Design of Materials with Extreme Thermal Expansion Using a Three-Phase Topology Optimization Method,

Abstract

Composites with extremal or unusual thermal expansion coefficients are designed using a three-phase topology optimization method. The composites are made of two different material phases and a void phase. The topology optimization method finds the distribution of material phases optimizing an objective function (e.g., thermoelasticity) subject to certain constraints, such as elastic symmetry or volume fractions of the constituent phases, within a periodic base cell. The effective properties of the material are found using numerical homogenization based on finite element discretization of the base cell. To benchmark the design method we first consider two-phase designs. Our optimal two-phase microstructures agree well with rigorous bounds and so-called Vigdergauz microstructures that realize the bounds. For three phases, the optimal microstructures are compared with new rigorous bounds and again it is shown that the method yields designed materials with thermoelastic properties close to the bounds. The three-phase design method is illustrated by designing materials having maximum directional thermal expansion (thermal actuators), zero isotropic thermal expansion (thermal actuators), zero isotropic thermal expansion, and negative isotropic thermal expansion. It is shown that materials with effective negative thermal expansion coefficients can be obtained by mixing two phases with positive thermal expansion coefficients and void.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1996
Accession Number
ADA321073

Entities

People

  • Ole Sigmund
  • Salvatore Torquato

Organizations

  • Princeton University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Climate Change
  • Composite Materials
  • Directional
  • Elastic Properties
  • Equations
  • Finite Element Analysis
  • Geometry
  • Linear Programming
  • Materials
  • Mathematical Programming
  • Mathematics
  • Mechanics
  • Optimization
  • Topology
  • Topology Optimization

Fields of Study

  • Materials science

Readers

  • Calculus or Mathematical Analysis
  • Nanocomposite Materials Science
  • Nuclear Civil Defense.