Advertisement

Nonlinear Elastic Problems

  • Igor V. AndrianovEmail author
  • Jan AwrejcewiczEmail author
  • Vladyslav V. DanishevskyyEmail author
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 77)

Abstract

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

References

  1. 1.
    Bakhvalov, N., and G. Panasenko. 1989. Averaging Processes in Periodic Media. Mathematical Problems in Mechanics of Composite Materials. Kluwer: Dordrecht.Google Scholar
  2. 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. 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.CrossRefGoogle Scholar
  4. 4.
    Benveniste, Y., and T. Miloh. 2001. Imperfect soft and stiff interfaces in two-dimensional elasticity. Mechanics of Materials 33: 309–324.CrossRefGoogle Scholar
  5. 5.
    Hashin, Z. 2001. Thin interphase/imperfect interface in conduction. Journal of Applied Physics 89: 2261–2267.CrossRefGoogle Scholar
  6. 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.CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Lenci, S. 1999. Bonded joints with nonhomogeneous adhesives. Journal of Elasticity 53: 23–35.CrossRefzbMATHMathSciNetGoogle Scholar
  8. 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.CrossRefzbMATHGoogle Scholar
  9. 9.
    Needleman, A. 1990. An analysis of tensile decohesion along an interface. Journal of the Mechanics and Physics of Solids 38: 289–324.CrossRefGoogle Scholar
  10. 10.
    Needleman, A. 1992. Micromechanical modelling of interfacial decohesion. Ultramicroscopy 40: 203–214.CrossRefMathSciNetGoogle Scholar
  11. 11.
    Tvergaard, V. 1990. Effect of fibre debonding in a whisker-reinforced metal. Materials Science and Engineering A 125: 203–213.CrossRefGoogle Scholar
  12. 12.
    Tvergaard, V. 1995. Fiber debonding and breakage in a whisker reinforced metal. Materials Science and Engineering A 90: 215–222.CrossRefGoogle Scholar
  13. 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.CrossRefzbMATHGoogle Scholar
  14. 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.CrossRefzbMATHMathSciNetGoogle Scholar
  15. 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.CrossRefGoogle Scholar
  16. 16.
    Levy, A.J. 1996. The effective dilatational response of fiber reinforced composites with nonlinear interface. Journal of Applied Mechanics 63: 357–364.CrossRefzbMATHGoogle Scholar
  17. 17.
    Levy, A.J. 2000. The fiber composite with nonlinear interface. Part I: Axial tension. Journal of Applied Mechanics 67: 727–732.CrossRefzbMATHGoogle Scholar
  18. 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.CrossRefGoogle Scholar
  19. 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.CrossRefMathSciNetGoogle Scholar
  20. 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. 21.
    Ponte Castaneda, P., and P. Suquet. 1998. Nonlinear composites. Advances in Applied Mechanics 34: 171–302.CrossRefzbMATHGoogle Scholar
  22. 22.
    Adams, D.F. 1974. Elastoplastic crack propagation in a transversely loaded unidirectional composite. Journal of Composite Materials 8: 38–54.CrossRefGoogle Scholar
  23. 23.
    Adams, D.F. 1970. Inelastic analysis of unidirectional composite subjected to transverse normal loading. Journal of Composite Materials 4: 310–328.CrossRefGoogle Scholar
  24. 24.
    Allred, R.E., and W.R. Hoover. 1974. Elastic-plastic Poisson’s ratio of borsic-aluminium. Journal of Composite Materials 8: 15–28.CrossRefGoogle Scholar
  25. 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

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Institut für Allgemeine MechanikRWTH Aachen UniversityAachenGermany
  2. 2.Automation, Biomechanics and MechatronicsLodz University of TechnologyŁódźPoland
  3. 3.School of Computing and MathematicsKeele UniversityKeeleUK

Personalised recommendations