Research Papers: Design Automation

Polytope Sector-Based Synthesis and Analysis of Microstructural Architectures With Tunable Thermal Conductivity and Expansion

[+] Author and Article Information
Jonathan B. Hopkins

Mechanical and Aerospace Engineering,
University of California, Los Angeles,
Los Angeles, CA 90095
e-mail: hopkins@seas.ucla.edu

Yuanping Song

Mechanical and Aerospace Engineering,
University of California, Los Angeles,
Los Angeles, CA 90095
e-mail: adamsong@ucla.edu

Howon Lee

Mechanical and Aerospace Engineering,
Rutgers, The State University of New Jersey,
Piscataway, NJ 08854
e-mail: howon.lee@rutgers.edu

Nicholas X. Fang

Mechanical Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: nicfang@mit.edu

Christopher M. Spadaccini

Materials Engineering Division,
Lawrence Livermore National Laboratory,
Livermore, CA 94550
e-mail: spadaccini2@llnl.gov

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 17, 2015; final manuscript received January 26, 2016; published online March 11, 2016. Assoc. Editor: James K. Guest.The United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States government purposes.

J. Mech. Des 138(5), 051401 (Mar 11, 2016) (10 pages) Paper No: MD-15-1227; doi: 10.1115/1.4032809 History: Received March 17, 2015; Revised January 26, 2016

The aim of this paper is to (1) introduce an approach, called polytope sector-based synthesis (PSS), for synthesizing 2D or 3D microstructural architectures that exhibit a desired bulk-property directionality (e.g., isotropic, cubic, orthotropic, etc.), and (2) provide general analytical methods that can be used to rapidly optimize the geometric parameters of these architectures such that they achieve a desired combination of bulk thermal conductivity and thermal expansion properties. Although the methods introduced can be applied to general beam-based microstructural architectures, we demonstrate their utility in the context of an architecture that can be tuned to achieve a large range of extreme thermal expansion coefficients—positive, zero, and negative. The material-property-combination region that can be achieved by this architecture is determined within an Ashby-material-property plot of thermal expansion versus thermal conductivity using the analytical methods introduced. These methods are verified using finite-element analysis (FEA) and both 2D and 3D versions of the design have been fabricated using projection microstereolithography.

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Fig. 1

A 2D microstructural architecture example that achieves tunable thermal expansion (a) and the same architecture shown deformed when subject to an increase in temperature (b)

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Fig. 2

Thermal expansion versus thermal conductivity Ashby chart

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Fig. 3

Square unit cell with triangular sectors (a); cubic (b), orthotropic (c), and fully anisotropic (d) planes of symmetry; triangular unit cell with triangular sectors (e) and its lattice (f); the triangular cell possesses isotropic planes of symmetry (g); hexagonal unit cell with triangular sectors (h) and its lattice (i); the hexagonal cell possesses isotropic planes of symmetry (j); and irregular triangle sectors can be used within unit cells (k) to make lattices (l) with extreme thermal expansion properties

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Fig. 4

A 3D lattice consisting of cube-shaped unit cells made of symmetric pyramidal sectors (a); its unit cells possess cubic planes of symmetry (b); a 3D lattice consisting of rhombic-dodecahedron-shaped unit cells also possesses cubic properties (c); and randomly shaped polytopes could produce isotropic bulk properties (d)

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Fig. 7

Single column within the lattice of Fig. 6(c) (a); tip temperature calculated iteratively (b); and temperature profiles in element (66) (c), element (71) (d), and element (78) (e)

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Fig. 6

Unit cell parameters (a), numbered elements and bodies (b), and lattice parameters (c)

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Fig. 5

2D (a) and 3D (b) microstructural architecture designs fabricated using projection microstereolithography

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Fig. 8

Thermal conductivity versus scale factor (a), convection coefficient (b), out-of-plane thickness (c), number of cell columns (d), and number of cell rows (e); unless otherwise specified, these plots were generated for a lattice with the parameters specified in Table 1 and with a scale factor = 1, N = 4, M = 3, and hc = 14 W/m2 C

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Fig. 9

Positive (a) and negative (b) thermal expansion versus thermal conductivity

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Fig. 10

Unit cell design parameters (a) and FEA verification (b)



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