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1.
The studies of the deformation of physically nonlinear homogeneous and composite materials are systematized. Algorithms to
determine the effective elastic properties and stress–strain state of particulate, laminated, fibrous, and laminated fibrous
composite materials with physically nonlinear components are outlined, and their deformation patterns are studied. Composites
are considered as two-component materials of random structure. Their effective properties are determined using the conditional
averaging method. The nonlinear equations that allow for the physical nonlinearity of the components are solved by an iterative
method. The relationship between macrostresses and macrostrains is established. Macrostress–macrostrain curves of homogeneous
and composite materials are analyzed
Translated from Prikladnaya Mekhanika, Vol. 44, No. 12, pp. 7–38, December 2008. 相似文献
2.
The structural theory of short-term damage is generalized to the case where the undamaged components of a particulate composite
deform nonlinearly under loads that induce a compound stress state. The basis for this generalization is the stochastic elasticity
equations for a particulate composite with porous components whose skeletons deform nonlinearly. Damage in a microvolume of
the material is assumed to occur in accordance with the Huber-Mises failure criterion. Balance equations for damaged microvolume
are derived for the physically nonlinear materials of the components. Together with the macrostress-macrostrain relationship
for a particulate composite with porous nonlinear components, they constitute a closed-form system of equations. This system
describes the coupled processes of physically nonlinear deformation and microdamage. Algorithms for calculating the microdamage-macrostrain
relationship and plotting stress-strain curves are proposed. Such curves are plotted for the case where the composite is subjected
to a combination of normal and tangential loads, and microdamages occur in the linearly hardened matrix and do not in the
linearly elastic inclusions. The stress-strain curves are examined depending on the volume fraction of inclusions and presence
of tangential stresses
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 12, pp. 48–57, December, 2006. 相似文献
3.
The structural theory of short-term damage is generalized to the case where the undamaged components of a granular composite deform nonlinearly. The basis for this generalization is the stochastic elasticity equations for a granular composite with porous components whose skeletons deform nonlinearly. Microvolumes of the composite components meet the Huber–Mises failure criterion. Damaged microvolume balance equations are derived for the physically nonlinear materials of the components. Together with the equations relating macrostresses and macrostrains of a granular composite with porous nonlinear components, they constitute a closed-form system. The system describes the coupled processes of physically nonlinear deformation and microdamage. Algorithms for calculating the microdamage–macrostrain relationship and plotting deformation diagrams are proposed. Uniaxial tension curves are plotted for the case where microdamages occur in the linearly hardened matrix and do not in the inclusions, which are linearly elastic 相似文献
4.
A Jones-Nelson model has been applied to depict nonlinear stress-strain relations of composite laminae, where mechanical properties
were expressed by strain energy density. The nonlinear material matrix is only a function of the strain energy density. Then
a material model could be conveniently applied under complex stress condition. In this paper, by introducing large displacement
stress-strain measurement and varying-Poisson's ratio idea, an improved Jones-Nelson material model is presented, where the
expanding problem of material properties and convergence problems are overcome. Meanwhile a discuss of the reorientation of
fiber and a material nonlinear analysis of rubber composite lamina under super large deformation conditions are made. The
prediction results of improved material model are in fairly good agreement with those of the experiments. 相似文献
5.
Deformation of Particulate Composite with Physically Nonlinear Inclusions and Microdamageable Matrix
The structural theory of short-term damage is generalized to the case where the matrix of a particulate composite has microdamages and the inclusions deform nonlinearly. The basis for this generalization is the stochastic elasticity equations of a porous-matrix particle-reinforced composite. Microvolumes of the matrix meet the Huber-Mises failure criterion. A balance equation for damaged microvolumes is derived. The balance equation and the equations relating macrostresses and macrostrains of a particulate composite with porous matrix and physically nonlinear inclusions constitute a closed-form system. The system describes the coupled processes of physically nonlinear deformation and microdamage. Algorithms for calculating the microdamage-macrostrain relationship and plotting deformation diagrams are proposed. Uniaxial tension curves are plotted for the case where the material of inclusions is linearly hardening__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 2, pp. 3–11, February 2005. 相似文献
6.
The structural theory of short-term damage is used to study the coupled processes of deformation and microdamage of a physically
nonlinear material in a combined stress state. The basis for the analysis is the stochastic elasticity equations for a physically
nonlinear porous medium. Damage in a microvolume of the material is assumed to occur in accordance with the Huber-Mises failure
criterion. The balance equation for damaged microvolumes is derived and added to the macrostress-macrostrain relations to
produce a closed-form system of equations. It describes the coupled processes of nonlinear deformation and microdamage of
the porous material. Algorithms are developed for calculating the dependence of microdamage on macrostresses and macrostrains
and plotting stress-strain curves for a homogeneous material under either biaxial normal loading or combined normal and tangential
loading. The plots are analyzed depending on the type of stress state
__________
Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 30–39, November 2006. 相似文献
7.
The structural theory of short-term damage is generalized to the case where the undamaged isotropic matrix of a fibrous composite
with transversely isotropic reinforcement deforms nonlinearly under loads that induce a combined stress state, microdamages
occurring in the matrix alone. The basis for this generalization is the stochastic elasticity equations for a fibrous composite
with porous matrix whose skeleton deforms nonlinearly. The Huber-Mises failure criterion is used to describe the damage of
microvolumes in the matrix. The damaged microvolume balance equation is derived for the physically nonlinear material of the
matrix based on the properties of the distribution function for the statistically homogeneous random field of ultimate microstrength.
Together with the macrostress-macrostrain relationship, they constitute a closed-form system of equations. This system describes
the coupled processes of physically nonlinear deformation and microdamage. Algorithms for calculating the dependences of macrostresses
and microdamages on macrostrains are proposed. Stress-strain curves for a composite with a linearly hardened matrix under
simultaneous normal and tangential loads are plotted. The effect of the volume fraction of reinforcement and tangential load
on the curves is examined
__________
Translated from Prikladnaya Mekhanika, Vol. 43, No. 3, pp. 48–59, March 2007. 相似文献
8.
The structural theory of microdamage of homogeneous and composite materials is generalized. The theory is based on the equations
and methods of the mechanics of microinhomogeneous bodies with stochastic structure. A single microdamage is modeled by a
quasispherical pore empty or filled with particles of a damaged material. The accumulation of microdamages under increasing
loading is modeled as increasing porosity. The damage within a single microvolume is governed by the Huber-Mises or Schleicher-Nadai
failure criterion. The ultimate strength is assumed to be a random function of coordinates with power-law or Weibull one-point
distribution. The stress-strain state and effective elastic properties of a composite with microdamaged components are determined
using the stochastic equations of elasticity. The equations of deformation and microdamage and the porosity balance equation
constitute a closed-form system of equations. The solution is found iteratively using conditional moments. The effect of temperature
on the coupled processes of deformation and microdamage is taken into account. Algorithms for plotting the dependences of
microdamage and macrostresses on macrostrains for composites of different structure are developed. The effect of temperature
and strength of damaged material on the stress-strain and microdamage curves is examined
__________
Translated from Prikladnaya Mekhanika, Vol. 43, No. 6, pp. 3–42, June 2007. 相似文献
9.
The structural theory of short-term damage is generalized to the case where undamaged components of an N-component laminate deform nonlinearly under loads that induce a combined stress state. The basis for this generalization
is the stochastic elasticity equations for an N-component laminate with porous components whose skeleton deforms nonlinearly. The Huber-Mises failure criterion is used to
describe the damage of microvolumes in the composite. The damaged microvolume balance equation is derived for the physically
nonlinear materials of the composite components. Together with the macrostress-macrostrain relationship, they constitute a
closed-form system of equations. This system describes the coupled processes of physically nonlinear deformation and microdamage.
For a two-component laminate, algorithms for calculating the microdamage-macrostrain relationship and plotting stress-strain
curves are proposed. Stress-strain curves are also plotted for the case where microdamages occur in the linearly hardening
component and do not in the linear elastic component under simultaneous normal and tangential loads. The effect of the volume
fraction of reinforcement and tangential load on the curves is examined
__________
Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 62–72, April 2007. 相似文献
10.
In this paper the double-inclusion model, originally developed to determine effective linear elastic properties of composite materials, is reformulated and extended to predict the effective nonlinear elastic–plastic response of two-phase particulate composites reinforced with spherical particles. The resulting problem of elastic–plastic deformation of a double-inclusion embedded in an infinite reference medium subjected to an incrementally applied far-field strain is solved by the finite element method. The proposed double-inclusion model is evaluated by comparison of the model predictions to the available exact results obtained by the direct approach using representative volume elements containing many particles. It is found that the double-inclusion formulation is capable of providing accurate prediction of the effective elastic–plastic response of two-phase particulate composites at moderate particle volume fractions. 相似文献
11.
本文用准三维有限元法研究了材料非线性对复合材料层合板热自山边界效应的影响,给出了修正型Hahn-Tsai非线性应力-应变关系的三维形式。由本文非线性分析方法得到的层间应力与以往由线性分析方法得到的层间应力做了比较,结果表明:材料非线性能显著降低层间剪应力的集中程度,但对层间正应力影响不太明显。 相似文献
12.
The structural theory of short-term microdamage is generalized to a laminated composite with a microdamageable matrix and
physically nonlinear reinforcement. The basis for the generalization is the stochastic elasticity equations of a laminated
composite with a porous matrix. Microvolumes in the matrix material meet the Huber-Mises failure criterion. The damaged-microvolume
balance equation for the matrix is derived. This equation and the equations relating macrostresses and macrostrains of a laminated
composite with porous matrix and physically nonlinear reinforcement constitute a closed-form system of equations. This system
describes the coupled processes of physically nonlinear deformation and microdamage occurring in different composite components.
Algorithms for computing the microdamage-macrostrain relationships and deformation diagrams are developed. Uniaxial tension
curves are plotted for a laminated composite with linearly hardening reinforcement
__________
Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 47–56, November 2005. 相似文献
13.
A structural theory of short-term microdamage is proposed for a two-component laminated composite with microdamageable reinforcement
and physically nonlinear matrix. The basis of the theory is the stochastic elasticity equations of a laminated composite with
a porous reinforcement. Microvolumes in the reinforcement material meet the Huber-Mises failure criterion. The damaged-microvolume
balance equation for the reinforcement is derived. This equation and the equations relating macrostresses and macrostrains
of a laminated composite with porous reinforcement and physically nonlinear matrix constitute a closed-form system of equations.
This system describes the coupled processes of physically nonlinear deformation and microdamage occurring in different composite
components. Algorithms for computing the microdamage-macrostrain relationships and deformation diagrams are developed. Uniaxial
tension curves are plotted for a laminated composite with linearly hardening matrix
__________
Translated from Prikladnaya Mekhanika, Vol. 41, No. 12, pp. 3–12, December 2005. 相似文献
14.
The theory of microdamageability of laminated materials is stated with account taken of the thermal effect. Microdamages in the components are simulated by pores empty or filled with particles of damaged material that resist compression. The fracture criterion is assumed to have the Nadai–Schleicher form, which takes into account the difference between the tensile and compressive ultimate loads, with the ultimate strength being a random function of coordinates with a power or Weibull distribution. The stress–strain state and the effective properties of the material are determined from the thermoelastic equations for laminated materials with porous components. The deformation and microdamage equations are closed by the equations of porosity balance corrected for the thermal effect. For various types of loading, nonlinear relations are derived for the coupled processes of deformation of a two-component laminated material and microdamage due to the thermal macrostrain of a component. The effect of physical and geometrical parameters on these processes is studied. 相似文献
15.
The structural theory of short-term damage is generalized to particulate composites with nonlinearly elastic matrix and microdamageable inclusions. The basis for this generalization is the stochastic elasticity equations for a particulate composite with porous inclusions. Microvolumes of the material meet the Huber-Mises failure criterion. The damaged-microvolume balance equation and the equations relating macrostresses and macrostrains of a particulate composite with porous inclusions and physically nonlinear matrix constitute a closed-form system. This system describes the coupled processes of physically nonlinear deformation and microdamage. Algorithms for computing the microdamage-macrostrain relationships and deformation curves are proposed. Uniaxial tension curves are plotted for a particulate composite with linearly hardening matrix__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 4, pp. 3–11, April 2005. 相似文献
16.
The theory of microdamageability of fibrous composites with transversally isotropic fibers and a microdamaged isotropic porous matrix is proposed. Microdamages in the matrix are simulated by pores filled with particles of the destroyed material that resist compression. The criterion of damage in the matrix microvolume is taken in the Schleicher–Nadai form. It accounts for the difference between the ultimate tensile and compressive loads. The ultimate strength is a random function of coordinates with Weibull distribution. The stress–strain state and effective properties of the material are determined from the stochastic equations of the elastic theory for a fibrous composite with porous components. The equations of deformation and microdamage are closed by the equations of porosity balance in the matrix. Nonlinear diagrams of the concurrent processes of deformation of fibrous materials and microdamage of the matrix are plotted. The effect of the physical and geometrical parameters on them is studied 相似文献
17.
The structural theory of short-term microdamage is generalized to a fibrous composite with a microdamageable matrix and physically
nonlinear fibers. The basis for the generalization is the stochastic elasticity equations of a fibrous composite with a porous
matrix. Microvolumes in the matrix material meet the Huber-Mises failure criterion. The damaged-microvolume balance equation
for the matrix is derived. This equation and the equations relating macrostresses and macrostrains of a fibrous composite
with porous matrix and physically nonlinear fibers constitute a closed-form system of equations. This system describes the
coupled processes of physically nonlinear deformation and microdamage occurring in different components of the composite.
Algorithms for computing the microdamage-macrostrain and macrostress-macrostrain relationships are developed. Uniaxial tension
curves are plotted for a fibrous composite with linearly hardening fibers
__________
Translated from Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 38–47, January 2006. 相似文献
18.
A structural theory of short-term microdamage is proposed for a fibrous composite with physically nonlinear matrix and microdamaged
reinforcement. The theory is based on the stochastic elasticity equations of a fibrous composite with porous fibers. Microvolumes
of the fiber material are damaged in accordance with the Huber-Mises failure criterion. A balance equation for damaged microvolumes
in the reinforcement is derived. This equation together with the equations relating macrostresses and macrostrains of a fibrous
composite with porous reinforcement and physically nonlinear matrix constitute a closed-form system. This system describes
the coupled processes of physically nonlinear deformation and microdamage that occur in different components of the composite.
Algorithms are proposed for computing the dependences of microdamage on macrostrains and macrostresses on macrostrains. Uniaxial
tension curves are plotted for a fibrous composite with a linearly hardening matrix
__________
Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 3–13, February 2006. 相似文献
19.
The structural theory of short-term damage is generalized to the case where the undamaged isotropic matrix of a fibrous composite with transversely isotropic fibers deforms nonlinearly, with microdamages occurring only in the matrix. The basis for this generalization is the stochastic elasticity equations for a fibrous composite with porous matrix whose skeleton deforms nonlinearly. Microvolumes of the matrix meet the Huber-Mises failure criterion. The damaged microvolume balance equation is derived for the physically nonlinear material of the matrix based on the properties of the ultimate microstrength distribution. Together with the equations relating macrostresses and macrostrains of the fibrous composite with porous nonlinear matrix, they constitute a closed-form system. This system describes the coupled processes of physically nonlinear deformation and microdamage. Algorithms for calculating the dependences of macrostresses and microdamages on macrostrains are proposed. Uniaxial tension curves are plotted for a fibrous composite with linearly hardening matrix.Translated from Prikladnaya Mekhanika, Vol. 40, No. 10, pp. 88–97, October 2004. 相似文献