Volumetric material growth: Mathematical theory

Abstract

A mathematical model of isotropic volumetric growth of a thermoelastic material based on a multiplicative representation of the distortion tensor is considered. The model represents a nonlinear compositetype system for determining the displacement field, temperature, and a scalar growth factor (implant). It includes the mechanical equilibrium equation, energy balance equation linearized with respect to temperature, and the implant evolution equation. The displacement and temperatures fields can have discontinuities in time. Rules for selecting physically acceptable solutions are stated. The existence of an almost strong solution satisfying the selection rules is proved.