The Kinematics and Dynamics Theories of a Total Lagrangian Finite Element Analysis Framework for Finite Deformation Multibody Dynamics

2026-02-18

AI Summary

This study addresses the challenging problem of dynamic modeling of deformable multibody systems involving large displacements, deformations, and rotations, along with kinematic constraints, contact, and friction. To this end, a unified absolute nodal coordinate formulation (ANCF) is developed within a total Lagrangian finite element framework (TL-FEA). The approach systematically classifies and enforces kinematic constraints while consistently deriving governing equations for beam, shell, and tetrahedral elements. It integrates St. Venant–Kirchhoff and Mooney–Rivlin hyperelastic constitutive models together with a finite-strain Kelvin–Voigt damping model. By employing a consistent tangent stiffness matrix, the method significantly enhances simulation accuracy, numerical stability, and physical consistency, enabling high-fidelity dynamic simulations of complex multibody systems.

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Abstract

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.

Problem

• finite deformation
• multibody dynamics
• kinematic constraints
• contact and friction
• large rotations

Innovation

• Total Lagrangian FEA
• ANCF elements
• finite deformation dynamics
• hyperelastic material models
• kinematic constraints