On the simulation of image-based cellular materials in a meshless style

Abstract

A meshfree method on fixed grids is devised for simulation of Poisson's equation on 3D image-based cellular materials. The non-boundary fitted discretization of such jagged voxel models of complex geometries is accomplished through embedding the micro-CT scan image in a Cartesian grid of nodes. The computational nodes inside the solid voxels are found by a simple point-in-membership test. Using a set of modified singular functions around the voids, along with the library-rational-exponential basis functions (EBFs) satisfying the governing differential equation, an enriched spatial solution is locally constructed on a generic computational cloud/cell (GCC) of nodes containing the voids. Within each GCC, the boundary conditions are satisfied through a weighted least-squares approximation. Finally, by establishing point-wise compatibility between the solutions of the GCCs a well-conditioned small linear system of equations is resulted. The results are compared with those of the finite element method (FEM) using extremely fine meshes with an excessive number of nodes.