The studies on the theory of deformation and short- and long-term damage of physically nonlinear homogeneous and composite materials are systematized. In the case of short-term damage, a single microdamage is modeled by an empty quasispherical pore occurring in place of a microvolume damaged by the Huber–Mises criterion. The ultimate microstrength is assumed to be a random function of coordinates. In the case of long-term damage, the damage criterion for a single microvolume is characterized by its stress-rupture strength determined by the dependence of the time to brittle fracture on the difference between the equivalent stress and its limit, which is the ultimate strength. The equation of porosity balance at an arbitrary time and the equations relating macrostresses and macrostrains constitute a closed system. Algorithms of calculating microdamage and macrostresses as functions of time and macrostrains are developed. The effect of nonlinearity on the curves is studied
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References
L. A. Alekseev and A. A. Svetashkov, “Revisiting the theory of deformation of filled elastomers with 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 the 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 medium with cracks,” 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 Strength Theory, Gordon & Breach, New York (1962).
V. P. Golub, “Nonlinear mechanics of damage and its applications,” in: Crack Resistance of Materials and Structural Members [in Russian], Naukova Dumka, Kyiv (1980), pp. 19–20.
V. P. Golub, “Creep damage accumulation: Nonlinear models,” 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 Composite Materials 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], À.S.Ê., 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. Collings, Failure of Materials in Mechanical Design: Analysis, Prediction, Prevention, Wiley & Sons, New York (1981).
V. P. Kogaev, “Fatigue resistance depending on stress concentration and absolute dimensions,” in: Some Issues of Fatigue Strength [in Russian], Mashgiz, Moscow (1955).
V. I. Kondaurov, “Modeling the processes of damage accumulation and dynamic failure in solids,” in: Studying the Properties of Substances in Extreme Conditions [in Russian], IVTAN, Ìoscow (1990), pp. 145–152.
T. A. Kontorova and O. A. Timoshenko, “Statistical theory of strength generalized to inhomogeneous stress state,” Zh. Tekhn. Fiz., 19, No. 3, 119–121 (1949).
T. A. Kontorova and Ya. I. Frenkel’, “Statistical theory of the brittle strength of real crystals,” Zh. Tekhn. Fiz., 11, No. 3, 173–183 (1941).
I. M. Kop’ev and A. S. Ovchinskii, Fracture 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, “Damage accumulation in composite materials: An entropy model,” in: Abstracts 3rd All-Union Conf. on Mechanics of Inhomogeneous Structures [in Russian], Pt. 2, Lviv, September 17–19 (1991), p. 198.
S. A. Lurie, I. I. Krivolutskaya, and A. R. Vvedenskii, “Accumulation of dispersed damages in composite materials: A micromechanical entropy model,” Tekhn. Ser. Konstr. Komp. Mater., No. 1, 5–12 (1995).
E. S. Pereverzev, Damage Accumulation Models in Durability Problems [in Russian], Naukova Dumka, Kyiv (1995).
Y. N. Rabotnov, Creep Problems in Structural Members, North-Holland, Amsterdam (1969).
A. R. Rzhanitsin, Theory of Structural Reliability Design [in Russian], Stroiizdat, Moscow (1978).
R. D. Salganik, “Mechanics of bodies with many cracks,” Izv. AN SSSR, Mekh. Tverd. Tela, No. 4, 149–158 (1973).
L. G. Sedrakyan, Statistical Strength Theory [in Russian], Izd. Arm. Inst. Stroimater. Sooruzh., Yerevan (1958).
S. V. Serensen, Fatigue of Metals [in Russian], VNIITMASh, Moscow (1949).
N. K. Snitko, “Structural theory of the strength of metals,” Zh. Tekhn. Fiz., 18, No. 6, 857–864 (1948).
V. P. Tamuzs, “Calculating the constants of a damaged material,” Mekh. Polim., No. 5, 838–845 (1977).
V. P. Tamusz and V. S. Kuksenko, Microfracture Mechanics of Polymeric Materials [in Russian], Zinatne, Riga (1978).
Ya. B. Fridman, Unified Theory of the Strength of Metals [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: Abstracts Int. Conf. on Dynamical System 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 loading,” in: Abstracts Int. Conf. on Dynamical System Modeling and Stability Investigation, Kyiv, May 22–29 (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 microdamage in physically nonlinear materials,” in: Abstracts Int. Conf. on Dynamical System Modeling and Stability Investigation, Kyiv, May 27–30 (2003), p. 370.
L. P. Khoroshun and E. N. Shikula, “Structural theory of the short-term microdamage of physically nonlinear composites,” in: Abstracts Int. Conf. on Dynamical System Modeling and Stability Investigation, Kyiv, May 23–25 (2005), p. 346.
B. B. Chechulin, “Statistical brittle strength theory revisited,” Zh. Tekhn. Fiz., 24, No. 2, 45–48 (1954).
E. M. Shevadin, I. A. Razov, R. E. Reshetnikova, and B. N. Serpenikov, “Nature of the scale effect in fracture of metals,” DAN SSSR, 113, No. 5, 1057–1060 (1957).
T. D. Shermergor, Theory of Elasticity of Microinhomogeneous Media [in Russian], Nauka, Moscow (1977).
E. N. Shikula, “Influence of the strength distribution in the components 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 in its components,” Dop. NAN Ukrainy, No. 5, 70–74 (1998).
S. Baste and B. Audoin, “On internal variables in anisotropic damage,” Eur. I. Mech., A, 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. 2. Long-term damage,” Int. Appl. Mech., 43, No. 2, 127–135 (2007).
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 microdamage of fibrous composite materials 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, “A theory of short-term microdamage for a homogeneous material under physically nonlinear deformation,” Int. Appl. Mech., 40, No. 4, 338–395 (2004).
L. P. Khoroshun and E. N. Shikula, “Short-term microdamageability of a 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 a 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 a 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, “Microdamage of a nonlinear elastic material in combined stress state,” Int. Appl. Mech., 42, No. 11, 1223–1230 (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 and long-term damage of particulate composites with stress-rupture microstrength described by a fractional-power function,” Int. Appl. Mech., 44, No. 10, 1075–1083 (2008).
L. P. Khoroshun and E. N. Shikula, “Micromechanics of long-term damage of particulate composites with unlimited microdurability,” Int. Appl. Mech., 44, No. 11, 1202–1212 (2008).
L. P. Khoroshun and E. N. Shikula, “Deformation of physically nonlinear stochastic composites,” Int. Appl. Mech., 44, No. 12, 1325–1351 (2008).
L. P. Khoroshun and E. N. Shikula, “Deformation and short-term damage of physically nonlinear stochastic composites,” Int. Appl. Mech., 45, No. 6, 613–634 (2009).
L. P. Khoroshun and E. N. Shikula, “Deformation and long-term damage of layered materials with stress-rupture microstrength described by an exponential power function,” Int. Appl. Mech., 45, No. 8, 873–881 (2009).
L. P. Khoroshun and E. N. Shikula, “Coupled deformation and long-term damage of layered materials with stress-rupture microstrength described by a fractional-power function,” Int. Appl. Mech., 45, No. 9, 991–999 (2009).
L. P. Khoroshun and E. N. Shikula, “Deformation and long-term damage of fibrous materials with the stress-rupture microstrength of the matrix described by a fractional-power function,” Int. Appl. Mech., 45, No. 11, 1196–1205 (2009).
L. P. Khoroshun and E. N. Shikula, “Coupled processes of deformation and long-term damage of fibrous materials with the microdurability of the matrix described by an exponential power function,” Int. Appl. Mech., 46, No. 1, 37–45 (2010).
L. P. Khoroshun and E. N. Shikula, “Influence of heating on the deformation and long-term damage of unreinforced materials,” Int. Appl. Mech., 46, No. 8, 857–863 (2010).
L. P. Khoroshun and E. N. Shikula, “Deformation and long-term damage of particulate composites under thermal loads,” Int. Appl. Mech., 46, No. 10, 1110–1118 (2010).
L. P. Khoroshun and E. N. Shikula, “Coupled processes of deformation and long-term damage of fibrous materials under thermal loading,” Int. Appl. Mech., 47, No. 1, 45–54 (2011).
L. P. Khoroshun and E. N. Shikula, “Coupled processes of deformation and long-term damage of layered materials under thermal loading,” Int. Appl. Mech., 47, No. 2, 169–176 (2011).
L. P. Khoroshun and E. N. Shikula, “Theory of long-term microdamage of physically nonlinear homogeneous materials,” Int. Appl. Mech., 47, No. 5, 535–544 (2011).
L. P. Khoroshun and E. N. Shikula, “Deformation and long-term damage of physically nonlinear particulate composites,” Int. Appl. Mech., 47, No. 6, 670–678 (2011).
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).
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Translated from Prikladnaya Mekhanika, Vol. 48, No. 4, pp. 3–66, July–August 2012.
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Khoroshun, L.P., Shikula, E.N. Deformation and damage of composite materials of stochastic structure: physically nonlinear problems (Review). Int Appl Mech 48, 359–413 (2012). https://doi.org/10.1007/s10778-012-0527-9
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DOI: https://doi.org/10.1007/s10778-012-0527-9