research-article

Multiscale shape–material modeling by composition

Authors:

Vadim ShapiroAuthors Info & Claims

Volume 102, Issue C

Pages 194 - 203

https://doi.org/10.1016/j.cad.2018.04.024

Published: 01 September 2018 Publication History

Abstract

We propose a formal framework for modeling multiscale material structures by recursive composition of two-scale material structures. The framework comprises three components: (1) single scale shape–material models, supported by single scale queries, to represent the geometry and spatial distribution of material property on each coarse and fine scales, (2) mechanisms to link the scales by establishing an explicit relationship between shape–material properties at fine scale and material properties at the coarse scale, and (3) multiscale queries abstracting fundamental multiscale operations by recursive composition. While the first component is consistent with classical solid heterogeneous material modeling, the second component manifests itself as a pair of conceptually new upscaling and downscaling functions. We show that classical solid modeling queries, exemplified by point membership testing, distance computation, and material evaluation, generalize to the corresponding multiscale queries that support implicit representations of multiscale structures as a composition of distinct single scale solid material models. The concept of neighborhood is indispensable in all three components. The framework provides a formal and consistent extension of solid modeling framework that underlies most commercial systems in use today, encompasses the variety of different approaches to multiscale modeling, identifies open issues and research problems with existing two-scale modeling methods, and provides foundations for next-generation systems by identifying key objects, classes, representation schemes, and API queries.

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Sitharam MYoungquist JNolan MPeters J(2022)Corner-sharing tetrahedra for modeling micro-structureComputer-Aided Design10.1016/j.cad.2019.05.015114:C(164-178)Online publication date: 20-Apr-2022
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Published In

cover image Computer-Aided Design

Computer-Aided Design Volume 102, Issue C

Sep 2018

225 pages

ISSN:0010-4485

Issue’s Table of Contents

Elsevier Ltd.

Publisher

Butterworth-Heinemann

United States

Publication History

Published: 01 September 2018

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Cited By

Kurzeja KRossignac J(2022)CTSPComputer-Aided Design10.1016/j.cad.2022.103212146:COnline publication date: 1-May-2022
https://dl.acm.org/doi/10.1016/j.cad.2022.103212
Hasanabadi A(2022)Two-scale microstructure construction by statistical correlation functionsComputer-Aided Design10.1016/j.cad.2021.103116142:COnline publication date: 1-Jan-2022
https://dl.acm.org/doi/10.1016/j.cad.2021.103116
Sitharam MYoungquist JNolan MPeters J(2022)Corner-sharing tetrahedra for modeling micro-structureComputer-Aided Design10.1016/j.cad.2019.05.015114:C(164-178)Online publication date: 20-Apr-2022
https://dl.acm.org/doi/10.1016/j.cad.2019.05.015
Liu XMeneghin MShapiro V(2021)An application programming interface for multiscale shape-material modelingAdvances in Engineering Software10.1016/j.advengsoft.2021.103046161:COnline publication date: 1-Nov-2021
https://dl.acm.org/doi/10.1016/j.advengsoft.2021.103046
Kurzeja KRossignac J(2019)RangeFinderComputer-Aided Design10.1016/j.cad.2019.03.002112:C(14-22)Online publication date: 1-Jul-2019
https://dl.acm.org/doi/10.1016/j.cad.2019.03.002

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