The human annulus fibrosus (HAF) is the major component in response to external forces for the intervertebral disk (IVD), which maintains the stability and flexibility of human spine. It can be assumed to be an anisotropic nearly incompressible hyperelastic composite consisting of collagen fibers and matrix in the numerical simulations of biomechanics. However, due to the geometric complexity and material nonlinearity of HAF, the conventional Finite Element Method (FEM) often gets into difficulties in mesh generation and uncertainty of accuracy control. In this paper, a modified composite-based constitutive model, which considers the slight compressibility of ground substance and the shear interaction between collagen fibers and matrix, is developed to describe the mechanical behavior of HAF. In addition, based on the gradient smoothing techniques, the selective 3D-edge-based and node-based smoothed finite element method (Selective 3D-ES/NS-FEM) is developed to alleviate volume locking and improve the accuracy of linear four-node tetrahedral (TET4) elements. Combined with the modified constitutive model, the Selective 3D-ES/NS-FEM is applied into the explicit dynamic analysis of HAF undergoing large deformation. By comparing with the experiment data in the literatures and the numerical results produced by conventional FEM, the presented approach is proved to possess excellent accuracy and efficiency in predicting the nonlinear mechanical behavior of HAF, as well as the orientation change of the collagen fibers. Moreover, the Selective 3D-ES/NS-FEM is demonstrated to have robust capability in handling element distortion, even with the simplest TET4 mesh. This study is significant to the biomechanical research of HAF, and has potential value for guiding the prevention and treatment of low back pain.

人体纤维环（HAF）是椎间盘（IVD）响应外力的主要组成部分，它保持人体脊柱的稳定性和灵活性。在生物力学数值模拟中，可以假设它是由胶原纤维和基质组成的各向异性几乎不可压缩的超弹性复合材料。然而，由于HAF的几何复杂性和材料非线性，传统的有限元法（FEM）经常在网格生成和精度控制的不确定性方面遇到困难。在本文中，开发了一种改进的基于复合材料的本构模型，该模型考虑了基质的轻微压缩性以及胶原纤维与基质之间的剪切相互作用，以描述 HAF 的力学行为。此外，基于梯度平滑技术，开发了基于 3D 边和基于节点的选择性平滑有限元方法 (Selective 3D-ES/NS-FEM) 来缓解体积锁定并提高线性四节点四面体 (TET4) 单元的精度。结合修改后的本构模型，Selective 3D-ES/NS-FEM应用于大变形HAF的显式动力学分析。通过与文献中的实验数据和常规有限元法产生的数值结果进行比较，证明所提出的方法在预测 HAF 的非线性力学行为以及胶原纤维的取向变化方面具有出色的准确性和效率。此外，选择性 3D-ES/NS-FEM 被证明在处理元素失真方面具有强大的能力，即使使用最简单的 TET4 网格也是如此。