A computational homogenization analysis of materials using the stabilized mesh-free method based on the radial basis functions

  • Ho Le Huy Phuc Department of Civil Engineering, International University, VNU-HCMC, Quarter 6, Thu Duc district, Vietnam
  • Le Van Canh Department of Civil Engineering, International University, VNU-HCMC, Quarter 6, Thu Duc district, Vietnam
  • Phan Duc Hung Faculty of Civil Engineering, Ho Chi Minh City University of Technology and Education, No 1 Vo Van Ngan street, Thu Duc district, Ho Chi Minh city, Vietnam

Abstract

This study presents a novel application of mesh-free method using the smoothed-radial basis functions for the computational homogenization analysis of materials. The displacement field corresponding to the scattered nodes within the representative volume element (RVE) is split into two parts including mean term and fluctuation term, and then the fluctuation one is approximated using the integrated radial basis function (iRBF) method. Due to the use of the stabilized conforming nodal integration (SCNI) technique, the strain rate is smoothed at discrete nodes; therefore, all constrains in resulting problems are enforced at nodes directly. Taking advantage of the shape function which satisfies Kronecker-delta property, the periodic boundary conditions well-known as the most appropriate procedure for RVE are similarly imposed as in the finite element method. Several numerical examples are investigated to observe the computational aspect of iRBF procedure. The good agreement of the results in comparison with those reported in other studies demonstrates the accuracy and reliability of proposed approach.

Keywords:

homogenization analysis; mesh-free method; radial point interpolation method; SCNI scheme.

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Published
22-01-2020
How to Cite
Phuc, H. L. H., L. V. Canh, and P. D. Hung. “A Computational Homogenization Analysis of Materials Using the Stabilized Mesh-Free Method Based on the Radial Basis Functions”. Journal of Science and Technology in Civil Engineering (STCE) - NUCE, Vol. 14, no. 1, Jan. 2020, pp. 65-76, doi:10.31814/stce.nuce2020-14(1)-06.
Section
Research Papers