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
References
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.
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).
N. N. Afanas’ev, Statistical Theory of Fatigue Strength of Metals [in Russian], Izd. AN USSR, Kyiv (1953).
Ya. S. Berezikovich, Approximate Calculations [in Russian], GITTL, Moscow–Leningrad (1949).
A. A. Vakulenko and L. M. Kachanov, “Continuum theory of cracked medium,” Izv. AN SSSR, Mekh. Tverd. Tela, No. 4, 159–166 (1971).
G. A. Vanin, Micromechanics of Composite Materials [in Russian], Naukova Dumka, Kyiv (1985).
S. D. Volkov, Statistical Theory of Strength [in Russian], Gos. Nauch.-Tekhn. Izd. Mashinostroit. Lit., Sverdlovsk–Moscow (1960).
V. P. Golub, “Nonlinear damage mechanics and its applications,” in: Crack Resistance of Materials and Structural Members [in Russian], Kyiv (1980), pp. 19–20.
V. P. Golub, “Nonlinear models of damage accumulation under creep,” Probl. Mashinostr. Avtomatiz., No. 1, 51–58 (1992).
V. P. Golub, “Constitutive equations in nonlinear damage mechanics,” Int. Appl. Mech., 29, No. 10, 794–804 (1993).
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).
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).
N. N. Davidenkov, Fatigue of Metals [in Russian], Izd. AN USSR, Kyiv (1947).
V. H. Kauderer, Nonlinear Mechanics [in German], Springer-Verlag, Berlin (1958).
L. M. Kachanov, Fundamentals of Fracture Mechanics [in Russian], Nauka, Moscow (1974).
J. A. Collins, Failure of Materials in Mechanical Design: Analysis, Prediction, Prevention, 2nd ed., Wiley-Interscience, New York (1993).
V. P. Kogaev, “Fatigue resistance associated with stress concentration and full sizes,” in: Some Problems of Fatigue Strength [in Russian], Mashgiz, Moscow (1955).
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.
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).
T. A. Kontorova and Ya. I. Frenkel’, “Statistical brittle fracture theory for real crystals,” Zh. Tekhn. Fiz., 11, No. 3, 173 (1941).
I. M. Kop’yev and A. S. Ovchinskii, Failure of Fiber-Reinforced Metals [in Russian], Nauka, Moscow (1977).
A. F. Kregers, “Mathematical modeling of the thermal expansion of spatially reinforced composites,” Mech. Comp. Mater., 24, No. 3, 316–325 (1988).
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.
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).
E. S. Pereverzev, Damage Accumulation Models in Endurance Problems [in Russian], Naukova Dumka, Kyiv (1995).
Yu. M. Rabotnov, Creep of Structural Members [in Russian], Nauka, Moscow (1966).
A. R. Rzhanitsyn, Theory of Structural Reliability Design [in Russian], Stroiizdat, Moscow (1978).
R. D. Salganik, “Mechanics of bodies with a great number of cracks,” Izv. AN SSSR, Mekh. Tverd. Tela, No. 4, 149–158 (1973).
L. G. Sedrakyan, Statistical Strength Theory Revisited [in Russian], Izd. Arm. Inst. Stroimater. Sooruzh., Yerevan (1958).
S. V. Serensen, Fatigue of Metals [in Russian], Izd. VNIITMASH, Moscow (1949).
N. K. Snitko, “On structural theory of strength of metals,” Zh. Tekhn. Fiz., 18, No. 6, 857 (1948).
V. P. Tamuzs, “Calculation of elasticity parameters of a material with defects,” Mech. Comp. Mater., 13, No. 5, 702–707 (1977).
V. P. Tamuzs and V. S. Kuksenko, Microfracture Mechanics of Polymer Materials [in Russian], Zinatne, Riga (1978).
Ya. B. Fridman, Unified Theory of Metal Strength [in Russian], Oborongiz, Moscow (1952).
L. P. Khoroshun, “Saturated porous media,” Int. Appl. Mech., 12, No. 12, 1231–1237 (1976).
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).
L. P. Khoroshun, “Conditional-moment method in problems of the mechanics of composite materials,” Int. Appl. Mech., 23, No. 10, 989–996 (1987).
L. P. Khoroshun, “Fundamentals of thermomechanics of porous saturated media,” Int. Appl. Mech., 24, No. 4, 315–325 (1988).
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).
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.
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).
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.
L. P. Khoroshun and E. N. Shikula, “Nonlinear deformational properties of dispersely strengthened materials,” Mech. Comp. Mater., 38, No. 4, 311–320 (2002).
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).
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.
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.
B. B. Chechulin, “Statistical brittle fracture theory revisited,” Zh. Tekhn. Fiz., 24, No. 2, 31–37 (1954).
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).
T. D. Shermergor, Theory of Elasticity of Microinhomogeneous Media [in Russian], Nauka, Moscow (1977).
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).
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).
S. Basle and A. Audoin, “On internal variables in anisotropic damage,” Eur. J. Mech. A/Solids, 10, No. 6, 587–606 (1991).
S. Chandrakanth and P. C. Pandey, “An isotropic damage model for ductile material,” Eng. Fract. Mater., 50, No. 4, 457–465 (1995).
A. N. Guz, “On one two-level model in the mesomechanics of cracked composites,” Int. Appl. Mech., 39, No. 3, 274–285 (2003).
L. P. Khoroshun, “Principles of the micromechanics of material damage. 1. Short-term damage,” Int. Appl. Mech., 34, No. 10, 1035–1041 (1998).
L. P. Khoroshun, “Micromechanics of short-term thermal microdamageability,” Int. Appl. Mech., 37, No. 9, 1158–1165 (2001).
L. P. Khoroshun, “Principles of the micromechanics of material damage. 1. Short-term Damage,” Int. Appl. Mech., 34, No. 10, 1035–1041 (1998).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
L. P. Khoroshun and E. N. Shikula, “Deformation of physically nonlinear stochastic composites,” Int. Appl. Mech., 44, No. 12, 1325–1351 (2008).
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).
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).
W. A. Weibull, “A statistical theory of the strength of materials,” Proc. Roy. Swed. Inst. Eng. Res., No. 151, 5–45 (1939).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Mekhanika, Vol. 45, No. 6, pp. 42–70, June 2009.
Rights 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
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-009-0217-4