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Nonlinear Elastic Problems

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Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 77))

Abstract

We begin with a multi-layer composite material, composed of interacting components \({{\varOmega }^{(1)}}\) and \({{\varOmega }^{(2)}}\) (Fig. 8.1).

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References

  1. Bakhvalov, N., and G. Panasenko. 1989. Averaging Processes in Periodic Media. Mathematical Problems in Mechanics of Composite Materials. Kluwer: Dordrecht.

    Google Scholar 

  2. Zaitsev, V.Yu., V.E. Nazarov, and V.I. Talanov. 2006. “Nonclassical” manifestations of microstructure-induced nonlinearities: new prospects for acoustic diagnostics. Physics-Uspekhi 49: 89–94.

    Google Scholar 

  3. Achenbach, J.D., and H. Zhu. 1990. Effect of interphases on micro and macromechanical behavior of hexagonal-array fiber composites. Journal of Applied Mechanics 57: 956–963.

    Article  Google Scholar 

  4. Benveniste, Y., and T. Miloh. 2001. Imperfect soft and stiff interfaces in two-dimensional elasticity. Mechanics of Materials 33: 309–324.

    Article  Google Scholar 

  5. Hashin, Z. 2001. Thin interphase/imperfect interface in conduction. Journal of Applied Physics 89: 2261–2267.

    Article  Google Scholar 

  6. Hashin, Z. 2002. Thin interphase/imperfect interface in elasticity with application to coated fiber composites. Journal of the Mechanics and Physics of Solids 50: 2509–2537.

    Article  MATH  MathSciNet  Google Scholar 

  7. Lenci, S. 1999. Bonded joints with nonhomogeneous adhesives. Journal of Elasticity 53: 23–35.

    Article  MATH  MathSciNet  Google Scholar 

  8. Nie, S., and C. Basaran. 2005. A micromechanical model for effective elastic properties of particulate composites with imperfect interfacial bonds. International Journal of Solids and Structures 42: 4179–4191.

    Article  MATH  Google Scholar 

  9. Needleman, A. 1990. An analysis of tensile decohesion along an interface. Journal of the Mechanics and Physics of Solids 38: 289–324.

    Article  Google Scholar 

  10. Needleman, A. 1992. Micromechanical modelling of interfacial decohesion. Ultramicroscopy 40: 203–214.

    Article  MathSciNet  Google Scholar 

  11. Tvergaard, V. 1990. Effect of fibre debonding in a whisker-reinforced metal. Materials Science and Engineering A 125: 203–213.

    Article  Google Scholar 

  12. Tvergaard, V. 1995. Fiber debonding and breakage in a whisker reinforced metal. Materials Science and Engineering A 90: 215–222.

    Article  Google Scholar 

  13. Espinosa, H.D., S.K. Dwivedi, and H.-C. Lu. 2000. Modelling impact induced delamination of woven fibre reinforced composites with contact/cohesive laws. Computer Methods in Applied Mechanics and Engineering 183: 259–290.

    Article  MATH  Google Scholar 

  14. Espinosa, H.D., P.D. Zavattieri, and S.K. Dwivedi. 1998. A finite deformation continuum/discrete model for the description of fragmentation and damage in brittle materials. Journal of the Mechanics and Physics of Solids 46: 1909–1942.

    Article  MATH  MathSciNet  Google Scholar 

  15. Espinosa, H.D., P.D. Zavattieri, and G.L. Emore. 1998. Adaptive FEM computation of geometric and material nonlinearities with application to brittle failure. Mechanics of Materials 29: 275–305.

    Article  Google Scholar 

  16. Levy, A.J. 1996. The effective dilatational response of fiber reinforced composites with nonlinear interface. Journal of Applied Mechanics 63: 357–364.

    Article  MATH  Google Scholar 

  17. Levy, A.J. 2000. The fiber composite with nonlinear interface. Part I: Axial tension. Journal of Applied Mechanics 67: 727–732.

    Article  MATH  Google Scholar 

  18. Tan, H., C. Liu, Y. Huang, and P.H. Geubelle. 2005. The cohesive law for the particle/matrix interfaces in high explosives. Journal of the Mechanics and Physics of Solids 53: 1892–1917.

    Article  Google Scholar 

  19. Perrins, W.T., D.R. McKenzie, and R.C. McPhedran. 1979. Transport properties of regular arrays of cylinders. Proceedings of the Royal Society of London A 369: 207–225.

    Article  MathSciNet  Google Scholar 

  20. Ponte Castaneda, P. 2002a. Second order homogenization estimates for nonlinear composites incorporating field fluctuation. I—Theory. Journal of Mechanics and Physics of Solids 50: 737–757.

    Google Scholar 

  21. Ponte Castaneda, P., and P. Suquet. 1998. Nonlinear composites. Advances in Applied Mechanics 34: 171–302.

    Article  MATH  Google Scholar 

  22. Adams, D.F. 1974. Elastoplastic crack propagation in a transversely loaded unidirectional composite. Journal of Composite Materials 8: 38–54.

    Article  Google Scholar 

  23. Adams, D.F. 1970. Inelastic analysis of unidirectional composite subjected to transverse normal loading. Journal of Composite Materials 4: 310–328.

    Article  Google Scholar 

  24. Allred, R.E., and W.R. Hoover. 1974. Elastic-plastic Poisson’s ratio of borsic-aluminium. Journal of Composite Materials 8: 15–28.

    Article  Google Scholar 

  25. Melbardis, Y.G, and A.F. Kregers. 1982. Deformability of a unidirectionally reinforced composite with an elastic-plastic matrix. Mechanics of Composite Materials 18 (2): 144–151.

    Google Scholar 

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Correspondence to Igor V. Andrianov , Jan Awrejcewicz or Vladyslav V. Danishevskyy .

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Andrianov, I.V., Awrejcewicz, J., Danishevskyy, V.V. (2018). Nonlinear Elastic Problems. In: Asymptotical Mechanics of Composites. Advanced Structured Materials, vol 77. Springer, Cham. https://doi.org/10.1007/978-3-319-65786-8_8

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  • DOI: https://doi.org/10.1007/978-3-319-65786-8_8

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