Nonconvex Model of Material Growth: Mathematical Theory

Abstract

The model of volumetric material growth is introduced in the framework of finite elasticity. The new results obtained for the model are presented with complete proofs. The state variables include the deformations, temperature and the growth factor matrix function. The existence of global in time solutions for the quasistatic deformations boundary value problem coupled with the energy balance and the evolution of the growth factor is shown. The mathematical results can be applied to a wide class of growth models in mechanics and biology.

Patterns of the fetal brain structures growth: MRIstudy

“…Classical mechanical concepts, including deformation, stretch, and strain rate pressure, play a crucial role in modeling brain shape and function. The volumetric material growth model is introduced in the framework of finite elasticity and can be applied to a wide class of growth models in mechanics and biology [3]. At the same time changes in brain volume inevitably lead to changes in cognitive abilities [4], Ultrasonography (US) continues to be one of the main methods of fetal imaging [5].…”