Large deformation analysis of a hyperplastic beam using experimental / FEM/ meshless collocation method

Abstract

In the present study, nonlinear numerical and experimental static bending analyses of hyperelastic beams are surveyed. Timoshenko's beam theory is used to obtain the Cauchy-Green deformation tensor. The governing equations are extracted using the neo-Hookean strain energy and Euler–Lagrange relation. Afterward, the nonlinear governing equations are solved numerically using the meshless collocation method (MCM). To validate the present investigation, a comparison study is accomplished between the acquired results from MCM and the experimental test of digital image correlation (DIC) and finite element method (FEM). The hyperelastic beam is made of natural rubber. Also, loading and boundary conditions are considered as concentrated force and clamped–clamped, respectively. In addition, the displacement contour is extracted by the DIC. The uniaxial tensile test based on the ASTM D412 standard is performed to extract the mechanical properties of natural rubber. The hyperelastic theory and neo-Hookean strain energy function are utilized to model the nonlinear behavior of rubber in the FEM. The error for the maximum displacement of system obtained from both numerical methods is less than 12% compared to the DIC. Additionally, it can be observed that in large deformations, unlike the FEM, MCM is able to predict the system's response with high accuracy.

KEYWORDS:

• Hyperelastic
• neo-hookean
• meshless collocation method
• finite element method
• experimental test
• DIC

Disclosure statement

No potential conflict of interest was reported by the author(s).

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.

Additional information

Funding

The authors did not receive support from any organization for the submitted work.