Three-phase model for a composite material with cylindrical circular inclusions. II: Application of Padé approximants. (English) Zbl 1423.74047
Summary: The solution of the Three-phase composite model (coinciding with the Maxwell Garnett formula) is transformed using the Padé approximants. The obtained Padé approximants fundamentally expand the applicability limits of the Maxwell Garnett solution. The explicit analytical formulae for the effective coefficient of thermal conductivity of the composite materials with periodic cylindrical inclusions of a circular cross-section are derived. The developed Padé approximants provide the accurate quantitative results as well as a qualitative picture of the asymptotic behavior for the effective coefficient of thermal conductivity for composites with inclusion of any conductivity, including the limiting cases of non-conducting and absolutely conducting inclusions; and with inclusions of small and large sizes, including very large, close to the limiting sizes.
For part I, see [A. L. Kalamkarov et al., Int. J. Eng. Sci. 78, 154–177 (2014; Zbl 1423.74046)].
For part I, see [A. L. Kalamkarov et al., Int. J. Eng. Sci. 78, 154–177 (2014; Zbl 1423.74046)].
MSC:
| 74A40 | Random materials and composite materials |
| 74E30 | Composite and mixture properties |
| 74Q15 | Effective constitutive equations in solid mechanics |
| 35B27 | Homogenization in context of PDEs; PDEs in media with periodic structure |
| 35Q74 | PDEs in connection with mechanics of deformable solids |
| 74F05 | Thermal effects in solid mechanics |
Keywords:
composite with cylindrical circular inclusions; effective coefficient of thermal conductivity; three-phase composite model; Padé approximants; Maxwell Garnett FormulaCitations:
Zbl 1423.74046References:
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