A meshfree approach for homogenization of mechanical properties of heterogeneous materials

In this paper, asymptotic homogenization and meshfree Solution Structure Method (SSM) are combined to develop a hybrid homogenization technique. This hybrid method makes it possible to capture accurate geometric information of material microstructure, directly from micrographs or Computed Tomography (CT) scans, and offers a completely automated numerical procedure. Homogenization methods often employ FEA to incorporate realistic geometry of the material's microstructure. However, generating a finite element mesh from images or 3D voxel data could be tedious, error-prone, and expensive. Also, in many practical situations, considerable manual modifications are often required. On the other hand, the SSM uses implicit mathematical functions to represent the geometric model. It could be implemented using different types of basis functions, either on a non-conforming structural grid or cloud of points. Adaptive numerical and geometric algorithms assure good geometric flexibility of SSM in handling complex structures. Furthermore, to accommodate material homogenization equations, the SSM is extended so it can provide the exact satisfaction of periodic boundary conditions without using any spatial meshes. To validate the developed method, the architecture of a computer software package is designed that provides an automated computational pipeline for material homogenization. Numerical examples are provided to evaluate the developed platform against other methods and previously published data.