A theory of volumetric growth for compressible elastic biological materials
A theory of volumetric growth for compressible elastic biological materials
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DOI：
10.1177/108128650100600601
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发表时间：
2001-12-01
影响因子：
2.6
通讯作者：
Van Dyke, TJ
中科院分区：
文献类型：
--
作者：
Klisch, SM;Van Dyke, TJ
本文提出了可压缩弹性材料体积增长的一般理论。作者推导出一套完整的控制方程，在本配置的弹性材料经历一个连续的增长过程。特别是，他们得到了两个本构限制的功能原理。首先，作者表明，一个不断增长的弹性材料的行为作为一个绿色弹性材料。其次，他们得到了一个表达式，该表达式将由于生长而产生的应力功率与由于生长而产生的能量变化率联系起来。然后，从更一般的理论推导出小增量增长的控制方程。增量增长边值问题的方程提供了描述增长的量的直观描述，并用于实现理论。该理论的主要特点说明了具体的例子，采用两个应变能函数，已被用来模拟生物材料。
A general theory of volumetric growth for compressible elastic materials is presented. The authors derive a complete set of governing equations in the present configuration for an elastic material undergoing a continuous growth process. In particular, they obtain two constitutive restrictions from a work-energy principle. First, the authors show that a growing elastic material behaves as a Green-elastic material. Second, they obtain an expression that relates the stress power due to growth to the rate of energy change due to growth. Then, the governing equations for a small increment of growth are derived from the more general theory. The equations for the incremental growth boundary-value problem provide an intuitive description of the quantities that describe growth and are used to implement the theory. The main features of the theory are illustrated with specific examples employing two strain energy functions that have been used to model biological materials.