Brain tissues are known for exhibiting complex nonlinear and time‐dependent properties, which require visco‐hyperelastic constitutive models for proper simulation. In this paper, a Total Lagrangian Explicit Selective Smoothed Finite Element Method (Selective S‐FEM) is formulated to analyze the dynamic behavior of incompressible brain tissues undergoing extremely large deformation. The proposed Selective S‐FEM deals with three‐dimensional problems using four‐node tetrahedron elements that can be automatically generated for geometrically complex soft tissues. It consists of the three key ingredients. (i) A visco‐hyperelastic constitutive model is developed within the framework of S‐FEM in the first time, allowing adequate modeling of the dynamic brain tissue behavior. (ii) Selective S‐FEM strategy is used for overcome the mesh distortion and the volumetric locking that often occurs in soft tissues. (iii) Total Lagrangian formulation is used in an explicit algorithm allowing rigorous simulation of extreme large deformation. (iv) A combined implementation of Selective S‐FEM with the visco‐hyperelastic constitutive model for dynamic simulations. The shear deformation is calculated by Face/Edge‐based S‐FEM, and the volume deformation is calculated by NS‐FEM. Numerical experiments show that Selective S‐FEM is a robust solver with good accuracy, and excellent ability to reduce element distortion effects in simulate time‐dependence behavior of bio‐tissues.

中文翻译：

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粘-超弹性本构模型的选择性平滑有限元方法分析脑组织的生物力学响应

众所周知，脑组织表现出复杂的非线性和随时间变化的特性，因此需要使用粘-超弹性本构模型进行正确的模拟。本文提出了一种总拉格朗日显式选择性平滑有限元方法（Selective S-FEM），以分析经历极大变形的不可压缩脑组织的动力学行为。拟议的选择性S-FEM使用四节点四面体元素处理三维问题，这些元素可以为几何复杂的软组织自动生成。它包含三个关键要素。（i）首次在S-FEM框架内开发了粘-超弹性本构模型，从而可以对动态脑组织行为进行适当的建模。（ii）选择性S-FEM策略用于克服软组织中经常发生的网格变形和体积锁定。（iii）在显式算法中使用总拉格朗日公式，可以对极端大变形进行严格模拟。（iv）动态仿真的选择性S-FEM与粘-超弹性本构模型的组合实现。剪切变形由基于面/边的S-FEM计算，体积变形由NS-FEM计算。数值实验表明，Selective S-FEM是一种鲁棒的求解器，具有良好的精度，并且在模拟生物组织的时间依赖性行为方面具有出色的减少元素失真效应的能力。（iii）在显式算法中使用总拉格朗日公式，可以对极端大变形进行严格模拟。（iv）动态模拟的选择性S-FEM与粘-超弹性本构模型的组合实现。剪切变形由基于面/边的S-FEM计算，体积变形由NS-FEM计算。数值实验表明，Selective S-FEM是一种鲁棒的求解器，具有良好的精度，并且在模拟生物组织的时间依赖性行为方面具有出色的减少元素失真效应的能力。（iii）在显式算法中使用总拉格朗日公式，可以对极端大变形进行严格模拟。（iv）动态仿真的选择性S-FEM与粘-超弹性本构模型的组合实现。剪切变形通过基于面/边的S-FEM计算，体积变形通过NS-FEM计算。数值实验表明，Selective S-FEM是一种鲁棒的求解器，具有良好的精度，并且在模拟生物组织的时间依赖性行为方面具有出色的减少元素失真效应的能力。