Nonconvex Model of Material Growth: Mathematical Theory

J. F. Ganghoffer; P. I. Plotnikov; J. Sokolowski

doi:10.1007/s00205-018-1259-8

Nonconvex Model of Material Growth: Mathematical Theory

J. F. Ganghoffer, P. I. Plotnikov, J. Sokolowski

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	839-910
Number of pages	72
Journal	Archive for Rational Mechanics and Analysis
Volume	230
Issue number	3
DOIs	https://doi.org/10.1007/s00205-018-1259-8
Publication status	Published - 1 Dec 2018

Keywords

VOLUMETRIC GROWTH
STRESS
TISSUE

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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.",

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AB - 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.

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KW - TISSUE

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Nonconvex Model of Material Growth: Mathematical Theory

Abstract

Keywords

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