Sample-based synthesis of two-scale structures with anisotropy

A vast majority of natural or synthetic materials are characterized by their anisotropic properties, such as stiffness. Such anisotropy is effected by the spatial distribution of the fine-scale structure and/or anisotropy of the constituent phases at a finer scale. In design, proper control of the anisotropymay greatly enhance the efficiency and performance of synthesized structures. We propose a sample-based two-scale structure synthesis approach that explicitly controls anisotropic effectivematerial properties of the structure on the coarse scale by orienting sampledmaterial neighborhoods at the fine scale. We first characterize the non-uniform orientations distribution of the sample structure by showing that the principal axes of an orthotropic material may be determined by the eigenvalue decomposition of its effective stiffness tensor. Such effective stiffness tensors can be efficiently estimated based on the two-point correlation functions of the fine-scale structures. Then we synthesize the two-scale structure by rotating fine-scale structures from the sample to follow a given target orientation field. The effectiveness of the proposed approach is demonstrated through examples in both 2D and 3D. © 2017 Elsevier Ltd. All rights reserved.