A Total Lagrangian Finite Element Framework for Multibody Dynamics: Part I -- Formulation

TL;DR

This paper introduces a comprehensive Total Lagrangian finite element framework for simulating multibody dynamics with deformable bodies, supporting complex material models and various constraints.

Contribution

It develops a unified formulation combining kinematic, constitutive, and constraint aspects for deformable multibody systems, enabling advanced simulations.

Findings

Framework effectively models finite-deformation multibody dynamics.

Supports diverse material models like Mooney-Rivlin and Neo-Hookean.

Facilitates coupling deformable bodies with engineering joints.

Abstract

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.