Theory of Short-Term Microdamageability of Granular Composite Materials

The theory of microdamageability of granular composites is outlined through the simulation of microdamages in the components by pores filled with compression-resisting particles of a destroyed material. The damage criterion for a microvolume of a component is taken in the Schleicher–Nadai form, which allows for the difference between the ultimate tensile and compressive loads. The ultimate strength is a random function of Weibull-distributed coordinates. The stress–strain state and the efficient properties of the material are determined from the stochastic equations of elastic theory for a granular composite with porous components. The equations of deformation and microdamage are closed by the equations of porosity balance in the components. Nonlinear diagrams of the concurrent processes of deformation in the granular material and microdamage in the matrix are plotted. The effect of the physical and geometrical parameters on them is studied     

Short-Term Microdamageability of Laminated Materials under Thermal Actions

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.     

Simulation of the Short-Term Microdamageability of Laminated Composites

The theory of microdamageability of multicomponent laminated composites is outlined through the simulation of microdamages in the components by pores filled with compression-resisting particles of the destroyed material. The damage criterion for a microvolume of a component is taken in the Schleicher–Nadai form, which allows for the difference between the ultimate tensile and compressive loads. The ultimate strength is a random function of Weibull-distributed coordinates. The stress–strain state and the efficient properties of the material are determined from the stochastic equations of the elastic theory for a laminated composite with porous components. The equations of deformation and microdamage are closed by the equations of porosity balance in the components. Nonlinear diagrams of the concurrent processes of deformation in the laminated material and microdamage in the matrix are plotted. The effect of the physical and geometrical parameters on them is studied     

Short-Term Damage Micromechanics of Laminated Fibrous Composites Under Thermal Actions

A microdamage theory is constructed for laminated fibrous materials with transversely isotropic fibers and a porous isotropic matrix under thermal actions. Microdamages in the matrix are simulated by pores, empty or filled with particles of the damaged material that resist compression. The fracture criterion for a microvolume of the matrix 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 fibrous materials with a porous matrix. The deformation and microdamage equations are closed by the porosity balance equations corrected for the thermal effect. For various types of loading, nonlinear relations are derived for the coupled processes of deformation of a laminated fibrous material and microdamage of the matrix due to the thermal macrostrain. The effect of physical and geometrical parameters on these processes is studied.     

Short-Term Microdamageability of Fibrous Composites with Transversally Isotropic Fibers and a Microdamaged Binder

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     

Short-Term Microdamageability of Fibrous Materials with Transversely Isotropic Fibers Under Thermal Actions

The theory of microdamageability of fibrous materials with transversely isotropic fibers is stated with account taken of the thermal effect. Microdamages in the isotropic matrix are simulated by pores empty or filled with particles of damaged material that resist compression. The fracture criterion for a microvolume of the matrix 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 fibrous materials with a porous matrix. 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 fibrous material and microdamage of the matrix due to the thermal macrostrain. The effect of physical and geometrical parameters on these processes is studied.     

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     

The Micromechanics of Short-Term Damageability of Fibrolaminar Composites

A theory of microdamageability is constructed for fibrous laminated composites consisting of transversally isotropic fibers and a microdamaged isotropic porous binder. Microdamages in the binder are simulated by pores filled with compression-resisting particles of the destroyed material. Damage in a microvolume of the binder is described by the Schleicher–Nadai strength criterion, which allows for the difference between the ultimate tensile and compressive loads. The ultimate strength is a random function of coordinates with the Weibull distribution. The stress–strain state and effective characteristics of the material are determined by solving the stochastic equations of elastic theory for a fibrous laminated composite with a porous binder. The equations of deformation and microdamageability are closed by the equations of porosity balance in the binder. Nonlinear diagrams of the concurrent processes of deformation of the fibrous laminated material and microdamage of the matrix for various physical and geometrical parameters are constructed     

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     

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 Microdamage of a Granular Material under Physically Nonlinear Deformation

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     

Theory of Short-Term Microdamageability for a Homogeneous Material under Physically Nonlinear Deformation

The structural theory of short-term damageability is generalized to the case of physically nonlinear deformation of an undamaged material. The stochastic elasticity equations for a porous medium whose skeleton deforms nonlinearly are used. The failure criterion for a microvolume of the material is assumed to be in the Huber–Mises form. The microdamage balance equation for a physically nonlinear material is derived. This equation and the macrostress–macrostrain relation for a porous physically nonlinear material constitute a closed-form system describing the coupled processes of physically nonlinear deformation and microdamage. An algorithm is constructed for computing microdamage–macrostrain relationships and plotting deformation curves. Such curves are plotted for the case of uniaxial tension     

Micromechanics of Short-Term Thermal Damageability

The structural theory of microdamageability of a homogeneous material is generalized to the case of a thermal action. The theory is based on the stochastic thermoelastic equations of a medium with micropores, hollow or filled with particles of a damaged material. This medium models a material with dispersed microdamages. The Schleicher–Nadai fracture criterion is used as the condition of origin of a micropore in a microvolume of an undestroyed material. It is assumed that the particles of the damaged material in the micropores do not resist shear and triaxial tension and behave as the undamaged material under triaxial compression. The porosity balance equation is corrected for the thermal component and together with the relations between macrostresses, macrostrains, and temperature forms a closed system describing the concurrent action of deformation and microdamage. Nonlinear stress–strain diagrams and dependences of microdamage on macrostrain and temperature are constructed     

Influence of the Physical Nonlinearity of the Matrix on the Deformation of a Particulate Composite with Microdamageable Inclusions

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.     

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.     

Influence of Physically Nonlinear Deformation on Short-Term Microdamage of a Laminar Material

The structural theory of short-term damage is generalized to the case where the undamaged components of an N-component laminar composite deform nonlinearly. The basis for this generalization is the stochastic elasticity equations for an N-component laminar composite with porous components whose skeleton deforms 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 composite components. Together with the equations relating macrostresses and macrostrains of the laminar composite with porous nonlinear components, they constitute a closed-form system. This system describes the coupled processes of physically nonlinear deformation and microdamage. For a two-component laminar composite, algorithms for calculating the microdamage–macrostrain relationship and plotting deformation curves are proposed. Uniaxial tension curves are plotted for the case where microdamages occur in the linearly hardening component and do not in the linearly elastic component     

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     

Influence of physically nonlinear deformation on short-term microdamage of a fibrous material

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.     

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.     

Short-term microdamage of laminated material with nonlinear matrix and microdamaged reinforcement

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.