This work presents a Total Lagrangian finite element formulation for deformable body dynamics. We employ the TL-FEA framework to simulate the time evolution of collections of bodies whose motion is constrained by kinematic constraints and which mutually interact through contact and friction. These bodies experience large displacements, large deformations, and large rotations. A systematic approach is proposed for classifying and posing kinematic constraints acting between the bodies present in the system. We derive the governing equations for ANCF beam, ANCF shell, and tetrahedral elements, and present hyperelastic material models including St. Venant-Kirchhoff and Mooney-Rivlin formulations with their corresponding internal force contributions and consistent tangent stiffness matrices. A finite-strain Kelvin-Voigt viscous damping model is incorporated in the TL-FEA formulation for numerical stability.

翻译：本文提出了一种适用于可变形体动力学的全拉格朗日有限元公式。我们采用TL-FEA框架来模拟物体集合的时间演化，这些物体的运动受运动学约束限制，并通过接触与摩擦相互交互作用。这些物体会经历大位移、大变形与大转动。本文提出了一种系统化方法，用于对系统中物体间作用的运动学约束进行分类与表述。我们推导了ANCF梁单元、ANCF壳单元及四面体单元的控制方程，并介绍了超弹性材料模型，包括St. Venant-Kirchhoff模型和Mooney-Rivlin模型及其相应的内力贡献与一致切线刚度矩阵。为提升数值稳定性，在TL-FEA公式中引入了有限应变Kelvin-Voigt粘性阻尼模型。