Mathematical Modeling of Volumetric Material Growth in Thermoelasticity

Abstract

The model of volumetric material growth is introduced in the framework of finite elasticity. The state variables include the deformations, temperature and the transplant matrix function. The wellposedness of the proposed model is shown. The existence of local in time classical solutions for the quasistatic deformations boundary value problem coupled with the energy balance and the growth evolution of the transplant is obtained. The new mathematical results for a broad class of growth models in mechanics and biology are presented with complete proofs.