presence of nutrients—Existence and uniqueness in one spatial dimension

Abstract

AbstractExistence 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 gradientFinto an elastic part and a growth‐related partG. After the transformation due to the growth process, governed byG, an elastic deformation described by is applied in order to restore the Dirichlet boundary conditions and, therefore, the current configuration might be stressed with a stress tensorS. 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 stressSand the pull‐back of a nutrient concentration in the current configuration, leading to a coupled system of ordinary differential equations.