A triphasic theory for growth in biological tissue - Basics and applications
A triphasic theory for growth in biological tissue - Basics and applications
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DOI：
10.1002/mawe.200600018
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发表时间：
2006-06-01
影响因子：
1.1
通讯作者：
Bluhm, J.
中科院分区：
文献类型：
--
作者：
Ricken, T.;Schwarz, A.;Bluhm, J.
本文提出了一个三相模型（固体，充满含营养物质的水的空隙），用于描述横观各向同性饱和生物组织的生长现象。这是在基于多孔介质理论（TPM）的宏观力学描述的框架内完成的。因此，生长的本构方程由应力状态和负责质量交换的营养物的局部比例决定。固体的横观各向同性行为影响应力响应和内部流体渗透率，这被认为是使用不变的亥姆霍兹自由能和横观各向同性渗透率函数的制定。在介绍了计算概念的发展框架后，包括大变形方程的控制弱公式的表示，一些有代表性的数值例子进行了检查。
A triphasic model (solid, interstices filled with water containing nutrients) is proposed for the phenomenological description of transversely isotropic saturated biological tissues including the phenomena of growth. This is done within the framework of a macromechanical description based on the Theory of Porous Media (TPM). Thereby, the constitutive equation of growth is determined by the state of stress and the local proportion of nutrients responsible for the mass exchange. The transversely isotropic behavior of the solid influences both the stress response and the internal fluid permeability, which is considered using an invariant formulation of the Helmholtz free energy and transversely isotropic permeability functions. After presenting the developed framework of the calculation concept including the representation of the governing weak formulations of the equations for large deformations, some representative numerical examples are examined.