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Title: Sample-based synthesis of two-scale structures with anisotropy

Abstract

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 anisotropy may greatly enhance the efficiency and performance of synthesized structures. In this paper, we propose a sample-based two-scale structure synthesis approach that explicitly controls anisotropic effective material properties of the structure on the coarse scale by orienting sampled material 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. Finally, the effectiveness of the proposed approach is demonstrated through examples in both 2D and 3D.

Authors:
ORCiD logo [1];  [1]
  1. Univ. of Wisconsin, Madison, WI (United States). Spatial Automation Lab.; International Computer Science Inst. (ICSI), Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE; National Science Foundation (NSF); National Inst. of Standards and Technology (NIST) (United States); Defense Advanced Research Projects Agency (DARPA) (United States)
OSTI Identifier:
1432971
Report Number(s):
LLNL-JRNL-731805
Journal ID: ISSN 0010-4485
Grant/Contract Number:
AC52-07NA27344; CMMI-1344205; CMMI-1361862; 70NANB14H232
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Computer Aided Design
Additional Journal Information:
Journal Volume: 90; Journal ID: ISSN 0010-4485
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 97 MATHEMATICS AND COMPUTING

Citation Formats

Liu, Xingchen, and Shapiro, Vadim. Sample-based synthesis of two-scale structures with anisotropy. United States: N. p., 2017. Web. doi:10.1016/j.cad.2017.05.013.
Liu, Xingchen, & Shapiro, Vadim. Sample-based synthesis of two-scale structures with anisotropy. United States. doi:10.1016/j.cad.2017.05.013.
Liu, Xingchen, and Shapiro, Vadim. Fri . "Sample-based synthesis of two-scale structures with anisotropy". United States. doi:10.1016/j.cad.2017.05.013. https://www.osti.gov/servlets/purl/1432971.
@article{osti_1432971,
title = {Sample-based synthesis of two-scale structures with anisotropy},
author = {Liu, Xingchen and Shapiro, Vadim},
abstractNote = {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 anisotropy may greatly enhance the efficiency and performance of synthesized structures. In this paper, we propose a sample-based two-scale structure synthesis approach that explicitly controls anisotropic effective material properties of the structure on the coarse scale by orienting sampled material 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. Finally, the effectiveness of the proposed approach is demonstrated through examples in both 2D and 3D.},
doi = {10.1016/j.cad.2017.05.013},
journal = {Computer Aided Design},
number = ,
volume = 90,
place = {United States},
year = {Fri May 19 00:00:00 EDT 2017},
month = {Fri May 19 00:00:00 EDT 2017}
}

Journal Article:
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