一种新的基于连续体的厚壳有限元用于动态软生物组织：Part 1 - 使用经典验证实验的初步基准测试
A New Continuum-Based Thick Shell Finite Element for Soft Biological Tissues in Dynamics: Part 1 - Preliminary Benchmarking Using Classic Verification Experiments
AI总结：
本文提出一种新的非线性厚连续体壳有限元，用于模拟动态软生物组织，验证其在处理大变形、复杂几何和粗网格时的准确性与效率。
摘要：
对于动态薄软生物组织的有限元模拟，壳元相比体积元能一次捕捉整个组织厚度，具有更大的临界时间步长。然而，现有壳元在处理不规则几何、超弹性、各向异性3D变形方面仍有局限。为此，我们开发了一种基于Mindlin-Reissner壳理论的新通用非线性厚连续体壳有限元，具备大弯曲、大畸变和大应变能力，嵌入更新拉格朗日公式和显式时间积分。我们进行了文献中可用的数值基准实验，聚焦于工程线弹性材料，验证并证明了新厚连续体壳FE在准确性、效率、处理大3D变形、曲面几何、粗网格以及计算速度方面的能力。该元素对三种类型的锁死（剪切、膜和体积）和扭曲效应不敏感。本文在生物医学领域的能力在 companion article (Part 2) 中得到展示，其中实现了各向异性不可压缩超弹性本构关系并进行了验证。
英文摘要：
For the finite element simulation of thin soft biological tissues in dynamics, shell elements, compared to volume elements, can capture the whole tissue thickness at once, and feature larger critical time steps. However, the capabilities of existing shell elements to account for irregular geometries, and hyperelastic, anisotropic 3D deformations characteristic of soft tissues are still limited. As improvement, we developed a new general nonlinear thick continuum-based (CB) shell finite element (FE) based on the Mindlin-Reissner shell theory, with large bending, large distortion and large strain capabilities, embedded in the updated Lagrangian formulation and explicit time integration. We performed numerical benchmark experiments available from the literature that focus on engineering linear elastic materials, which, verified and proved the new thick CB shell FE to: 1) be accurate an efficient 2) be powerful in handling large 3D deformations, curved geometries, 3) accommodate coarse distorted meshes, and 4) achieve comparatively fast computational times. The new element was also insensitive to three types of locking (shear, membrane and volumetric), and warping effects. The capabilities of the present thick CB shell FE in the biomedical realm are illustrated in a companion article (Part 2), in which anisotropic incompressible hyperelastic constitutive relations are implemented and verified.
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