abstract
- © 2022 Elsevier Inc. All rights reserved.An efficient numerical method for calculation of local fields and effective elastic properties of 3D-media containing inclusions and cracks is considered. For a finite heterogeneous region embedded in an infinite homogeneous host medium, the elasticity problem is reduced to the solution of volume (for stress fields) and surface (for crack openings) integral equations. For numerical solution, these equations are discretized using Gaussian approximating functions concentrated at the nodes of a regular grid covering the region. For such functions, the elements of the matrix of the discretized problem are calculated in explicit analytical forms and numerical integration is excluded from the construction of the elements of these matrices. For the solution of the homogenization problem, a representative volume element (RVE) of heterogeneous media is introduced. The RVE is embedded in the homogeneous host medium and subjected to a constant external field. The influence of the heterogeneities outside of the RVE is taken into account by the self-consistent effective field method. For reliable calculation of the effective elastic stiffness tensors of particulate composites and cracked media, optimal shapes and sizes of the RVE are indicated. The results are compared to the other numerical methods available in the literature.