Methods of theory of random functions in problems of macroscopic properties of microinhomogeneous media

Khoroshun, L. P.

doi:10.1007/bf00902836

Cited by 74 publications

(80 citation statements)

References 4 publications

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“…We shall use the equations of associated thermoelasticity of two-component mixtures for a monodirectional fibrous material and the stress equations [3]. Since the stressed state is assumed to be two-dimensional, i.e., <oii> = <o22 > = O, then, eliminating <~rr > = pleZ~r + p2e2~r, we obtain …”

Section: {--A (Dl + Dz) --(B~d 2 + B2dl) • [A' (D~ + Dz)' + 2a (Dl --mentioning

confidence: 99%

“…Thus, in the case of a monodirectional fibrous composite, the equation of thermal conductivity is given by (1.1) where k:* is the effective coefficient of thermal conductivity across the fibers, kj ~ is the effective coefficient of thermal conductivity in the longitudinal direction, p* =PlP: + P~P2 is the mean density, c* = (plclp: + p2caP2)/p* is the mean specific heat, and p:, c:, k:, p:, P2, c2, k2 and P2 are the volumetric concentrations, the specific heat values, the thermal conductivity coefficients, and the densities of the fibers and the matrix, respectively. According to [3], the effective thermal conductivity coefficients k:* and k:3* are defined by the expressions Equations (I. i) and (i. 3) and the effective thermophysical characteristics appearing in them have meaning if the concept "of "temperature at the macropoint of the composite" holds; i.e., if we contemplate the temperature in an elementary volume containing the matrix and a sufficient number of fibers.…”

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confidence: 99%

“…The temperature distribution must then be calculated on the basis of a more accurate continuous model -the so-called two-temperature model [3].…”

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confidence: 99%

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Thermoelasticity problem for monodirectional fiber composite exposed to pulsed thermal action

Vorobei¹,

Ivanov²,

Khoroshun³

1986

Soviet Applied Mechanics

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Section: {--A (Dl + Dz) --(B~d 2 + B2dl) • [A' (D~ + Dz)' + 2a (Dl --mentioning

confidence: 99%

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Thermoelasticity problem for monodirectional fiber composite exposed to pulsed thermal action

Vorobei¹,

Ivanov²,

Khoroshun³

1986

Soviet Applied Mechanics

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“…Here the average stresses á ñ s jk 2 in the matrix are related to the average strains á ñ e jk 2 as follows: Given macrostrains á ñ e jk , the average stresses á ñ e ij 2 in the matrix are related to them as follows [2,7,9]: it is easy to verify that the root p 2 is within [ p 02 , 1] since…”

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confidence: 99%

Deformation and long-term damage of fibrous materials with the stress-rupture microstrength of the matrix described by a fractional-power function

Khoroshun

Shikula

2009

Int Appl Mech

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The theory of long-term damage is generalized to unidirectional fibrous composites. The damage of the matrix is modeled by randomly dispersed micropores. The damage criterion for a microvolume is characterized by its stress-rupture strength. It is determined by the dependence of the time to brittle failure 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 the matrix at an arbitrary time is formulated. Algorithms of calculating the time dependence of microdamage and macrostresses or macrostrains are developed and corresponding curves are plotted in the case of stress-rupture microstrength described by a fractional power function Keywords: composite materials, stochastic structure, stress-strain state, long-term damage, porosity of matrix, effective characteristics, porosity balance equation, fractional power function Introduction. One of the possible failure mechanisms in materials and structural members is the occurrence and development of dispersed microdamages, which commonly lead to the formation of main cracks. Physically, the damage of a material can be considered as dispersed defects such as microcracks, microvoids or damaged microvolumes. They reduce the effective or bearing portion of the material, which resists loads.There are three types of damage models. The models of the first type proceed from the micrononuniformity of the elastic and strength properties of the material, resulting in dispersed microdamages under loading, which are modeled by microcracks or micropores. The damage equations are derived from the theory of deformation of structurally inhomogeneous media and certain failure criteria for microvolumes of the material. The models of the second type formally introduce a damage parameter as a measure of discontinuity of the material but do not indicate its physical meaning and postulate an evolutionary equation that relates the damage rate and the applied stress. The models of the third type describe damage by thermodynamic (rather than structural) parameters, which contribute, together with stresses and strains, to the laws of thermodynamics. This gives formal relationships among stresses, strains, and damage parameters.It is obvious that the models of the first type most adequately represent real damage processes. The ideas and methods of the mechanics of stochastically inhomogeneous media make it possible to describe the coupled processes of deformation and short-term damage of both homogeneous [11,12] and composite [14][15][16][17] materials and to study these processes over a wide range of mechanical properties, including thermal effects [10,12,[18][19][20][21] and physically nonlinear deformation [22][23][24][25][26][27][28][29][30][31][32][33][34][35].However, experimental data on and observations of the behavior of structural members and structures suggest that damage can be either short-term (occurring inst...

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“…Given macrostrains á ñ e jk , the average stresses á ñ s jk 2 in the matrix are related to the macrostrains á ñ e jk as follows [2,7]: and epoxy resin with the following characteristics of the undamaged portion [4]:…”

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Coupled processes of deformation and long-term damage of fibrous materials with the microdurability of the matrix described by an exponential power function

Khoroshun

Shikula

2010

Int Appl Mech

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The theory of long-term damage is generalized to fibrous composites. The damage of the matrix is modeled by randomly dispersed micropores. The damage criterion for a microvolume is characterized by its stress-rupture strength. It is determined by the dependence of the time to brittle failure on the difference between the equivalent stress and its limit, which is the ultimate strength, according to the Huber-von Mises criterion, and assumed to be a random function of coordinates. An equation of damage (porosity) balance in the matrix at an arbitrary time is formulated. Algorithms of calculating the time dependence of microdamage and macrostresses or macrostrains are developed and corresponding curves are plotted in the case of stress-rupture microstrength described by an exponential power function Keywords: fibrous composite, stochastic structure, long-term damage, effective characteristics, porosity balance equation, exponential power microdurability function Introduction. When subject to long-term loading, structural members may fail suddenly because of the occurrence and development of dispersed microdamages, which commonly lead to the formation of main cracks. Physically, the damage of a material can be considered as dispersed defects in the form of microcracks, microvoids or damaged microvolumes. They reduce the effective or bearing portion of the material, which resists loads.There are three types of damage models. The models of the first type proceed from the micrononuniformity of the elastic and strength properties of the material and assume a mechanism whereby dispersed microdamages, which are modeled by microcracks or micropores, form under loading. The damage equations are derived from the theory of deformation of structurally inhomogeneous materials and certain failure criteria for structural elements of the material. The models of the second type formally introduce a damage parameter as a measure of discontinuity of the material but do not indicate its physical meaning and postulate an evolutionary equation that relates the damage rate and the applied stress. The models of the third type describe damage by thermodynamic parameters, which contribute, together with stresses and strains, to the laws of thermodynamics. This gives formal relationships among stresses, strains, and damage parameters.The informal models of the first type most adequately represent real damage processes. The ideas and methods of the mechanics of stochastically inhomogeneous materials make it possible to describe the coupled processes of deformation and short-term (instantaneous) damage of both homogeneous and composite materials under high loads and to study these processes over a wide range of mechanical properties, including thermal effects and physically nonlinear deformation.Experimental data on and observations of the real behavior of structural members and structures suggest that damage can be either short-term (occurring instantaneously after the application of stresses or strains) or long-term (building up with time aft...

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Methods of theory of random functions in problems of macroscopic properties of microinhomogeneous media

Cited by 74 publications

References 4 publications

Thermoelasticity problem for monodirectional fiber composite exposed to pulsed thermal action

Thermoelasticity problem for monodirectional fiber composite exposed to pulsed thermal action

Deformation and long-term damage of fibrous materials with the stress-rupture microstrength of the matrix described by a fractional-power function

Coupled processes of deformation and long-term damage of fibrous materials with the microdurability of the matrix described by an exponential power function

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