Volumetric Material Growth: Mathematical Theory
Corresponding Member of the RAS P. I. Plotnikova, b*, J. F. Ganghofferc**, and J. Sokolowskid, e***
Translated by I. Ruzanova
a Lavrent’ev Institute of Hydrodynamics,
Siberian Branch, Russian Academy of Sciences,
pr. Akademika Lavrent’eva 15, Novosibirsk, 630090 Russia
b Novosibirsk State University, ul. Pirogova 2,
Novosibirsk, 630090 Russia
c LEMTA, Nancy University, Nancy, France
d Institut Élie Cartan Nancy, Université de Lorraine,
France
e System Research Institute, Polish Academy of Sciences, Newelska 6, 01-447 Warsaw, Poland
Correspondence to: *e-mail: plotnikov@hydro.nsc.ru,
**e-mail: jean-francois.Ganghoffer@univ-lorraine.fr,
***e-mail: Jan.Sokolowski@univ-lorraine.fr
Received 25 April, 2016
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 composite-type 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.
DOI: 10.1134/S1064562416050045