受力构型中圆柱变形的混合触发体积增长定律

IF 1.7 4区 工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Mathematics and Mechanics of Solids Pub Date : 2024-05-02 DOI:10.1177/10812865241242998
Xin Zhuan, Debao Guan, Hao Gao, Peter Theobald, Xiaoyu Luo
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引用次数: 0

摘要

软组织生长在各种生理应用中都至关重要,而数学建模在理解其基本过程中发挥着关键作用。体积生长理论是这方面常用的数学框架。我们之前对体积生长理论的研究主要集中在定义加载和受压配置下的增量生长张量,结果表明这种方法与残余箍应力分布的实验观察结果非常吻合。然而,考虑到所采用的假设,该方法在准确预测生长时间轴方面存在局限性。在这项工作中,我们通过纳入初始残余应变的影响并引入新的混合触发生长演化规律来解决这些问题。在这一生长规律中,我们不使用生长饱和作为上限,因为这一假设不能代表许多生理条件。相反,我们提出软组织的生长会导致新的平衡状态。为了说明这一观点,我们引入了生长不相容函数,表示为[公式:见正文]。我们建立了[公式:见正文]与类似心脏或动脉结构的简化圆柱几何体中开口角之间的分析关系。我们提出了一种既受应力驱动又受不相容性驱动的修正生长定律/我们的结果表明,使用这种混合触发生长定律,组织不会无限生长。相反,应力驱动的平衡不相容状态将会达到。此外,通过在模型中考虑初始开口角,我们可以精确地追踪心脏的生长历史,这与测量幼猪从出生到成熟的开口角所获得的实验数据一致。
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A mixed trigger volumetric growth law for cylindrical deformation in stressed configurations
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 [Formula: see text]. We establish the analytical relationship between [Formula: see text] 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.
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来源期刊
Mathematics and Mechanics of Solids
Mathematics and Mechanics of Solids 工程技术-材料科学:综合
CiteScore
4.80
自引率
19.20%
发文量
159
审稿时长
1 months
期刊介绍: Mathematics and Mechanics of Solids is an international peer-reviewed journal that publishes the highest quality original innovative research in solid mechanics and materials science. The central aim of MMS is to publish original, well-written and self-contained research that elucidates the mechanical behaviour of solids with particular emphasis on mathematical principles. This journal is a member of the Committee on Publication Ethics (COPE).
期刊最新文献
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