A theory of long-term damage of physically nonlinear homogeneous materials is proposed. Damage is modeled by randomly dispersed micropores. The failure criterion for a microvolume is characterized by its stress-rupture strength. It is 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, according to the Huber–Mises criterion, and assumed to be a random function of coordinates. An equation of damage (porosity) balance in a physically nonlinear material at an arbitrary time is formulated. Algorithms of calculating the time dependence of microdamage and macrostresses are developed and the corresponding curves are plotted. The effect of the nonlinearity of the material on its macrodeformation and damage is analyzed
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References
Ya. S. Berezikovich, Approximate Calculations [in Russian], GITTL, Moscow–Leningrad (1949).
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).
L. M. Kachanov, Fundamentals of Fracture Mechanics [in Russian], Nauka, Moscow (1974).
A. F. Kregers, “Mathematical modeling of the thermal expansion of spatially reinforced composites,” Mech. Comp. Mater., 24, No. 3, 316–325 (1988).
V. P. Tamusz and V. S. Kuksenko, Microfracture Mechanics of Polymeric Materials [in Russian], Zinatne, Riga (1978).
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, “Principles of the micromechanics of material damage. 1. Short-term damage,” Int. Appl. Mech., 34, No. 10, 1035–1041 (1998).
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, “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 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 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).
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Translated from Prikladnaya Mekhanika, Vol. 47, No. 5, pp. 68–78, September 2011.
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Khoroshun, L.P., Shikula, E.N. Theory of long-term microdamage of physically nonlinear homogeneous materials. Int Appl Mech 47, 535–544 (2011). https://doi.org/10.1007/s10778-011-0475-9
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DOI: https://doi.org/10.1007/s10778-011-0475-9