Zhuan, X., Guan, D., Theobald, P. and Luo, X. (2024) A mixed trigger volumetric growth law for cylindrical deformation in stressed configurations. Mathematics and Mechanics of Solids, (doi: 10.1177/10812865241242998) (Early Online Publication)
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Abstract
Soft tissue growth is crucial across various physiological applications, with mathematical modelling playing a pivotal role in understanding the underlying processes. The volumetric growth theory serves as a commonly used mathematical framework in this context. Our previous research on volumetric growth theory primarily concentrated on defining the incremental growth tensor in loaded and stressed configurations, revealing that this approach closely aligns with experimental observations of residual hoop stress distribution. However, given the assumptions employed, the approach has limitations in accurately predicting the growth timeline. In this work, we address these issues by incorporating the effect of initial residual strain and introducing a new mixed trigger growth evolution law. In this growth law, we do not use growth saturation as an upper limit, as this assumption cannot represent many physiological conditions. Instead, we propose that growth in soft tissues leads to a new equilibrium state. To illustrate this idea, we introduce a growth incompatibility function, denoted as I. We establish the analytical relationship between I and the opening angle in a simplified cylindrical geometry resembling the structure of the heart or arteries. We put forth a revised growth law that is both stress and incompatibility driven/Our results show that by using this mixed trigger growth law, tissues will not grow indefinitely. Instead, a stress-driven homeostasis incompatibility state will be reached. In addition, by accounting for the initial opening angle in the model, we can accurately trace the growth history of the heart, aligning with experimental data obtained from measuring the opening angle in young pigs from birth to maturity.
Item Type: | Articles |
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Additional Information: | This project is funded by the UK Engineering and Physical Sciences Research Council (EPSRC) grants (EP/S014284, EP/S030875, EP/N014642 and EP/S020950). |
Status: | Early Online Publication |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Luo, Professor Xiaoyu and Guan, Mr Debao and Zhuan, Xin |
Authors: | Zhuan, X., Guan, D., Theobald, P., and Luo, X. |
College/School: | College of Science and Engineering College of Science and Engineering > School of Mathematics and Statistics College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Journal Name: | Mathematics and Mechanics of Solids |
Publisher: | SAGE Publications |
ISSN: | 1081-2865 |
ISSN (Online): | 1741-3028 |
Published Online: | 02 May 2024 |
Copyright Holders: | Copyright © The Author(s) 2024 |
First Published: | First published in Mathematics and Mechanics of Solids 2024 |
Publisher Policy: | Reproduced under a Creative Commons licence |
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