We present a Total Lagrangian finite element framework for finite-deformation multibody dynamics. The framework combines a compact kinematic representation, a deformation-gradient-based formulation, an element-agnostic constitutive interface, and a systematic constraint-construction machinery for coupling deformable bodies through engineering joints. Within this setting, we derive the equations of motion for collections of deformable bodies and formulate their response in the presence of external loads, frictional contact forces, and constraint reaction forces. The framework accommodates field forces applied pointwise, over surfaces, or throughout volumes, and supports material models of practical interest, including Mooney-Rivlin, Neo-Hookean, and Kelvin-Voigt. A companion paper discusses the GPU-accelerated implementation of the framework outlined herein and reports on numerical experiments and benchmark results.

翻译：我们提出了一种适用于有限变形多体动力学的全拉格朗日有限元框架。该框架融合了紧凑的运动学表示、基于变形梯度的公式化表述、与单元无关的材料本构建模接口，以及用于通过工程关节耦合可变形体的系统化约束构造机制。在此框架下，我们推导了可变形体集合的运动方程，并描述了其在外部载荷、摩擦接触力及约束反力作用下的响应。该框架支持点施加、表面施加或体积施加的场力作用，并涵盖了具有实际工程意义的材料模型，包括Mooney-Rivlin、Neo-Hookean和Kelvin-Voigt模型。配套论文将讨论本文所概述框架的GPU加速实现，并报告数值实验及基准测试结果。