Huang, R., Ogden, R. and Penta, R. (2021) Mathematical modelling of residual-stress based volumetric growth in soft matter. Journal of Elasticity, 145(1-2), pp. 223-241. (doi: 10.1007/s10659-021-09834-8)
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Abstract
Growth in nature is associated with the development of residual stresses and is in general heterogeneous and anisotropic at all scales. Residual stress in an unloaded configuration of a growing material provides direct evidence of the mechanical regulation of heterogeneity and anisotropy of growth. The present study explores a model of stress-mediated growth based on the unloaded configuration that considers either the residual stress or the deformation gradient relative to the unloaded configuration as a growth variable. This makes it possible to analyze stress-mediated growth without the need to invoke the existence of a fictitious stress-free grown configuration. Furthermore, applications based on the proposed theoretical framework relate directly to practical experimental scenarios involving the “opening-angle” in arteries as a measure of residual stress. An initial illustration of the theory is then provided by considering the growth of a spherically symmetric thick-walled shell subjected to the incompressibility constraint.
Item Type: | Articles |
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Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Ogden, Professor Raymond and Penta, Dr Raimondo |
Authors: | Huang, R., Ogden, R., and Penta, R. |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Journal Name: | Journal of Elasticity |
Publisher: | Springer |
ISSN: | 0374-3535 |
ISSN (Online): | 1573-2681 |
Published Online: | 20 May 2021 |
Copyright Holders: | Copyright © 2021 The Authors |
First Published: | First published in Journal of Elasticity 145(1-2): 223-241 |
Publisher Policy: | Reproduced under a Creative Commons licence |
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