一种新的基于连续体的厚壳有限元用于动态软生物组织：第二部分——各向异性超弹性与不可压缩性方面
A New Continuum-Based Thick Shell Finite Element for Soft Biological Tissues in Dynamics: Part 2 - Anisotropic Hyperelasticity and Incompressibility Aspects
AI总结：
本文提出了一种基于连续体的厚壳有限元，用于模拟大三维应变和变形，结合各向异性超弹性本构关系和不可压缩性特性，验证了其在软生物组织建模中的可靠性与效率。
摘要：
在 companion 文章（第一部分）中，我们介绍了基于 Mindlin-Reissner 理论开发的一种厚连续体（CB）壳有限元（FE）。我们通过线弹性材料属性验证了该元素在建模大三维变形时的精度、效率和锁紧不敏感性。在本文中，我们开发并实现了基于更新拉格朗日（UL）公式中的动能描述，以各向异性不可压缩超弹性本构关系，使 CB 壳 FE 能够准确模拟非常大的三维应变和变形。具体而言，我们开发了在层坐标系统中的变形度量，提出了三种非线性超弹性应变建模技术，并实现了无需使用惩罚因子或拉格朗日乘数即可直接施加不可压缩性和零法向应力条件。在将本工作应用于生物医学领域时，我们进行了多项实验，研究了不同几何形状和加载条件下橡胶状材料和软生物组织的机械行为。本文 FE 结果与分析和/或实验数据之间的良好一致证明了 CB 壳 FE 结合当前本构技术在建模、分析和预测软生物组织机械行为方面的高可靠性和效率。
英文摘要：
In a companion article (Part 1), we presented the development of a thick continuum-based (CB) shell finite element (FE) based on Mindlin-Reissner theory. We verified the accuracy, efficiency and locking insensitivity of the element in modeling large 3D deformations, using linear elastic material properties. In the present article, we developed and implemented the kinetics description, within the updated Lagrangian (UL) formulation, of anisotropic incompressible hyperelastic constitutive relations that enable the CB shell FE to accurately model very large 3D strains and deformations. Specifically, we developed the measures of deformation in the lamina coordinate system, presented three techniques to model nonlinear hyperelastic strains, and enabled the direct enforcement of incompressibility and of the zero normal stress condition without using a penalty factor or a Lagrange multiplier. Moving towards the application of the present work to the biomedical realm, we performed multiple experiments concerning mechanical behavior of rubber-like materials and soft biological tissues in different geometries and loading conditions. Excellent agreements between the present FE results and the analytical and/or experimental data proved the CB shell FE combined with the present constitutive techniques to be a highly reliable and efficient tool for modeling, analyzing, and predicting mechanical behavior of soft biological tissues.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
