Seshaiyer Padmanabhan, Humphrey Jay D
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA.
J Biomech Eng. 2003 Jun;125(3):363-71. doi: 10.1115/1.1574333.
Quantification of the mechanical behavior of hyperelastic membranes in their service configuration, particularly biological tissues, is often challenging because of the complicated geometry, material heterogeneity, and nonlinear behavior under finite strains. Parameter estimation thus requires sophisticated techniques like the inverse finite element method. These techniques can also become difficult to apply, however, if the domain and boundary conditions are complex (e.g. a non-axisymmetric aneurysm). Quantification can alternatively be achieved by applying the inverse finite element method over sub-domains rather than the entire domain. The advantage of this technique, which is consistent with standard experimental practice, is that one can assume homogeneity of the material behavior as well as of the local stress and strain fields. In this paper, we develop a sub-domain inverse finite element method for characterizing the material properties of inflated hyperelastic membranes, including soft tissues. We illustrate the performance of this method for three different classes of materials: neo-Hookean, Mooney Rivlin, and Fung-exponential.
对超弹性膜在其使用构型下，特别是生物组织的力学行为进行量化，往往具有挑战性，这是由于其复杂的几何形状、材料非均质性以及有限应变下的非线性行为。因此，参数估计需要诸如逆有限元法等复杂技术。然而，如果域和边界条件复杂（例如非轴对称动脉瘤），这些技术也可能难以应用。作为替代方法，可以通过在子域而非整个域上应用逆有限元法来实现量化。这种与标准实验实践一致的技术的优点在于，可以假设材料行为以及局部应力和应变场的均匀性。在本文中，我们开发了一种子域逆有限元法，用于表征充气超弹性膜（包括软组织）的材料特性。我们展示了该方法对三类不同材料的性能：新胡克材料、穆尼 - 里夫林材料和冯 - 指数材料。
