A phase-filed method for structural topology optimization with three material phases

Michael Yu Wang, Shiwei Zhou

Research output: Chapter in Book/Report/Conference proceedingConference PaperOther

2 Citations (Scopus)

Abstract

In this paper we present a phase-field method to the problem of shape and topology synthesis of structures with three materials. A single phase model is developed based on the classical phase-transition theory in the fields of mechanics and material sciences. The multi-material synthesis is formulated as a continuous optimization problem within a fixed reference domain. As a single parameter, the phase-field model represents regions made of any of the three distinct material phases and the interface between the regions. The Van der Waals-Cahn-Hilliard theory is applied to define a dynamic process of phase transition. The Γ-convergence theory is used for an approximate numerical solution to this free-discontinuity problem without any explicit tracking of the interface. Within this variational framework, we show that the phase-transition theory leads to a well-posed problem formulation with the effects of "domain regularization" and "region segmentation" incorporated naturally. The proposed phase-field method is illustrated with several 2D examples that have been extensively used in the recent literature of topology optimization, especially in the homogenization based methods. It is further suggested that such a phase-field approach may ‡ represent a promising alternative to the widely-used homogenization models for the design of heterogeneous materials and solids, with a possible extension to a general model of multiple material phases.

Original languageEnglish
Title of host publicationCollection of Technical Papers - 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference
PublisherAmerican Institute of Aeronautics and Astronautics
Pages2902-2922
Number of pages21
ISBN (Print)1563477165, 9781563477164
Publication statusPublished - 2004
Externally publishedYes
EventAIAA/ISSMO Multidisciplinary Analysis and Optimization Conference 2004 - Albany, United States of America
Duration: 30 Aug 20041 Sept 2004
Conference number: 10th
https://arc.aiaa.org/doi/book/10.2514/MMAOC04

Publication series

NameCollection of Technical Papers - 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference
Volume5

Conference

ConferenceAIAA/ISSMO Multidisciplinary Analysis and Optimization Conference 2004
Country/TerritoryUnited States of America
CityAlbany
Period30/08/041/09/04
Internet address

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