Mathematical modelling of residual-stress based volumetric growth in soft matter

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)

[img] Text
238883.pdf - Published Version
Available under License Creative Commons Attribution.

1MB

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
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

University Staff: Request a correction | Enlighten Editors: Update this record

Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
303232EPSRC Centre for Multiscale soft tissue mechanics with MIT and POLIMI (SofTMech-MP)Xiaoyu LuoEngineering and Physical Sciences Research Council (EPSRC)EP/S030875/1M&S - Mathematics
172141EPSRC Centre for Multiscale soft tissue mechanics with application to heart & cancerRaymond OgdenEngineering and Physical Sciences Research Council (EPSRC)EP/N014642/1M&S - Mathematics