Computational modeling of thin biological membranes can aid the design of better medical devices. Remarkable biological membranes include skin, alveoli, blood vessels, and heart valves. Isogeometric analysis is ideally suited for biological membranes since it inherently satisfies the C1-requirement for Kirchhoff-Love kinematics. Yet, current isogeometric shell formulations are mainly focused on linear isotropic materials, while biological tissues are characterized by a nonlinear anisotropic stress-strain response. Here we present a thin shell formulation for thin biological membranes. We derive the equilibrium equations using curvilinear convective coordinates on NURBS tensor product surface patches. We linearize the weak form of the generic linear momentum balance without a particular choice of a constitutive law. We then incorporate the constitutive equations that have been designed specifically for collagenous tissues. We explore three common anisotropic material models: Mooney-Rivlin, May Newmann-Yin, and Gasser-Ogden-Holzapfel. Our work will allow scientists in biomechanics and mechanobiology to adopt the constitutive equations that have been developed for solid three-dimensional soft tissues within the framework of isogeometric thin shell analysis.

中文翻译：

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用于生物膜的等几何 Kirchhoff-Love 壳配方

薄生物膜的计算建模可以帮助设计更好的医疗设备。显着的生物膜包括皮肤、肺泡、血管和心脏瓣膜。等几何分析非常适合生物膜，因为它本质上满足 Kirchhoff-Love 运动学的 C1 要求。然而，当前的等几何壳公式主要集中在线性各向同性材料上，而生物组织的特点是非线性各向异性应力应变响应。在这里，我们提出了一种用于薄生物膜的薄壳配方。我们使用 NURBS 张量积表面补丁上的曲线对流坐标推导出平衡方程。我们将通用线性动量平衡的弱形式线性化，而无需特别选择本构定律。然后我们结合了专为胶原组织设计的本构方程。我们探索了三种常见的各向异性材料模型：Mooney-Rivlin、May Newmann-Yin 和 Gasser-Ogden-Holzapfel。我们的工作将使生物力学和机械生物学的科学家能够在等几何薄壳分析的框架内采用为固体三维软组织开发的本构方程。