Coupled deformation and long-term damage of layered materials with stress-rupture microstrength described by a fractional-power function

The theory of long-term damage of homogeneous materials is generalized to layered materials. The damage of the components (layers) 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 tensile strength, according to the Huber–Mises criterion, and assumed to be a random function of coordinates. An equation of damage (porosity) balance in the components 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 a fractional power microdurability function     

Coupled processes of deformation and long-term damage of fibrous materials under thermal loading

A theory of long-term damage of fibrous composites under thermal loading is set up. The damage of the matrix 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 Schleicher–Nadai failure 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 taking into account the thermal component. Algorithms of calculating the time dependence of microdamage and macrostresses are developed. Corresponding curves are plotted. The effect of temperature on the deformation and microdamage of the material is studied     

Coupled processes of deformation and damage of composites with orthotropic inclusions and unbounded rupture-stress function

The theory of long-term damage of homogeneous materials, which is based on the equations of the mechanics of stochastically inhomogeneous materials, is generalized to composite materials reinforced with orthotropic ellipsoidal inclusions. The microdamage of the composite components 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 failure on the difference between the equivalent stress and its limit, which is the tensile strength, according to the Huber–Mises criterion, and assumed to be a random function of coordinates. Given macrostresses or macrostrains, an equation of porosity balance in the composite components at an arbitrary time is formulated. The time dependence of microdamage and macrostresses or macrostrains is established in the case of unlimited stress-rupture microstrength described by an exponential power function     

Deformation and long-term damage of orthotropic composites with limited stress-rupture microstrength

The theory of long-term microdamage of homogeneous materials based on the mechanics of stochastically inhomogeneous materials is generalized to a composite with orthotropic inclusions. The damage of the composite components 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 tensile strength, according to the Huber–Mises criterion, and assumed to be a random function of coordinates. Given macrostresses or macrostrains, an equation of damage (porosity) balance in the composite components at an arbitrary time is derived. The time dependence of microdamage and macrostresses or macrostrains in a discrete-fiber-reinforced composite with limited stress-rupture microstrength described by a fractional-power function is plotted     

Deformation and long-term damage of particulate composites under thermal loads

A theory of long-term damage of particulate composite materials under thermal load is proposed. The damage of the composite components is modeled by randomly dispersed micropores. The failure criterion for a single microvolume is determined by its stress-rupture strength, which, in turn, is determined by the dependence of the time to brittle failure on the difference between the equivalent stress and its limit, which characterizes the ultimate strength according to the Schleicher–Nadai criterion. The damage (porosity) balance equation is derived for an arbitrary time, taking the thermal effect into account. Algorithms for calculating microdamage and macrostresses as functions of time are developed     

Theory of long-term microdamage of physically nonlinear homogeneous materials

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     

Influence of heating on the deformation and long-term damage of unreinforced materials

A theory of long-term damage of homogeneous materials under thermal load is proposed. The damage of the material is modeled by randomly dispersed micropores. The failure criterion for a single microvolume is determined by its stress-rupture strength, which, in turn, is determined by the dependence of the time to brittle failure on the difference between the equivalent stress and its limit, which characterizes the ultimate strength according to the Schleicher–Nadai criterion. The damage (porosity) balance equation is derived for an arbitrary time, taking the thermal effect into account. Algorithms for calculating microdamage and macrostresses as functions of time are developed, and respective curves are plotted. The effect of temperature on the macrodeformation and damage curves is studied     

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

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     

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

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     

Deformation and long-term damage of layered materials with stress-rupture microstrength described by an exponential power function

The theory of long-term damage of homogeneous materials is generalized to layered materials. The damage of the components is modeled by randomly dispersed micropores. The damage criterion for a microvolume is characterized by its stress-rupture strength. It is determined by the exponential power dependence of the time to brittle failure on the difference between the equivalent stress and its limit, which is the tensile strength, according to the Huber–Mises criterion, and assumed to be a random function of coordinates. An equation of damage (porosity) balance in the components 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 exponential power microdurability function     

Long-term damage of discrete-fiber-reinforced composites with transversely isotropic inclusions and stress-rupture microstrength described by an exponential power function

The theory of long-term damage of homogeneous materials, which is based on the equations of the mechanics of stochastically inhomogeneous materials, is generalized to discrete-fiber-reinforced composite materials. The microdamage of the composite components 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 failure on the difference between the equivalent stress and its limit. Given macrostresses and macrostrains, an equation of damage (porosity) balance in the composite components at an arbitrary time is formulated. The time dependence of microdamage and macrostresses or macrostrains is established in the case of stress-rupture microstrength described by an exponential power function Translated from Prikladnaya Mekhanika, Vol. 45, No. 2, pp. 19–29, February 2009.     

Micromechanics of long-term damage of particulate composites with unlimited microdurability

The theory of long-term damage of homogeneous materials is generalized to particulate composite materials. The damage of the composite components 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 tensile strength, according to the Huber–Mises criterion, and assumed to be a random function of coordinates. An equation of damage (porosity) balance in the composite components at an arbitrary time is formulated. Algorithms of calculating the time dependence of microdamage and macrostresses or macrostrains are developed and relevant curves are plotted in the case of unlimited microdurability Translated from Prikladnaya Mekhanika, Vol. 44, No. 11, pp. 7–17, November 2008.     

Deformation and long-term damage of particulate composites with stress-rupture microstrength described by a fractional-power function

The theory of long-term damage of homogeneous materials is generalized to particulate composite materials. The damage of the composite components 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 tensile strength, according to the Huber-Mises criterion, and assumed to be a random function of coordinates. An equation of damage (porosity) balance in the composite components 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 limited microdurability Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 3–12, October 2008.     

Deformation and Microdamage of a Discrete-Fibrous Composite with Transversely Isotropic Components

The theory of microdamage for materials with a transversely isotropic matrix and unidirectional ellipsoid-like fibers is set forth. Microdamage is modeled by empty pores. The failure criterion for a microvolume is assumed to have the Huber–Mises form where the ultimate strength is a random function of coordinates with a power or Weibull distribution. The stress–strain state and effective properties of the material are determined from the theory of elasticity for materials with a transversely isotropic matrix and unidirectional fibers. The deformation and microdamage equations are closed by the porosity-balance equations. The nonlinear dependences of the coupled processes of deformation and microdamage on macrodeformations are constructed. The effect of physical and geometrical parameters on the processes is studied     

Mesomechanics of deformation and short-term damage of linear elastic homogeneous and composite materials

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.     

Short-Term Damage of a Transversely Isotropic Piezoelectric Material with Complex Strain-Stress State

The microdamage of porous transversely isotropic piezoelectric materials under complex macrostress is studied. The microdamages are modeled by pores. The damage of a microvolume is defined by the generalized Huber-Mises failure criterion for a transversely isotropic medium. The ultimate strength is a random function of coordinates with exponential or Weibull distribution. The stress-strain state and effective properties of the material are determined from the stochastic equations of electroelasticity. The deformation and microdamage equations are closed by the porosity balance equations. Deformation curves are plotted for two values of macrostrain or macrostress and different values of electric intensity. The influence of electric intensity on the microdamage of piezoelectric materials is studied__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 3, pp. 79–92, March 2005.     

Deformation and long-term damage of physically nonlinear particulate composites

The theory of long-term damage is generalized to particulate composite materials with physically nonlinear components. The damage of the components 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 components at an arbitrary time is formulated. Algorithms of calculating the time dependence of are developed. The effect on the nonlinearity of the matrix on the damage and macrodeformation curves is examined     

Deformation and long-term damage of homogeneous and composite materials of stochastic structure (Review)

The studies of mathematical models for the coupled processes of deformation and long-time damage of stochastic composite materials are systematized. Damage is modeled by stochastically arranged micropores. The damage of 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, according to the Huber–Mises or Schleicher–Nadai criteria, and assumed to be a random function of coordinates. The equation of damage balance at an arbitrary time and the equations relating macrostresses and macrostrains constitute a closed system. Algorithms of calculating the time dependence of microdamage and macrostresses are developed. The effect of temperature and nonlinearity on the curves is studied     

Microdamage of a nonlinear elastic material in combined stress state

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.     

Modeling the Short-Term Damageability of a Transversely Isotropic Piezoelectric Material

A short-term microdamage theory for porous transversely isotropic piezoelectric materials is set forth. Microdamages are modeled by pores. The fracture criterion for a microvolume of a transversely isotropic medium is assumed to have the Huber–Mises form. The ultimate strength is a random function of coordinates with an exponential or Weibull distribution. The stress–strain distribution and effective properties of the material are determined from the stochastic electroelastic equations. The deformation and microdamage equations are closed by the porosity balance equations. For various values of electric intensity, the microdamage–macrodeformation relationships and deformation curves are plotted. The effect of electric intensity on the microdamage of piezoelectric materials is studied