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     

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.     

Deformation Characteristics of Laminar Composites under Nonlinear Strains

It is shown that the type of governing relations in a composite can change, namely, a laminar composite formed by layers of physically linear materials under nonlinear strains should be described by nonlinear Hooke's law. Local stresses can be not proportional to elastic constants of the layers under nonlinear strains.     

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     

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     

材料非线性对复合材料层合板热自由边界效应的影响

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。     

Approximate Analytical Solution of a Physically Nonlinear Spatial Problem on the Elastic Equilibrium of a Multilayer Rectangular Plate

A three-dimensional boundary-value problem for a multilayer rectangular plate is solved under the physically nonlinear theory of elasticity. Various types of interlayer contact conditions are considered. The nonlinear relation between stresses and small strains is assumed to be of the Kauderer form. The solution is represented by a series in powers of a dimensionless small parameter. The problem posed is reduced to a recurrent sequence of linear boundary-value problems. The stress distribution and the effect of physical nonlinearity on the elastic equilibrium of the plate are studied     

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 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.     

Physically and Geometrically Nonlinear Static Problems for Thin-Walled Multiply Connected Shells

Physically and geometrically nonlinear two-dimensional problems are formulated for multiply connected thin shells (weakened by several curvilinear holes). A technique and algorithm are proposed for their solution with allowance for elastoplastic strains and finite deflections of shells under static loading. Numerical results for a shell with two circular holes are presented and the stress concentration is analyzed     

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.     

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.     

Thermomechanical Model of Growing Cylindrical Bodies Made of Physically Nonlinear Materials

The finite-element method is used together with the theory of growing bodies to model the residual stress-strain state of cylindrical bodies with built-up layers. The case of two built-up layers is analyzed. Numerical and experimental results are compared __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 9, pp. 118–126, September 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.     

A Numerical Method to Material and Geometric Nonlinear Analysis of Cable Structures

In this article, a numerical method is presented for computing the stiffness matrix and compatibility relations of cables under uniform distributed loads on any direction. Both the geometrical and material nonlinearities, including softening and yielding of material, are taken into account and the catenary cable element with gauss integration scheme is employed. The proposed formulation includes the effect of uniform distributed loads on any direction and 3D nodal forces to assess the geometric and possible material nonlinearity of cables. The derived equations are then applied to the analysis of cable structures. The accuracy of the responses obtained by the proposed method is evaluated by several benchmark solutions available in the literature. Results of numerical examples indicate the capability of the proposed stiffness matrix in prediction of the elastic and inelastic responses of cables. The proposed formulation is therefore recommended for cable elements to be used in the analysis of cable structures.     

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.     

Physically Nonlinear Deformation of a Long Orthotropic Cylindrical Shell with Elliptic Cross-Section*

International Applied Mechanics - The stress–strain state of long cylindrical shells with elliptical cross-section is studied. The shells are made of a nonlinear elastic orthotropic organic...     

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.