Structural zoom for linear composite materials based on adaptive mesh and homogenization

Abstract

In this work, an efficient method to investigate linear elastic fields around defects in heterogeneous structures is proposed. The technique combines the ideas of structural zoom methods, where a fine mesh is used in the vicinity of a defect, and where a coarse mesh is employed in regions far from the defect, in which a simplified model can be applied. When heterogeneous materials are involved, the coupling between the fine and coarse domains can be delicate. In this study, a fine mesh is used in a domain surrounding a defect (hole, crack, etc.) and describing explicitly the embedded heterogeneities. An adaptive mesh is used in the rest of the domain, liking the fine mesh of the zoomed region and the boundary if the structure. To take into account heterogeneities which can possibly cut the boundary of the fine mesh, non-constant homogenized properties are defined in the elements of the adaptive mesh taking into account the local underlying microstructure. As a result, solution in the fine mesh can handle effects of non-separated scales (strain gradients, boundary effects), even if large contrasts are involved. In addition to its use for studying localized defects, the potential of the technique to analyze fields in the whole structure through parallel computing is also investigated. In this case, a multi-domain version of the technique is provided, where the localization process is repeated for a decomposition of the heterogeneous structure.