Yoon Y J, Yang G, Cowin S C
The Department of Mechanical Engineering, The School of Engineering of The City College and The Graduate School of The City University of New York, New York, NY 10031, USA.
Biomech Model Mechanobiol. 2002 Jun;1(1):83-93. doi: 10.1007/s10237-002-0008-x.
A method is illustrated for determining the effective transversely isotropic (or isotropic) elastic constants from measured orthotropic elastic constants. This method consists of constructing upper and lower bounds on the effective transversely isotropic (or isotropic) elastic constants using the known orthotropic values. This method is illustrated using three sets of elastic constants for bone. Fortunately, the upper and lower bounds are very close. Thus very good approximations for the effective transversely isotropic (or isotropic) elastic constants for cortical and cancellous bone are obtained from previously published data on the orthotropic elastic constants for those tissue types. This work is undertaken to build a greater database for the transversely isotropic elastic constants of bone with the intention of employing them in a transversely isotropic model of bone poroelasticity. An interesting aspect of the present result is that the Voigt and Reuss bounds are very tight for these anisotropic materials. This is not always the case for these bounds.
阐述了一种从测量得到的正交各向异性弹性常数确定有效横观各向同性（或各向同性）弹性常数的方法。该方法包括利用已知的正交各向异性值构建有效横观各向同性（或各向同性）弹性常数的上下界。使用三组骨的弹性常数对该方法进行了说明。幸运的是，上下界非常接近。因此，从先前发表的关于这些组织类型的正交各向异性弹性常数的数据中，可以得到皮质骨和松质骨有效横观各向同性（或各向同性）弹性常数的非常好的近似值。开展这项工作是为了建立一个更大的骨横观各向同性弹性常数数据库，以便将其应用于骨多孔弹性的横观各向同性模型中。当前结果的一个有趣方面是，对于这些各向异性材料，Voigt和Reuss界非常紧密。对于这些界来说，情况并非总是如此。
