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Thermo-elastic properties of heterogeneous materials with imperfect interfaces: generalized Levin’s formula and Hill’s connections. (English) Zbl 1170.74017
Summary: We study thermo-elastic properties of heterogeneous materials containing spherical particles or cylindrical fibres. The interface between the matrix and second-phase inhomogeneity is imperfect with either the displacement or stress experiencing a jump across it. We relate the effective coefficient of thermal expansion (CTE) to effective elastic moduli, and thereby generalize Levin’s formula [V. M. Levin, Mech. Solids 2, 58–61 (1967)], and reveal two connections among the effective elastic moduli, thereby generalizing Hill’s connections [R. Hill, J. Mech. Phys. Solids 12, 199–212 (1964)]. In contrast to the classical results, the effective CTE in the presence of an imperfect interface is strongly dependent on the size of the inhomogeneity, besides the interface elastic and thermo-elastic properties. This size dependence has been accurately captured by simple scaling laws.

74F05 Thermal effects in solid mechanics
74Q15 Effective constitutive equations in solid mechanics
74E05 Inhomogeneity in solid mechanics
74E30 Composite and mixture properties
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