Thermo-elastic properties of heterogeneous materials with imperfect interfaces: Generalized Levin's formula and Hill's connections

Journal of the Mechanics and Physics of Solids

Volumn 55, Issue 5, 2007, Pages 1036-1052

  Duan, H L ^a   Karihaloo, B L ^a  

^a CARDIFF UNIVERSITY   (United Kingdom)

Author keywords

Coefficient of thermal expansion; Generalized Hill's connections; Generalized Levin's formula; Interface stress model; Linear spring interface model

Indexed keywords

ELASTIC MODULI; INTERFACES (COMPUTER); LINEAR SYSTEMS; MATHEMATICAL MODELS; THERMAL EXPANSION;

GENERALIZED HILL'S CONNECTIONS; GENERALIZED LEVIN'S FORMULA; INTERFACE STRESS MODELS; LINEAR SPRING INTERFACE MODELS;

THERMOELASTICITY;

EID: 34047227518     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2006.10.006     Document Type: Article

References (33)

1. Benveniste Y. Thermal expansion of polycrystalline aggregates consisting of elongated crystals and containing cylindrical pores or inclusions. J. Mech. Phys. Solids 44 (1996) 137-153
2. Benveniste Y. A general interface model for a three-dimensional curved thin anisotropic interphase between two anisotropic media. J. Mech. Phys. Solids 54 (2006) 708-734
3. Benveniste Y., and Miloh T. Imperfect soft and stiff interfaces in two-dimensional elasticity. Mech. Mater. 33 (2001) 309-323
4. Chen T.Y., and Dvorak G.J. Fibrous nanocomposites with interface stress: Hill's and Levin's connections for effective moduli. Appl. Phys. Lett. 88 (2006) 211912
5. Chen, T.Y., Dvorak, G.J., Yu, C.C., 2006. Size-dependent elastic properties of unidirectional nano-composites with interface stresses. Acta Mech. in press, doi:10.007/s00707-006-0371-2.
6. Chen, T.Y., Dvorak, G.J., Yu, C.C., 2007. Solids containing spherical nano-inclusions with interface stresses: effective properties and thermal mechanical connections. Int. J. Solids Struct. 44, 941-955.
7. Cuenot S., Frétigny C., Demoustier-Champagne S., and Nysten B. Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy. Phys. Rev. B 69 (2004) 165410
8. Diao J.K., Gall K., and Dunn M.L. Atomistic simulation of the structure and elastic properties of gold nanowires. J. Mech. Phys. Solids 52 (2004) 1935-1962
9. Duan H.L., Wang J., Huang Z.P., and Karihaloo B.L. Eshelby formalism for nano-inhomogeneities. Proc. R. Soc. A 461 (2005) 3335-3353
10. Duan H.L., Wang J., Huang Z.P., and Karihaloo B.L. Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress. J. Mech. Phys. Solids 53 (2005) 1574-1596
11. Duan H.L., Wang J., Karihaloo B.L., and Huang Z.P. Nanoporous materials can be made stiffer than non-porous counterparts by surface modification. Acta Mater. 54 (2006) 2983-2990
12. Dvorak G.J. On uniform-fields in heterogeneous media. Proc. R. Soc. A 431 (1990) 89-110
13. Gibiansky L.V., and Torquato S. Thermal expansion of isotropic multiphase composites and polycrystals. J. Mech. Phys. Solids 45 (1997) 1223-1252
14. Gibiansky L.V., and Torquato S. New method to generate three-point bounds on effective properties of composites: application to viscoelasticity. J. Mech. Phys. Solids 46 (1998) 749-783
15. Gurtin M.E., and Murdoch A.I. A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal. 57 (1975) 291-323
16. Hashin Z. Thermal-expansion of polycrystalline aggregates. I. Exact analysis. J. Mech. Phys. Solids 32 (1984) 149-157
17. Hashin Z. Thermoelastic properties of fiber composites with imperfect interface. Mech. Mater. 8 (1990) 333-348
18. Hashin Z. Thermoelastic properties of particulate composites with imperfect interface. J. Mech. Phys. Solids 39 (1991) 745-762
19. Hashin Z. Thin interphase/imperfect interface in elasticity with application to coated fiber composites. J. Mech. Phys. Solids 50 (2002) 2509-2537
20. Hill R. Theory of mechanical properties of fibre-strengthened materials-I. Elastic behavior. J. Mech. Phys. Solids 12 (1964) 199-212
21. Jiang B., and Weng G.J. A generalized self-consistent polycrystal model for the yield strength of nanocrystalline materials. J. Mech. Phys. Solids 52 (2004) 1125-1149
22. Levin V.M. On the coefficients of thermal expansion of heterogeneous materials. Mech. Solids 2 (1967) 58-61
23. Miller R.E., and Shenoy V.B. Size-dependent elastic properties of nanosized structural elements. Nanotechnology 11 (2000) 139-147
24. Murdoch A.I. Thermodynamical theory of elastic-material interfaces. Q. J. Mech. Appl. Math. 29 (1976) 245-275
25. Murdoch A.I. Some fundamental aspects of surface modelling. J. Elasticity 80 (2005) 33-52
26. Pathak S., and Shenoy V.B. Size dependence of thermal expansion of nanostructures. Phys. Rev. B 72 (2005) 113404
27. Povstenko Y.Z. Theoretical investigation of phenomena caused by heterogeneous surface-tension in solids. J. Mech. Phys. Solids 41 (1993) 1499-1514
28. Sharma P., Ganti S., and Bhate N. Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities. Appl. Phys. Lett. 82 (2003) 535-537
29. Shenoy V.B. Atomistic calculations of elastic properties of metallic fcc crystal surfaces. Phys. Rev. B 71 (2005) 094104
30. Tan H., Liu C., Huang Y., and Geubelle P.H. The cohesive law for the particle/matrix interfaces in high explosives. J. Mech. Phys. Solids 53 (2005) 1892-1917
31. Wang J., Duan H.L., Zhang Z., and Huang Z.P. An anti-interpenetration model and connections between interphase and interface models in particle-reinforced composites. Int. J. Mech. Sci. 47 (2005) 701-708
32. Wang J., Duan H.L., Huang Z.P., and Karihaloo B.L. A scaling law for properties of nano-structured materials. Proc. R. Soc. A 462 (2006) 1355-1363
33. Yakobson B.I., and Smalley R.E. Fullerene nanotubes: C-1000000 and beyond. Am. Sci. 85 (1997) 324-337