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

TL;DR

This work presents a Total Lagrangian finite element formulation for deformable body dynamics and derives the governing equations for ANCF beam, ANCF shell, and tetrahedral elements, and presents hyperelastic material models including St. Venant-Kirchhoff and Mooney-Rivlin formulations with their corresponding internal force contributions and consistent tangent stiffness matrices.

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.

Figures (4)

• Figure 1: Key element configurations.
• Figure 2: Visualization of a fully-parameterized 2-node ANCF beam element 3243.
• Figure 3: Visualization of a fully-parameterized 4-node ANCF shell element 3443.
• Figure 4: Visualization of a 10-node tetrahedron (T10) element.