notesum.ai

Published at December 3

Design of thermal meta-structures made of functionally graded materials using isogeometric density-based topology optimization

cs.CE

Released Date: December 3, 2024

Authors: Chintan Jansari, Stéphane P. A. Bordas, Marco Montemurro¹, Elena Atroshchenko²

Aff.: ¹Université de Bordeaux; ²University of New South Wales

Arxiv: http://arxiv.org/pdf/2412.02318v1

Refer to caption

Model name	Effective thermal conductivity ( $\kappa_{\rm eff}$ )	$v$ - range	$\kappa_{\rm eff}$ - range (in W/mK)
Micromechanics models ( $\kappa_{m}$ is thermal conductivity of a matrix material, $\kappa_{i}$ is thermal conductivity of a filler; here, $\kappa_{m}=\kappa_{\rm copper}=398$ W/mK and $\kappa_{i}=\kappa_{\rm PDMS}=0.27$ W/mK)
Effective Medium Theory (EMT) [79]	$\kappa_{\rm eff}=\dfrac{1}{4}\left(\tau+\sqrt{\tau^{2}+8\kappa_{i}\kappa_{m}}\right)$ with $\tau=(3v-1)\kappa_{i}+\left(3(1-v)-1\right)\kappa_{m}$	[0, 1]	[0.27, 398]
Maxwell [79]	$\kappa_{\rm eff}=\kappa_{m}\dfrac{2\kappa_{m}+\kappa_{p}-2v(\kappa_{m}-\kappa_% {p})}{2\kappa_{m}+\kappa_{p}+v(\kappa_{m}-\kappa_{p})}$	[0, 1]	[0.27, 398]
Empirical models based on experimental data ( $\kappa_{m}=\kappa_{\rm copper}=398$ W/mK)
Lotus type porous copper [83]	$\kappa_{\rm eff}=\kappa_{m}\dfrac{1-v}{1+v}$	[0, 0.7]	[70.24, 398]
Cu-Sn-Pb composite [84]	$\kappa_{\rm eff}=\kappa_{m}\left(ae^{bv}+ce^{dv}\right))$ $a=9.34008\times 10^{-1}$ , $b=-2.81400\times 10^{1}$ , $c=7.08923\times 10^{-2}$ , $d=1.14783\times 10^{-3}$	[0, 0.3]	[28.31, 399.95]
Empirical models based on numerical homogenization of graded lattice structure (of copper), ( $\kappa_{m}=\kappa_{\rm copper}=398$ W/mK)
Truncated CubOctaHedron (TCOH) [53]	$\kappa_{\rm eff}=\kappa_{m}\sum\limits_{i=1}^{7}C_{i}v^{i}$ , $C_{1}=0.4231$ , $C_{2}=0.1236$ , $C_{3}=0.0933$ , $C_{4}=0.0902$ , $C_{5}=0.0899$ , $C_{6}=0.0899$ , $C_{7}=0.0899$	[0.2, 0.8]	[36.01, 228.52]
Gyroid [53]	$\kappa_{\rm eff}=\kappa_{m}\sum\limits_{i=1}^{7}C_{i}v^{i}$ , $C_{1}=0.5934$ , $C_{2}=0.1119$ , $C_{3}=0.0631$ , $C_{4}=0.0583$ , $C_{5}=0.0578$ , $C_{6}=0.0577$ , $C_{7}=0.0577$	[0.2, 0.9]	[7.13, 397.96]