Thermal conductivity and Young's modulus of cubic-cell metamaterials
Source abstract
Abstract
Abstract It is shown that the popular quasi-laminate solutions for the relative (thermal) conductivity of cellular materials with cubic cells (closed or open) are in conflict with the upper Hashin-Shtrikman bound and thus inadmissible. However, numerical modeling can be used to estimate the porosity dependence of conductivity and leads to results that are below the upper Hashin-Shtrikman bound, as required for cubic and isotropic materials. The numerical results predict differences of up to 0.073 relative property units (RPU) between closed- and open-cell materials. For porosities approaching 100%, i.e. infinitely thin walls, both the analytical and the numerical solution for closed cubic cells approach the upper Hashin-Shtrikman bound. Moreover, the porosity dependence of the relative conductivity for closed cubic cells is very close to the upper Hashin-Shtrikman bound in the whole range of porosities and is correlated to the relative Young modulus via a cross-property relation based on the Hashin-Shtrikman bounds.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Composite Material Mechanics · Thermal properties of materials · Numerical methods in engineering
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (65)
Show source-provided references
1. Gibson · 1997 · 175
2. Processing, microstructure, properties, applications and curvature-based classification schemes of porous ceramics
3. Principles of heat flow in porous insulators10.1111/j.1151-2916.1935.tb19340.x ↗
4. Method of calculation of thermal conduction coefficient of capillary porous material
5. A basic study of heat transfer through foam insulation10.1177/0021955X8402000203 ↗
6. Bare · 1988 · 77
7. The thermal conductivity of foams I – models for heat conduction10.1088/0022-3727/26/5/003 ↗
8. Heat conduction and porosity correction for diverse two-phase systems10.1088/0022-3727/28/8/005 ↗
9. Heat conduction and a porosity correction term for spherical and cubic particels in a simple cubic packing10.1088/0022-3727/31/14/011 ↗
10. Prediction of effective thermal conductivity of cellular ceramics10.1016/S0735-1933(98)00002-5 ↗
11. Thermal conductivity of coal ash and slags and models used10.1016/S0016-2361(00)00033-8 ↗
12. An experimental study on the thermal conductivity of aluminium foams by using the transient plane source method10.1016/j.ijheatmasstransfer.2007.11.062 ↗
13. Prediction of elastic constants of multiphase materials
14. The deformation of foamed elastic10.5254/1.3539591 ↗
15. The effect of the elastic modulus of the aggregate on the elastic modulus, creep and creep recovery of concrete10.1680/macr.1964.16.48.129 ↗
16. Discussion of The effect of the elastic modulus of the aggregate on the elastic modulus, creep and creep recovery of concrete by Counto10.1680/macr.1965.17.52.142 ↗
17. Elastic properties of filled and porous epoxy composites10.1016/0020-7403(67)90053-7 ↗
18. Mechanical behavior of lightweight ceramics
19. Elastic properties of two-phase composites10.1111/j.1151-2916.1994.tb05390.x ↗
20. Analytic approximations for the elastic moduli of two-phase materials
21. On the absence of Eshelby's property for non-ellipsoidal inclusions10.1016/S0020-7683(98)00025-0 ↗
22. Maxwell · 1873 · 435
23. The effective permeability of mixtrures of solids10.1016/S0031-8914(46)80066-1 ↗
24. The elastic constants of materials loaded with non-rigid fillers10.1063/1.1697691 ↗
25. Elastic constants of a solid containing spherical holes10.1088/0370-1301/63/1/302 ↗
26. The determination of the elastic field of an ellipsoidal inclusion, and related problems10.1098/rspa.1957.0133 ↗
27. The effect of inclusion shape on the elastic moduli of a two-phase material10.1016/0020-7683(66)90002-3 ↗
28. Torquato · 2002 · 403
29. Conductivity of porous materials with spheroidal pores10.1016/j.jeurceramsoc.2013.12.040 ↗
30. Young's modulus of isotropic porous materials with spheroidal pores10.1016/j.jeurceramsoc.2014.04.009 ↗
31. Young's modulus and thermal conductivity of model materials with convex or concave pores – from analytical predictions to numerical results10.1016/j.jeurceramsoc.2018.01.040 ↗
32. Young's modulus and thermal conductivity of closed-cell, open-cell and inverse ceramic foams – model-based predictions, cross-property predictions and numerical calculations10.1016/j.jeurceramsoc.2018.01.019 ↗
33. Modeling of Young's modulus and thermal conductivity evolution of partially sintered alumina ceramics with pore changes from concave to convex10.1016/j.jeurceramsoc.2017.12.033 ↗
34. Relative Young's modulus and thermal conductivity of isotropic porous ceramics with randomly oriented spheroidal pores – model-based relations, cross-property predictions and numerical calculations10.1016/j.jeurceramsoc.2018.04.051 ↗
35. Shear and bulk moduli of isotropic porous and cellular alumina ceramics predicted from thermal conductivity via cross-property relations10.1016/j.ceramint.2018.01.254 ↗
36. A cross-property relation between the tensile modulus and the thermal conductivity of porous materials10.1016/j.ceramint.2005.07.009 ↗
37. A generalized cross-property relation between the elastic moduli and conductivity of isotropic porous materials with spheroidal pores
38. Correlation between elastic and electric properties for metal foams – theory and experiment10.1023/A:1022674130262 ↗
39. Elastic and electric properties of closed-cell aluminum foams – cross-property connection10.1016/j.msea.2006.01.064 ↗
40. Die Theorie des Mischkörpers für das Feld der stationären Strömung
41. Critical assessment 18: elastic and thermal properties of porous materials – rigorous bounds and cross-property relations10.1080/02670836.2015.1114697 ↗
42. Über die Beziehung zwischen den beiden Elastizitätskonstanten isotroper Körper10.1002/andp.18892741206 ↗
43. Minimum solid area models for the effective properties of porous materials – a refutation
44. A variational approach to the theory of the effective magnetic permeability of multiphase materials10.1063/1.1728579 ↗
45. Effective properties of suspensions, composites and porous materials10.1016/j.jeurceramsoc.2006.04.169 ↗
46. Nye · 1985 · 20
47. A variational approach to the theory of the elastic behavior of multiphase materials10.1016/0022-5096(63)90060-7 ↗
48. Milton · 2002 · 113
49. Micromechanics of heterogeneous media
50. The sigmoidal average – a powerful tool for predicting the thermal conductivity of composite ceramics10.1088/1742-6596/395/1/012021 ↗
51. On the effective moduli of isotropic two-phase elastic composites10.1177/002199837400800108 ↗
52. A study of the differential scheme for composite materials10.1016/0020-7225(77)90058-1 ↗
53. A differential scheme for the effective moduli of composites10.1016/0167-6636(85)90002-X ↗
54. A generalized cross-property relation between the elastic moduli and conductivity of isotropic porous materials with spheroidal pores
55. Liquid intrusion and alternative methods for the characaterization of macroporous materials (IUPAC Technical report)10.1351/PAC-REP-10-11-19 ↗
56. Microstructure characterization of mullite foam by image analysis, mercury porosimetry and X-ray computed microtomography10.1016/j.ceramint.2018.04.019 ↗
57. Microstructure characterization via stereological relations – a shortcut for beginners10.1016/j.matchar.2015.04.013 ↗
58. A generalized class of transformation matrices for the reconstruction of sphere size distributions from section circle size distributions10.13168/cs.2017.0010 ↗
59. Wave propagation in a stratified medium10.1190/1.1438187 ↗
60. The explicit-jump immersed interface method: finite difference methods for PDEs with piecewise smooth solutions10.1137/S0036142997328664 ↗
61. Wiegmann · 2006
62. Digital rock physics benchmarks – part II: computing effective properties10.1016/j.cageo.2012.09.008 ↗
63. Computational homogenization of elasticity on a staggered grid10.1002/nme.5008 ↗
64. Effective elastic properties of alumina-zirconia composite ceramics − part III: calculation of elastic moduli for polycrystalline alumina and zirconia from monocrystal data
65. Effective thermal and thermoelastic moduli of alumina, zirconia and alumina-zirconia composite ceramics