Department of Applied Mathematics and Science, Khalifa University of Science, Technology and Research, Sharjah, UAE.
Biomech Model Mechanobiol. 2013 Apr;12(2):215-23. doi: 10.1007/s10237-012-0393-8. Epub 2012 Apr 13.
Principal axis formulations are regularly used in isotropic elasticity, but they are not often used in dealing with anisotropic problems. In this paper, based on a principal axis technique, we develop a physical invariant orthotropic constitutive equation for incompressible solids, where it contains only a one variable (general) function. The corresponding strain energy function depends on six invariants that have immediate physical interpretation. These invariants are useful in facilitating an experiment to obtain a specific constitutive equation for a particular type of materials. The explicit appearance of the classical ground-state constants in the constitutive equation simplifies the calculation for their admissible values. A specific constitutive model is proposed for passive myocardium, and the model fits reasonably well with existing simple shear and biaxial experimental data. It is also able to predict a set of data from a simple shear experiment.
主轴公式在各向同性弹性中经常使用，但在处理各向异性问题时并不常用。在本文中，我们基于主轴技术，为不可压缩固体开发了一种物理不变量正交各向异性本构方程，其中仅包含一个变量（通用）函数。相应的应变能函数取决于具有直接物理解释的六个不变量。这些不变量有助于进行实验以获得特定类型材料的特定本构方程。本构方程中经典基态常数的显式出现简化了其允许值的计算。提出了一种用于被动心肌的具体本构模型，该模型与现有的简单剪切和双向实验数据拟合得相当好。它还能够预测一组来自简单剪切实验的数据。
