Asymptotic models of dilute composites with imperfectly bonded inclusions

International Journal of Solids and Structures

Volumn 35, Issue 24, 1998, Pages 3239-3258

  Bigoni, D ^a   Serkov, S K ^b   Valentini, M ^a   Movchan, A B ^b  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b UNIVERSITY OF BATH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BONDING; CRACKS; DEFECTS; ELASTIC MODULI; INCLUSIONS; LOADS (FORCES); MATHEMATICAL MODELS; STIFFNESS;

CIRCULAR DEFECT; CIRCULAR INCLUSION; DILUTE ELASTIC COMPOSITES; INTERFACIAL STIFFNESS;

COMPOSITE MATERIALS;

COMPOSITES; MATHEMATICAL MODELS;

EID: 0032143639     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7683(97)00366-1     Document Type: Article

References (32)

1. Aboudi, J. (1991) Mechanics of Composite Materials. ELsevier, Amsterdam.
2. Acerbi, E. and Buttazzo, G. (1996a) Reinforcement problems in the calculus of variations. Ann. Inst. Henri Poincaré, Analyse non Lineairé 3, 273-284.
3. Acerbi, E. and Buttazzo, G. (1996b) Limit problems for plates surrounded by soft material. Arch. Rational Mech. Anal. 92, 355-370.
4. Achenbach, J. D. and Zhu, H. (1989) Effect of interfacial zone on mechanical behaviour and failure of fiber-reinforced composites. Journal of the Mechanics and Physics of Solids 37, 381-393.
5. Bigoni, D., Ortiz, M. and Needleman, A. (1997) Effect of interfacial compliance on bifurcation of a layer bonded to a substrate, International Journal of Solids and Structures 34, 4305-4326.
6. Eshelby, J. D. (1957) The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proceedings of the Royal Society of London A 241, 376-396.
7. Gao, Z. (1995) A circular inclusion with imperfect interface: Eshelby's tensor and related problems. Journal of Applied Mechanics 62, 860-866.
8. Geymonat, G. and Krasucki, F. (1996) A limit model of a soft, thin joint. In Partial Differential Equations and Applications, ed. P. Marcellini, G. Talenti and E. Vesentini, pp. 165-173. Marcel Dekker, New York.
9. Goland, M. and Reissner, E. (1944) The stresses in cemented joints. Journal of Applied Mechanics A17-A27.
10. Gong, S. X. and Meguid, S. A. (1993) On the elastic fields of an elliptical inhomogeneity under plane deformation. Proceedings of the Royal Society of London A 443, 457-471.
11. Hashin, Z. and Shtrikman, S. (1963) A variational approach to the theory of the elastic behaviour of multiphase materials. Journal of the Mechanics and Physics of Solids 11, 127-140.
12. Hashin, Z. (1990) Thermoelastic properties of fiber composites with imperfect interface. Mechanics of Materials 8, 333-348.
13. Hashin, Z. (1991) Composite materials with viscoelastic interphase: creep and retaxation. Mechanics of Materials 11, 135-148.
14. Hashin, Z. (1992) Extremum-principles for elastic heterogeneous media with imperfect interfaces and their application to bounding of effective moduli. Journal of the Mechanics and Physics of Solids 40, 767-781.
15. Jones, J. P. and Whittier, J. S. (1967) Waves at a flexibly bonded interface. Journal of Applied Mechanics 34, 905-909.
16. Klarbring, A. (1991) Derivation of a model of adhesively bonded joints by the asymptotic expansion method. International Journal of Engineering Science 29, 493-512.
17. Levy, A. J. (1991) The debonding of elastic inclusions and inhomogeneities. Journal of the Mechanics and Physics of Solids 39, 477-505.
18. Lipton, R. (1997) Variational methods, bounds, and size effects for composites with highly conducting interface. Journal of the Mechanics and Physics of Solids 45, 361-384.
19. Lipton, R. and Vernescu, B. (1995) Variational methods, size effects and extremal microstructures for elastic composites with imperfect interface. Mathematical Models and Methods in Applied Sciences 5, 1139-1173.
20. Lurie, K. A. and Cherkaev, A. V. (1987) On G-closure. J. Optimization Th. Appl., 53, 319-327.
21. Mal, A. K. and Bose, S. K. (1974) Dynamic elastic moduli of a suspension of imperfectly bonded spheres. Proc. Camb. Phil. Soc. 76, 587-599.
22. Movchan, A. B. and Movchan, N. V. (1995) Mathematical Modelling of Solids with Non Regular Boundaries. CRC Press.
23. Movchan, A. B. and Serkov, S. K. (1997) The Pólya Szegö matrices in asymptotic models of dilute composites. Journal of Applied Mathematics, in press.
24. Muskhelishvili, N. I. (1953) Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff, Groningen.
25. Nemat-Nasser, S. and Hori, M. (1993) Micromechanics: Overall Properties of Heterogeneous Materials. North-Holland Series in Applied Mathematics and Mechanics, 37, North-Holland.
26. Pólya, G. and Szegö, G. (1951) Isoperimetric Inequalities in Mathematical Physics. Princeton.
27. Qu, J. (3993) The effect of slightly weakened interfaces on the overall elastic properties of composite materials. Mechanics of Materials 14, 269-281.
28. Sendeckyj, G. P. (1970) Elastic inclusion problems in plane elastostatics. International Journal of Solids and Structures 6, 1535-1543.
29. Suo, Z., Needleman, A. and Ortiz, M. (1992) Stability of solids with interfaces. Journal of the Mechanics and Physics of Solids 40, 613-640.
30. Tullini, N., Savoia, M. and Horgan, C. O. (1997) End effects in multilayered orthotropic strips with imperfect bonding. Mechanics of Materials 26, 23-34.
31. Valentini, M., Serkov, S. K., Bigoni, D. and Movchan, A. B. (1997) Crack propagation in a brittle elastic material with defects, submitted.
32. Yu, I. W. and Sendeckyj, G. P. (1974) Multiple circular inclusion problems in plane elasto-statics. Journal of Applied Mechanics, Transactions of ASME 41, 215-221.