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.

中文翻译：

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受热-机械耦合启发的生物软组织生长和萎缩的非弹性本构定律


本研究提出了一种热-机械耦合启发的非弹性本构定律，用于生物软组织的生长和萎缩 （体积和质量的增加和减少）。受热-机械耦合启发的公式实现了机械场和标量场（比如营养场）之间的多物理场建模，标量场表示营养源在体内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分量和生长分量，从耗散优化问题中推导出生长和萎缩的演化规律作为稳态条件，其数学作与标准弹塑性材料建模相同。由于提出的公式，模拟了在自然生物体中看到的几种特征材料反应。特别是，成功认识到生物软组织的生长和萎缩并不完全由平均应力值决定，甚至在恒定的压缩/拉伸状态下也可能发生。此外，当生物软组织反复生长和萎缩时，由于硬化变量的积累，会发生类似细胞衰老的材料反应，从而生物软组织对促进生长和萎缩的外部因素变得不敏感。 提出了两个单元素水平的数值示例来演示所提出的配方的基本材料响应，并准备了两个结构数值示例来展示由机械和营养领域两种状态决定的一些特征性生长和萎缩趋势。