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     

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     

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.     

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.     

Short-term microdamageability of a fibrous composite with physically nonlinear matrix and microdamaged reinforcement

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.     

Deformation of a laminated composite with a physically nonlinear reinforcement and microdamageable matrix

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.     

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.     

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.     

Deformation of a fibrous composite with physically nonlinear fibers and microdamageable matrix

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.     

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.     

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     

Deformation and short-term damage of physically nonlinear stochastic composites

The studies on the deformation and short-term damage of physically nonlinear homogeneous and composite materials are systemized. A single microdamage is modeled by an empty quasispherical pore in place of a microvolume damaged in accordance with the Huber–von Mises failure criterion. The ultimate microstrength is assumed to be a random function of coordinates. The porosity balance equation is derived. Together with the macrostress–macrostrain relationship, it constitutes a closed-form system of equations. The damage–macrostrain relationship and macrostress–macrostrain curves for homogeneous and composite materials are analyzed     

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 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 microdamage of a physically nonlinear particulate material under a combination of normal and tangential loads

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 __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 12, pp. 48–57, December, 2006.     

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.     

Short-term microdamage of a physically nonlinear fibrous material under simultaneous normal and tangential loads

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.     

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.     

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     

Short-term microdamage of a physically nonlinear laminate under simultaneous normal and tangential loads

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.