Skip to main content
Log in

Deformation and short-term damage of physically nonlinear stochastic composites

  • To the Beginning of the Third Millennium
  • Published:
International Applied Mechanics Aims and scope

The studies on the deformation and short-term damage of physically nonlinear homogeneous and composite materials are systemized. A single microdamage is modeled by an empty quasispherical pore in place of a microvolume damaged in accordance with the Huber–von Mises failure criterion. The ultimate microstrength is assumed to be a random function of coordinates. The porosity balance equation is derived. Together with the macrostress–macrostrain relationship, it constitutes a closed-form system of equations. The damage–macrostrain relationship and macrostress–macrostrain curves for homogeneous and composite materials are analyzed

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. L. A. Alekseev and A. A. Svetashkov, “To the theory of deformation of the filled elastomers, considering microstructural damages,” in: Solid Mechanics [in Russian], NII Prikl. Mat. Mekh., Tomsk (1990), pp. 10–20.

    Google Scholar 

  2. V. N. Aptukov and V. L. Belousov “A model of anisotropic damage for bodies. Communication 1. General relationships,” Strength of Materials, 26, No. 2, 110–115 (1994).

    Article  Google Scholar 

  3. N. N. Afanas’ev, Statistical Theory of Fatigue Strength of Metals [in Russian], Izd. AN USSR, Kyiv (1953).

    Google Scholar 

  4. Ya. S. Berezikovich, Approximate Calculations [in Russian], GITTL, Moscow–Leningrad (1949).

    Google Scholar 

  5. A. A. Vakulenko and L. M. Kachanov, “Continuum theory of cracked medium,” Izv. AN SSSR, Mekh. Tverd. Tela, No. 4, 159–166 (1971).

  6. G. A. Vanin, Micromechanics of Composite Materials [in Russian], Naukova Dumka, Kyiv (1985).

    Google Scholar 

  7. S. D. Volkov, Statistical Theory of Strength [in Russian], Gos. Nauch.-Tekhn. Izd. Mashinostroit. Lit., Sverdlovsk–Moscow (1960).

    Google Scholar 

  8. V. P. Golub, “Nonlinear damage mechanics and its applications,” in: Crack Resistance of Materials and Structural Members [in Russian], Kyiv (1980), pp. 19–20.

  9. V. P. Golub, “Nonlinear models of damage accumulation under creep,” Probl. Mashinostr. Avtomatiz., No. 1, 51–58 (1992).

  10. V. P. Golub, “Constitutive equations in nonlinear damage mechanics,” Int. Appl. Mech., 29, No. 10, 794–804 (1993).

    Article  MathSciNet  Google Scholar 

  11. A. N. Guz, L. P. Khoroshun, G. A. Vanin, et al., Materials Mechanics, Vol. 1 of the three-volume series Mechanics of Composites and Structural Members [in Russian], Naukova Dumka, Kyiv (1982).

    Google Scholar 

  12. A. N. Guz, L. P. Khoroshun, M. I. Mikhailova, D. V. Babich, and E. N. Shikula, Applied Research, Vol. 12 of the 12-volume series Mechanics of Composite Materials [in Russian], A.S.K., Kyiv (2003).

    Google Scholar 

  13. N. N. Davidenkov, Fatigue of Metals [in Russian], Izd. AN USSR, Kyiv (1947).

    Google Scholar 

  14. V. H. Kauderer, Nonlinear Mechanics [in German], Springer-Verlag, Berlin (1958).

    Google Scholar 

  15. L. M. Kachanov, Fundamentals of Fracture Mechanics [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  16. J. A. Collins, Failure of Materials in Mechanical Design: Analysis, Prediction, Prevention, 2nd ed., Wiley-Interscience, New York (1993).

    Google Scholar 

  17. V. P. Kogaev, “Fatigue resistance associated with stress concentration and full sizes,” in: Some Problems of Fatigue Strength [in Russian], Mashgiz, Moscow (1955).

    Google Scholar 

  18. V. I. Kondaurov, “Modeling damage accumulation and dynamic failure of solids,” in: Research of the Properties of Substances in Extreme Conditions [in Russian], Moscow (1990), pp. 145–152.

  19. T. A. Kontorova and O. A. Timoshenko, “Generalization of statistical strength theory to an inhomogeneous stress state,” Zh. Tekhn. Fiz., 19, No. 3, 5–31 (1949).

    Google Scholar 

  20. T. A. Kontorova and Ya. I. Frenkel’, “Statistical brittle fracture theory for real crystals,” Zh. Tekhn. Fiz., 11, No. 3, 173 (1941).

    Google Scholar 

  21. I. M. Kop’yev and A. S. Ovchinskii, Failure of Fiber-Reinforced Metals [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  22. A. F. Kregers, “Mathematical modeling of the thermal expansion of spatially reinforced composites,” Mech. Comp. Mater., 24, No. 3, 316–325 (1988).

    Article  Google Scholar 

  23. S. A. Lurie, “On one entropy model of damage accumulation in a composite,” in: Abstracts 3rd All-Union Conf. on Mechanics of Inhomogeneous Structures [in Russian] (Lvov, September 17–19, 1991), Pt. 2, Lvov (1991), p. 198.

  24. S. A. Lurie, I. M. Krivolutskaya, and A. R. Vedenskii, “On one micromechanical entropy model of dispersed damages accumulated in composite materials,” Tekhnologiya, Ser. Konstr. Komp. Mater., No. 1, 5–12 (1995).

  25. E. S. Pereverzev, Damage Accumulation Models in Endurance Problems [in Russian], Naukova Dumka, Kyiv (1995).

    Google Scholar 

  26. Yu. M. Rabotnov, Creep of Structural Members [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  27. A. R. Rzhanitsyn, Theory of Structural Reliability Design [in Russian], Stroiizdat, Moscow (1978).

    Google Scholar 

  28. R. D. Salganik, “Mechanics of bodies with a great number of cracks,” Izv. AN SSSR, Mekh. Tverd. Tela, No. 4, 149–158 (1973).

  29. L. G. Sedrakyan, Statistical Strength Theory Revisited [in Russian], Izd. Arm. Inst. Stroimater. Sooruzh., Yerevan (1958).

    Google Scholar 

  30. S. V. Serensen, Fatigue of Metals [in Russian], Izd. VNIITMASH, Moscow (1949).

    Google Scholar 

  31. N. K. Snitko, “On structural theory of strength of metals,” Zh. Tekhn. Fiz., 18, No. 6, 857 (1948).

    Google Scholar 

  32. V. P. Tamuzs, “Calculation of elasticity parameters of a material with defects,” Mech. Comp. Mater., 13, No. 5, 702–707 (1977).

    Google Scholar 

  33. V. P. Tamuzs and V. S. Kuksenko, Microfracture Mechanics of Polymer Materials [in Russian], Zinatne, Riga (1978).

    Google Scholar 

  34. Ya. B. Fridman, Unified Theory of Metal Strength [in Russian], Oborongiz, Moscow (1952).

    Google Scholar 

  35. L. P. Khoroshun, “Saturated porous media,” Int. Appl. Mech., 12, No. 12, 1231–1237 (1976).

    MATH  Google Scholar 

  36. L. P. Khoroshun, “Methods of theory of random functions in problems of macroscopic properties of microinhomogeneous media,” Int. Appl. Mech., 14, No. 2, 113–124 (1978).

    MathSciNet  MATH  Google Scholar 

  37. L. P. Khoroshun, “Conditional-moment method in problems of the mechanics of composite materials,” Int. Appl. Mech., 23, No. 10, 989–996 (1987).

    MATH  Google Scholar 

  38. L. P. Khoroshun, “Fundamentals of thermomechanics of porous saturated media,” Int. Appl. Mech., 24, No. 4, 315–325 (1988).

    MathSciNet  MATH  Google Scholar 

  39. L. P. Khoroshun, B. P. Maslov, E. N. Shikula, and L. V. Nazarenko, Statistical Mechanics and Effective Properties of Materials, Vol. 3 of the 12-volume series Mechanics of Composite Materials [in Russian], Naukova Dumka, Kyiv (1993).

    Google Scholar 

  40. L. P. Khoroshun and E. N. Shikula, “Deformation of particulate composites with microdamages,” in: Proc. Int. Conf. on Dynamic Systems: Modeling and Stability Investigation, Kyiv, May 25–29 (1999), p. 79.

  41. L. P. Khoroshun and E. N. Shikula, “Influence of temperature on the microdamage of a particulate material,” Visn. Kyiv. Univ., Ser. Fiz.-Mat. Nauky, No. 5, 382–387 (2001).

    Google Scholar 

  42. L. P. Khoroshun and E. N. Shikula, “Short-term microdamage of particulate composites under thermal loads,” in: Proc. Int. Conf. on Dynamic Systems: Modeling and Stability Investigation, Kyiv, May 22–25 (2001), p. 335.

  43. L. P. Khoroshun and E. N. Shikula, “Nonlinear deformational properties of dispersely strengthened materials,” Mech. Comp. Mater., 38, No. 4, 311–320 (2002).

    Article  Google Scholar 

  44. L. P. Khoroshun and E. N. Shikula, “Influence of temperature on the short-term microdamage of laminated materials,” Teor. Prikl. Mekh., No. 37, 50–58 (2003).

  45. L. P. Khoroshun and E. N. Shikula, “Coupled processes of deformation and microdamageability of physically nonlinear materials,” in: Proc. Int. Conf. on Dynamic Systems: Modeling and Stability Investigation, Kyiv, May 27–30 (2003), p. 370.

  46. L. P. Khoroshun and E. N. Shikula, “Structural theory of short-term microdamageability of physically nonlinear composites,” in: Proc. Int. Conf. on Dynamic Systems: Modeling and Stability Investigation, Kyiv May 23–25 (2005), p. 346.

  47. B. B. Chechulin, “Statistical brittle fracture theory revisited,” Zh. Tekhn. Fiz., 24, No. 2, 31–37 (1954).

    Google Scholar 

  48. E. M. Shevadin, I. A. Razov, R. E. Reshetnikova, and B. N. Serpenikov, “Nature of the scale effect in fracture of metals,” Dokl. AN SSSR, 113, No. 5, 1057 (1957).

    Google Scholar 

  49. T. D. Shermergor, Theory of Elasticity of Microinhomogeneous Media [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  50. E. N. Shikula, “Influence of the strength distribution law on the deformation of a particulate composite with microdamages,” Dop. NAN Ukrainy, No. 4, 88–93 (1998).

  51. E. N. Shikula, “Dependence of the elastic properties of a laminated composite on the strength distribution law in the components,” Dop. NAN Ukrainy, No. 5, 70–74 (1998).

  52. S. Basle and A. Audoin, “On internal variables in anisotropic damage,” Eur. J. Mech. A/Solids, 10, No. 6, 587–606 (1991).

    Google Scholar 

  53. S. Chandrakanth and P. C. Pandey, “An isotropic damage model for ductile material,” Eng. Fract. Mater., 50, No. 4, 457–465 (1995).

    Article  Google Scholar 

  54. A. N. Guz, “On one two-level model in the mesomechanics of cracked composites,” Int. Appl. Mech., 39, No. 3, 274–285 (2003).

    Article  Google Scholar 

  55. L. P. Khoroshun, “Principles of the micromechanics of material damage. 1. Short-term damage,” Int. Appl. Mech., 34, No. 10, 1035–1041 (1998).

    Article  Google Scholar 

  56. L. P. Khoroshun, “Micromechanics of short-term thermal microdamageability,” Int. Appl. Mech., 37, No. 9, 1158–1165 (2001).

    Article  Google Scholar 

  57. L. P. Khoroshun, “Principles of the micromechanics of material damage. 1. Short-term Damage,” Int. Appl. Mech., 34, No. 10, 1035–1041 (1998).

    Article  Google Scholar 

  58. L. P. Khoroshun and E. N. Shikula, “Effect of the strength scatter of the components on the deformation of a particulate composite with microcracks,” Int. Appl. Mech., 33, No. 8, 626–631 (1997).

    Article  Google Scholar 

  59. L. P. Khoroshun and E. N. Shikula, “Effect of the spread of the strength of the components on the deformation of a laminar composite with microfailures,” Int. Appl. Mech., 33, No. 9, 679–684 (1997).

    Article  Google Scholar 

  60. L. P. Khoroshun and E. N. Shikula, “Effect of the random character of the microscopic strength of the binder on the deformation of a fiber composite,” Int. Appl. Mech., 33, No. 10, 788–793 (1997).

    Article  Google Scholar 

  61. L. P. Khoroshun and E. N. Shikula, “Effect of the spread of strength characteristics of the binder on the deformation of laminar-fibrous materials,” Int. Appl. Mech., 34, No. 1, 39–45 (1998).

    Article  Google Scholar 

  62. L. P. Khoroshun and E. N. Shikula, “The theory of short-term microdamageability of granular composite materials,” Int. Appl. Mech., 36, No. 8, 1060–1066 (2000).

    Article  Google Scholar 

  63. L. P. Khoroshun and E. N. Shikula, “Simulation of the short-term microdamageability of laminated composites,” Int. Appl. Mech., 36, No. 9, 1181–1186 (2000).

    Article  Google Scholar 

  64. L. P. Khoroshun and E. N. Shikula, “Short-term microdamageability of fibrous composites with transversally isotropic fibers and a microdamaged binder,” Int. Appl. Mech., 36, No. 12, 1605–1611 (2000).

    Article  Google Scholar 

  65. L. P. Khoroshun and E. N. Shikula, “The micromechanics of short-term damageability of fibrolaminar composites,” Int. Appl. Mech., 36, No. 5, 638–646 (2001).

    Article  Google Scholar 

  66. L. P. Khoroshun and E. N. Shikula, “A note on the theory of short-term microdamageability of granular composites under thermal actions,” Int. Appl. Mech., 38, No. 1, 60–67 (2002).

    Article  MATH  Google Scholar 

  67. L. P. Khoroshun and E. N. Shikula, “Short-term microdamageability of laminated materials under thermal actions,” Int. Appl. Mech., 38, No. 4, 432–439 (2002).

    Article  Google Scholar 

  68. L. P. Khoroshun and E. N. Shikula, “Short-term microdamageability of fibrous materials with transversely isotropic fibers under thermal actions,” Int. Appl. Mech., 38, No. 6, 701–709 (2002).

    Article  Google Scholar 

  69. L. P. Khoroshun and E. N. Shikula, “Short-term damage micromechanics of laminated fibrous composites under thermal actions,” Int. Appl. Mech., 38, No. 9, 1083–1093 (2002).

    Article  Google Scholar 

  70. L. P. Khoroshun and E. N. Shikula, “Theory of short-term microdamage for a homogeneous material under physically nonlinear deformation,” Int. Appl. Mech., 40, No. 4, 388–395 (2004).

    Article  Google Scholar 

  71. L. P. Khoroshun and E. N. Shikula, “Short-term microdamageability of granular material under physically nonlinear deformation,” Int. Appl. Mech., 40, No. 6, 656–663 (2004).

    Article  Google Scholar 

  72. L. P. Khoroshun and E. N. Shikula, “Influence of physically nonlinear deformation on short-term microdamage of a laminar material,” Int. Appl. Mech., 40, No. 8, 878–885 (2004).

    Article  Google Scholar 

  73. L. P. Khoroshun and E. N. Shikula, “Influence of physically nonlinear deformation on short-term microdamage of a fibrous material,” Int. Appl. Mech., 40, No. 10, 1137–1144 (2004).

    Google Scholar 

  74. L. P. Khoroshun and E. N. Shikula, “Deformation of particulate composite with physically nonlinear inclusions and microdamageable matrix,” Int. Appl. Mech., 41, No. 2, 111–117 (2005).

    Article  Google Scholar 

  75. L. P. Khoroshun and E. N. Shikula, “Influence of the physical nonlinearity of the matrix on the deformation of a particulate composite with microdamageable inclusions,” Int. Appl. Mech., 41, No. 4, 345–351 (2005).

    Article  Google Scholar 

  76. L. P. Khoroshun and E. N. Shikula, “Deformation of a laminated composite with a physically nonlinear reinforcement and microdamageable matrix,” Int. Appl. Mech., 41, No. 11, 1246–1253 (2005).

    Article  Google Scholar 

  77. L. P. Khoroshun and E. N. Shikula, “Short-term microdamage of laminated material with nonlinear matrix and microdamaged reinforcement,” Int. Appl. Mech., 41, No. 12, 1331–1338 (2005).

    Article  Google Scholar 

  78. L. P. Khoroshun and E. N. Shikula, “Deformation of fibrous composite with physically nonlinear fibers and microdamageable matrix,” Int. Appl. Mech., 42, No. 1, 32–39 (2006).

    Article  Google Scholar 

  79. L. P. Khoroshun and E. N. Shikula, “Short-term microdamageability of a fibrous composite with physically nonlinear matrix and microdamaged reinforcement,” Int. Appl. Mech., 42, No. 2, 127–135 (2006).

    Article  Google Scholar 

  80. L. P. Khoroshun and E. N. Shikula, “Short-term microdamage of a physically nonlinear particular material under a combination of normal and tangential loads,” Int. Appl. Mech., 42, No. 12, 1356–1363 (2006).

    Article  Google Scholar 

  81. L. P. Khoroshun and E. N. Shikula, “Short-term microdamage of a physically nonlinear fibrous material under simultaneous normal and tangential loads,” Int. Appl. Mech., 43, No. 3, 282–290 (2007).

    Article  Google Scholar 

  82. L. P. Khoroshun and E. N. Shikula, “Short-term microdamage of a physically nonlinear laminate under simultaneous normal and tangential loads,” Int. Appl. Mech., 43, No. 4, 409–417 (2007).

    Article  Google Scholar 

  83. L. P. Khoroshun and E. N. Shikula, “Mesomechanics of deformation and short-term damage of linear elastic homogeneous and composite materials,” Int. Appl. Mech., 43, No. 6, 591–620 (2007).

    Article  Google Scholar 

  84. L. P. Khoroshun and E. N. Shikula, “Deformation of physically nonlinear stochastic composites,” Int. Appl. Mech., 44, No. 12, 1325–1351 (2008).

    Article  Google Scholar 

  85. E. N. Shikula, “Dependence of the deformational properties of a fiber composite on the binder strength distribution,” Int. Appl. Mech., 34, No. 2, 129–135 (1998).

    Google Scholar 

  86. E. N. Shikula, “Dependence of the strain properties of fibrous composite laminates on the fiber-strength distribution law,” Int. Appl. Mech., 34, No. 3, 250–256 (1998).

    Google Scholar 

  87. W. A. Weibull, “A statistical theory of the strength of materials,” Proc. Roy. Swed. Inst. Eng. Res., No. 151, 5–45 (1939).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to L. P. Khoroshun.

Additional information

Translated from Prikladnaya Mekhanika, Vol. 45, No. 6, pp. 42–70, June 2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khoroshun, L.P., Shikula, E.N. Deformation and short-term damage of physically nonlinear stochastic composites. Int Appl Mech 45, 613–634 (2009). https://doi.org/10.1007/s10778-009-0217-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-009-0217-4

Keywords

Navigation