A mixed trigger volumetric growth law for cylindrical deformation in stressed configurations

Zhuan, Xin, Guan, Debao, Gao, Hao, Theobald, Peter ORCID: https://orcid.org/0000-0002-3227-7130 and Luo, Xiaoyu 2024. A mixed trigger volumetric growth law for cylindrical deformation in stressed configurations. Mathematics and Mechanics of Solids 29 (9) , pp. 1915-1931. 10.1177/10812865241242998

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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 . We establish the analytical relationship between 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:	Article
Date Type:	Publication
Status:	Published
Schools:	Engineering
Publisher:	SAGE Publications
ISSN:	1081-2865
Date of First Compliant Deposit:	4 June 2024
Date of Acceptance:	12 March 2024
Last Modified:	18 Nov 2024 14:24
URI:	https://orca.cardiff.ac.uk/id/eprint/169059

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