A Total Lagrangian Finite Element Framework for Multibody Dynamics: Part I -- Formulation
This work provides a unified computational framework for simulating multibody dynamics with finite deformations, which is important for engineers and researchers in fields like robotics, biomechanics, and structural mechanics.
The paper presents a Total Lagrangian finite element framework for finite-deformation multibody dynamics that combines a compact kinematic representation, deformation-gradient-based formulation, element-agnostic constitutive interface, and systematic constraint construction for coupling deformable bodies through engineering joints. The framework supports various material models and external loads, with a companion paper covering GPU-accelerated implementation and benchmarks.
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.