Equivalence between short-time biphasic and incompressible elastic material responses
Equivalence between short-time biphasic and incompressible elastic material responses
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DOI：
10.1115/1.2720918
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发表时间：
2007-06-01
影响因子：
1.7
通讯作者：
Weiss, Jeffrey A.
中科院分区：
文献类型：
--
作者：
Ateshian, Gerard A.;Ellis, Benjamin J.;Weiss, Jeffrey A.
多孔渗透组织通常用多孔介质理论如双相理论来建模。本文从第一性原理出发，研究了任意变形和本构关系的短时双相和不可压缩弹性响应的等价性。这种等效性在椎间盘的无侧限压缩和有限变形下的关节接触问题中得到说明，使用两种不同的本构关系，对于软骨的固体基质，其中一种关系解释了在该组织中观察到的拉伸模量和压缩模量之间的巨大差异。在一般条件下证明这种等效性，为使用不可压缩弹性材料的现有有限元代码作为双相分析的实际替代品提供了基本原理，只要只寻求短时间的双相响应。在实践中，不可压缩弹性分析代表了短期响应的双相分析[GRAPHICS]，其中Delta是特征维数，[GRAPHICS]是弹性张量，K是固体矩阵的水力渗透率张量。关于执行问题，特别是当不可压缩弹性的有限元公式采用由加性偏差和体积分量组成的不耦合应变能函数时，提供了某些注意事项。
Porous-permeable tissues have often been modeled using porous media theories such as the biphasic theory. This study examines the equivalence of the short-time biphasic and incompressible elastic responses for arbitrary deformations and constitutive relations from first principles. This equivalence is illustrated in problems of unconfined compression of a disk, and of articular contact under finite deformation, using two different constitutive, relations for the solid matrix of cartilage, one of which accounts for the large disparity observed between the tensile and compressive moduli in this tissue. Demonstrating this equivalence under general conditions provides a rationale for using available finite element codes for incompressible elastic materials as a practical substitute for biphasic analyses, so long as only the short-time biphasic response is sought. In practice, an incompressible elastic analysis is representative of a biphasic analysis over the short-term response[GRAPHICS]here Delta is a characteristic dimension,[GRAPHICS]is the elasticity tensor and K is the hydraulic permeability tensor of the solid matrix. Certain notes of caution are provided with regard to implementation issues, particularly when finite element formulations of incompressible elasticity employ an uncoupled strain energy function consisting of additive deviatoric and volumetric components.