Nonlinear analysis of three-dimensional hyperelastic problems using radial point interpolation method

Hoai Linh  Le Nguyen; Vay Siu Lo; Thien Tich Truong; Nha Thanh Nguyen

doi:10.15625/2525-2518/19248

Author affiliations

Authors

Hoai Linh Le Nguyen Department of Engineering Mechanics, Faculty of Applied Science, University of Technology (HCMUT), 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City 700000, Viet Nam
Vay Siu Lo Department of Engineering Mechanics, Faculty of Applied Science, University of Technology (HCMUT), 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City 700000, Viet Nam
Thien Tich Truong Department of Engineering Mechanics, Faculty of Applied Science, University of Technology (HCMUT), 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City 700000, Viet Nam
Nha Thanh Nguyen Department of Engineering Mechanics, Faculty of Applied Science, University of Technology (HCMUT), 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City 700000, Viet Nam https://orcid.org/0000-0001-9733-5189

DOI:

https://doi.org/10.15625/2525-2518/19248

Keywords:

three-dimensional hyperelasticity, large deformation, RPIM, Meshless

Abstract

Hyperelastic materials are primarily common in real life as well as in industry applications, and studying this kind of material is still an active research area. Naturally, the characteristic of hyperelastic material will be expressed when it undergoes large deformation, so the geometrical nonlinear effect should be considered. To analyze the behavior of hyperelastic material, the Neo-Hookean model is imposed in this study because of its simplicity. The model shows the nonlinear behavior when the deformation becomes large due to the nonlinear displacement-strain relation. This constitutive relation also gives a good correlation with experimental data. This study performs a meshless method, namely the radial point interpolation method (RPIM), to analyze the nonlinear behavior of Neo-Hookean hyperelastic material under a finite deformation state in three-dimensional space. The standard Newton-Raphson technique is applied to obtain the nonlinear solutions. Unlike mesh-based approaches, the meshless method shows its advantages in large deformation problems due to its mesh independence. In this paper, the numerical results of three-dimensional problems that undergo large deformation will be calculated and validated with solutions derived from previous studies. By investigating the obtained results, the superior ability of RPIM in hyperelastic problems can be proved.

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