Nonconvex Model of Material Growth: Mathematical Theory

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 sol...

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Bibliographic Details
Published in:Archive for rational mechanics and analysis 2018-12, Vol.230 (3), p.839-910
Main Authors: Ganghoffer, J. F., Plotnikov, P. I., Sokolowski, J.
Format: Article
Language:English
Subjects:
Boundary value problems
Classical Mechanics
Complex Systems
Deformation
Elasticity
Fluid- and Aerodynamics
Growth factors
Growth models
Mathematical and Computational Physics
Mathematical models
Mathematics
Matrix methods
Physics
Physics and Astronomy
Theoretical
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Summary: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.
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-018-1259-8