A moving Kriging meshfree approach for analyzing large deformation of a hyperelastic model
Author affiliations
DOI:
https://doi.org/10.15625/0866-7136/23957Keywords:
hyperelastic model, meshfree method, Moving Kriging interpolation, large deformationAbstract
This study introduces a meshfree Moving Kriging (MK) interpolation framework specifically designed to simulate the large deformation behavior of hyperelastic materials. In numerical analysis, the Moving Kriging (MK) interpolation method is a well-known meshfree approach developed based on the Element-Free Galerkin (EFG) method. Hyperelastic materials, characterized by complex and nonlinear constitutive relationships, represent a distinct class of elastic solids. These materials are typically analyzed within the framework of finite deformation theory due to their ability to undergo large strains. Therefore, understanding their nonlinear behavior under significant deformation is essential for accurate modeling and analysis. Compared to traditional mesh-based methods, meshfree approaches demonstrate notable advantages in handling large deformation problems. To evaluate the performance of the proposed framework, several deformation scenarios were tested, with validation carried out using a standard hyperelastic model -- the Neo-Hookean model -- through two benchmark problems: a rectangular plate and Cook's membrane. The material properties for these problems were obtained from the literature to ensure reliability. The accuracy of the numerical algorithm and the implemented program was verified by benchmarking the obtained results against reference solutions generated using MATLAB.
Downloads
References
Angoshtari, A., Shojaei, M. F., & Yavari, A. (2017). Compatible-strain mixed finite element methods for 2D compressible nonlinear elasticity. Computer Methods in Applied Mechanics and Engineering, 313, 596–631. https://doi.org/10.1016/j.cma.2016.09.047
Belytschko, T., Krongauz, Y., Organ, D., Fleming, M., & Krysl, P. (1996). Meshless Methods: An Overview and Recent Developments. Computer Methods in Applied Mechanics and Engineering, 139(1–4), 3–47. https://doi.org/10.1016/s0045-7825(96)01078-x
Bui, T. Q., Nguyen, M. N., & Zhang, C. (2011). A moving Kriging interpolation-based element-free Galerkin method for structural dynamic analysis. Computer Methods in Applied Mechanics and Engineering, 200(13–16), 1354–1366. https://doi.org/10.1016/j.cma.2010.12.017
Hassani, R., Ansari, R., & Rouhi, H. (2019). Large deformation analysis of 2D hyperelastic bodies based on the compressible nonlinear elasticity: A numerical variational method. International Journal of Non-Linear Mechanics, 116, 39–54. https://doi.org/10.1016/j.ijnonlinmec.2019.05.003
Khosrowpour, E., Hematiyan, M. R., & Hajhashemkhani, M. (2019). A strong-form meshfree method for stress analysis of hyperelastic materials. Engineering Analysis with Boundary Elements, 109, 32–42. https://doi.org/10.1016/j.enganabound.2019.09.013
Reese, S. (2002). On the Equivalent of Mixed Element Formulations and the Concept of Reduced Integration in Large Deformation Problems. International Journal of Nonlinear Sciences and Numerical Simulation, 3(1), 1–34. https://doi.org/10.1515/ijnsns.2002.3.1.1
Vu, T. V., Nguyen, T. N., Nguyen, M. N., Truong, T. T., & Bui, T. Q. (2021). A Meshfree Method Based on Integrated Radial Basis Functions for 2D Hyperelastic Bodies. In Lecture Notes in Mechanical Engineering (pp. 990–1003). Springer Singapore. https://doi.org/10.1007/978-981-16-3239-6_78
Zhang, Y., Ge, W., Zhang, Y., Zhao, Z., & Zhang, J. (2018). Topology Optimization of Hyperelastic Structure Based on a Directly Coupled Finite Element and Element-Free Galerkin Method. Advances in Engineering Software, 123, 25–37. https://doi.org/10.1016/j.advengsoft.2018.05.006
Downloads
Published
How to Cite
License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
