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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.

MSC:
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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