A thermal-mechanical coupling-inspired inelastic constitutive law for the growth and atrophy of biological soft tissues

IF 5 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids Pub Date : 2025-05-16 DOI:10.1016/j.jmps.2025.106159

Jike Han , Yuka Yokoyama , Taiji Adachi , Shinji Nishiwaki

{"title":"A thermal-mechanical coupling-inspired inelastic constitutive law for the growth and atrophy of biological soft tissues","authors":"Jike Han , Yuka Yokoyama , Taiji Adachi , Shinji Nishiwaki","doi":"10.1016/j.jmps.2025.106159","DOIUrl":null,"url":null,"abstract":"<div><div>This study proposes a thermal-mechanical coupling-inspired inelastic constitutive law for the growth and atrophy (for the increase and decrease of volume and mass) of biological soft tissues. The thermal-mechanical coupling-inspired formulation realizes the multiphysics modeling between the mechanical field and a scalar field, say the nutrition field, that represents the transportations of the nutrition source inside of the body and the nutrition flux on the surface. Accordingly, biological soft tissues can exhibit growth and atrophy without any displacement or force loadings, which is analogous to thermal strain. On the other hand, the inelastic constitutive modeling decomposes the deformation gradient tensor into the elastic and growth components, and the evolution laws for the growth and atrophy are derived as the stationary conditions from the dissipation optimization problem, whose mathematical manipulation is the same as the standard elastoplastic material modeling. Thanks to the proposed formulation, several characteristic material responses that are seen in natural organisms are imitated. In particular, it is successfully realized that the growth and atrophy of biological soft tissues are not exclusively determined by the value of the mean stress, and can occur even under a constant compression/tension state. Also, when biological soft tissues are subjected to repeated growth and atrophy, the cellular aging-like material response occurs due to the accumulation of hardening variables, by which biological soft tissues become insensitive to external factors that encourage growth and atrophy. Two single-element level numerical examples are presented to demonstrate the basic material responses of the proposed formulation, and two structural numerical examples are prepared to show a few characteristic growth and atrophy trends that are determined by both states of the mechanical and nutrition fields.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"202 ","pages":"Article 106159"},"PeriodicalIF":5.0000,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of The Mechanics and Physics of Solids","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022509625001358","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

Abstract

This study proposes a thermal-mechanical coupling-inspired inelastic constitutive law for the growth and atrophy (for the increase and decrease of volume and mass) of biological soft tissues. The thermal-mechanical coupling-inspired formulation realizes the multiphysics modeling between the mechanical field and a scalar field, say the nutrition field, that represents the transportations of the nutrition source inside of the body and the nutrition flux on the surface. Accordingly, biological soft tissues can exhibit growth and atrophy without any displacement or force loadings, which is analogous to thermal strain. On the other hand, the inelastic constitutive modeling decomposes the deformation gradient tensor into the elastic and growth components, and the evolution laws for the growth and atrophy are derived as the stationary conditions from the dissipation optimization problem, whose mathematical manipulation is the same as the standard elastoplastic material modeling. Thanks to the proposed formulation, several characteristic material responses that are seen in natural organisms are imitated. In particular, it is successfully realized that the growth and atrophy of biological soft tissues are not exclusively determined by the value of the mean stress, and can occur even under a constant compression/tension state. Also, when biological soft tissues are subjected to repeated growth and atrophy, the cellular aging-like material response occurs due to the accumulation of hardening variables, by which biological soft tissues become insensitive to external factors that encourage growth and atrophy. Two single-element level numerical examples are presented to demonstrate the basic material responses of the proposed formulation, and two structural numerical examples are prepared to show a few characteristic growth and atrophy trends that are determined by both states of the mechanical and nutrition fields.

查看原文本刊更多论文

生物软组织生长和萎缩的热-力耦合启发的非弹性本构律

本研究提出了生物软组织生长和萎缩（体积和质量的增加和减少）的热-力耦合启发的非弹性本构律。热-机械耦合启发的公式实现了机械场和标量场（即营养场）之间的多物理场建模，该标量场表示体内营养源的运输和表面的营养通量。因此，生物软组织可以在没有任何位移或力载荷的情况下表现出生长和萎缩，这类似于热应变。另一方面，非弹性本构建模将变形梯度张量分解为弹性和生长分量，并从耗散优化问题中导出生长和萎缩的演化规律作为平稳条件，其数学操作与标准弹塑性材料建模相同。由于提出的公式，在自然生物体中看到的几种特征物质反应被模仿。特别是，成功地认识到生物软组织的生长和萎缩并不完全由平均应力的值决定，甚至在恒定的压缩/拉伸状态下也会发生。此外，当生物软组织遭受反复生长和萎缩时，由于硬化变量的积累，生物软组织对促进生长和萎缩的外部因素变得不敏感，从而发生细胞老化样物质反应。给出了两个单元素水平的数值例子来证明所提出的公式的基本材料响应，并准备了两个结构数值例子来展示由机械和营养领域的两种状态决定的一些特征生长和萎缩趋势。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of The Mechanics and Physics of Solids 物理-材料科学：综合

CiteScore

9.80

自引率

9.40%

发文量

276

审稿时长

52 days

期刊介绍： The aim of Journal of The Mechanics and Physics of Solids is to publish research of the highest quality and of lasting significance on the mechanics of solids. The scope is broad, from fundamental concepts in mechanics to the analysis of novel phenomena and applications. Solids are interpreted broadly to include both hard and soft materials as well as natural and synthetic structures. The approach can be theoretical, experimental or computational.This research activity sits within engineering science and the allied areas of applied mathematics, materials science, bio-mechanics, applied physics, and geophysics. The Journal was founded in 1952 by Rodney Hill, who was its Editor-in-Chief until 1968. The topics of interest to the Journal evolve with developments in the subject but its basic ethos remains the same: to publish research of the highest quality relating to the mechanics of solids. Thus, emphasis is placed on the development of fundamental concepts of mechanics and novel applications of these concepts based on theoretical, experimental or computational approaches, drawing upon the various branches of engineering science and the allied areas within applied mathematics, materials science, structural engineering, applied physics, and geophysics. The main purpose of the Journal is to foster scientific understanding of the processes of deformation and mechanical failure of all solid materials, both technological and natural, and the connections between these processes and their underlying physical mechanisms. In this sense, the content of the Journal should reflect the current state of the discipline in analysis, experimental observation, and numerical simulation. In the interest of achieving this goal, authors are encouraged to consider the significance of their contributions for the field of mechanics and the implications of their results, in addition to describing the details of their work.