Two ANCF Hyperelastic Reduced Beam Elements Based on Neo-Hookean and Yeoh Models

Abstract

This paper develops two novel reduced beam elements of the absolute nodal coordinate formulation (ANCF) based on neo-Hookean and Yeoh hyperelastic models with generalized internal forces calculated via one-dimensional integration. The initial elements employ three-dimensional integration to compute generalized internal forces, which are the complex expressions of section coordinates y. To improve computational efficiency, the generalized internal forces are simplified using Taylor series expansion, enabling a transition from three-dimensional to one-dimensional integration. Comparative analysis reveals that all proposed elements achieve displacement predictions consistent with reference solutions of ANSYS or publicly available experimental data while delivering substantial computational advantages: the simplified formulation reduces calculation time to 16.7% of the initial ANCF element requirements, corresponding to a five-fold efficiency improvement. The inherent adaptability of beam elements to coarse meshes enables substantially higher computational efficiency compared to solid-element formulations in slender structure analysis. So, the simplified beam element proposed is nearly 100 times faster than the solid element used in ANSYS. A dynamic example comparing circular and rectangular cross-section beams further demonstrates the versatility of the proposed elements. This work provides a computationally efficient and accurate framework for modeling hyperelastic materials in soft robotics and other applications requiring large deformation analysis.