Discrete-continuum model of symmetric separation of a material

A problem of the beginning of motion of a finite-width cut in a linearly elastic plane under the action of symmetric external loading is formulated. The material on the way of cut propagation forms a layer (interaction layer). The stress-strain state of the material is postulated to be homogeneous across this layer. A system of integral boundary equations is obtained for determining the stress-strain state. Based on this system of equations, a discrete model of separation of the layer material is constructed under the assumption of a constant stress-strain state in an element of the interaction layer. The stress distribution in the pre-fracture zone is determined. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 134–140, January–February, 2009.     

Finding the elastic strain limit at the tip region of a physical cut with arbitrarily loaded faces

A model describing the stress-strain state in the neighborhood of a physical cut with an arbitrary distribution of external load along its faces is presented. The stress-strain state of a material layer bounded by the continuations of the cut faces is considered. The interaction between the layer and the external half-planes leads to a closed system of integrodifferential equations for the mean stress components in the layer, which splits into two equations for the mean normal stresses and an equation for the mean shear stress. Numerical solutions of the system for the cases of symmetric and antisymmetric loading of the faces by concentrated forces are given. Conditions for the transition of the tip region of the cut to the state of plasticity and fracture are considered.     

Solution of one problem of fracture mechanics

This paper considers a model for the opening-mode fracture separation process based on the introduction of an interaction layer. This layer is defined as the region of localization of the fracture process. The stress-strain state of the layer material is uniform in the cross section of the layer. A study is made of the deformation of a double-cantilever beam weakened by a notch whose width is equal to the thickness of the interaction layer. The problem is solved in a linearly geometrical approximation. The thickness of the interaction layer is estimated, and a method for solving the formulated problem is proposed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 121–127, July–August, 2007.     

Stability of composite shells of revolution

An approach to solving the buckling problem for shells made of a composite material with one plane of elastic symmetry is presented. The approach employs complex Fourier series. The prebuckling stress-strain state is assumed to be geometrically nonlinear. The stability of a cylindrical shell under axial compression and uniform side pressure is analyzed using the Runge-Kutta method with discrete orthogonalization. The numerical results are compared with analytical solutions __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 3, pp. 109–124, March 2008.     

STRESS-STRAIN STATE OF ELASTOPLASTIC BODIES WITH CRACK

A physical cut model is used to describe the changes in the stress-strain state(SSS)in elastoplastic bodies weakened by cracks. The distance between the crack edges is considered to be finite in contrast to the mathematical cut. The interactive layer with a thickness limited by the possibility of using the hypothesis of continuity is distinguished on the physical cut extension.Distribution of stresses and strains over the layer thickness is constant and does not depend on the geometry of the boundary between the cut and the interactive layer. The relationship between stresses and strains is determined by the deformation plasticity theory. The problem of plane strain or plane stress state of an arbitrary finite body weakened by a physical cut is reduced to solving a system of two variational equations for displacement fields in the body parts adjacent to the interactive layer. The proposed approach eliminates the singularity in stress distribution in contrast to the mathematical cut model. Use of local strength criteria allows us to determine the time, point and direction of the fracture initiation. Possibilities of the proposed model are illustrated by solving the problems of determining the SSS of a rectangular body weakened by a physical cut under symmetric and antisymmetric loadings.     

Elastic plane with a physical cut loaded by an antisymmetric system of forces

The problem of determining the stress-strain state of an elastic plane with a physical cut loaded by an antisymmetric system of forces is posed and solved under the condition that the tangential stresses are homogeneous across the thickness of the layer continuing the cut.     

On finite-element solution of spatial thermoviscoelastoplastic problems

A finite-element algorithm is proposed for the analysis of the thermoviscoelastoplastic stress-strain state of bodies under complex loading (thermal and mechanical). It is assumed that an arbitrary element of the body deforms along a rectilinear or slightly curved path. The three-dimensional stress-strain state of the body’s elements is determined using the iterative method of additional strains. The technique is tested by analyzing the three-dimensional viscoelastic stress-strain state of a hollow cylinder and the thermoplastic state of a disk __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 16–25, May 2006.     

Dynamics of a prestressed incompressible layered half-space under moving load

The paper addresses a plane problem: a concentrated force acts on a plate resting on an elastic half-space with homogeneous prestrain. The equations of motion of the plate incorporate shear and rotary inertia. The half-space is assumed to be incompressible and isotropic in the natural state. The elastic potential is given in general form and is only specified for numerical purposes. The dependence of the critical velocity of the load and the stress-strain state on the prestresses is analyzed for different ratios between the stiffnesses of the layer and half-space and different contact conditions. The calculations are carried out for a half-space with Bartenev-Khazanovich potential __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 3, pp. 36–54, March 2008.     

Investigation of the elastoplastic deformation and the fracture criterion of a transversally isotropic material subject to uniaxial compression in a direction parallel to the isotropy plane

The stress-strain state and fracture of a transversally isotropic material subject to uniaxial compression in a direction parallel to the isotropy plane is studied. The deformation theory of the plasticity of a transversally isotropic body was used to analyze the stress-strain state. The fracture analysis of the material is carried out using a proposed variant of the strain-strength criterion. Theoretical and experimental data on the stress-strain state and the strength of a transversally isotropic material are compared. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 3, pp. 67–71, March, 2000.     

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.     

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.     

Creep of axisymmetrically loaded plates with allowance for damage accumulation in their material

The Rabotnov kinetic creep theory was used to calculate the stress-strain state and damage accumulation in the material of axisymmetrically loaded circular and ring plates at any time before the beginning of fracture. It is shown that the solution of the problem can be reduced to solving the same problem under the assumption of steady-state creep of the material. The unsteady creep problem is solved by multiplying the known solution of the steady-state creep problem by certain functions of the coordinates and time, which are determined from a corresponding system of equations. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 157–168, September–October, 2006.     

Numerical study of nonlinear dynamics of hydroelastically connected, plane curvilinear rods

The nonlinear dynamics of hydroelastically connected, plane curvilinear rods is studied. We take into account the reciprocal effect of deformation and hydrodynamics processes, large displacements and strains of the rods, the preliminary static stress-strain state, and the nonstationary fluid flow. A method is proposed for numerical solution of initial boundary-value problems. The effects of the hydroelastic interaction are investigated. The effect of various factors on the dynamics of a damaged pipeline is analyzed. Institute of Mechanics, Nizhnii Novgorod State University, Nizhnii Novgorod 603600. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 212–219, January–February, 1999.     

Methods of determining the stress-strain state and fracture toughness of gas- and oil-line pipe (survey)

Conclusion We have surveyed the existing methods of determining the stress-strain state and fracture toughness of gas and oil lines. The discussion illustrated the promise of methods of evaluating the stress-strain state that are based on allowance for the strain-hardening of the material of the pipe or plastic indicators attached to its surface and deformed along with it. The first method, being destructive, can be used to evaluate the effect of different shaping methods on the strength of the pipe material, to analyze accidental pipeline fractures, and to generate a data bank on the stress-strain state of sections of a pipeline that have lost their longitudinal stability and are scheduled for replacement. Information obtained from the first method can also be used to establish correlations between the geometric parameters of such sections (deflection, curvature) and their stress-strain state. This will make it possible, with the use of reliable statistical methods, to predict the stress level on curved sections of pipelines without having to cut out samples for testing and analysis. Translated from Prikladnaya Mekhanika, Vol. 33, No. 8, pp. 3–30, August, 1997.     

Ellipticity conditions of the static equations of nonlinear elasticity

The relations of the nonlinear model of the theory of elasticity are considered. The Cauchy and the strain gradient tensors are taken to be the characteristics of the stress-strain state of a body. Sufficient conditions under which the static equations of elasticity are of elliptic type are established. These conditions are expressed in the form of constraints imposed on the derivatives of the elastic potential with respect to the strain-measure characteristics. The cases of anisotropic and isotropic bodies are treated, including the case where the Almansi tensor is taken to be the strain measure. The plane strain of a body is investigated using actual-state variables. Novosibirsk State University, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 196–203, March–April, 1999.     

复杂应力状态下岩土材料非线性本构模型研究

基于统一强度理论,将洛德参数引入统一强度理论,推导出材料的统一强度参数,进而分析中间主应力以及主剪应力系数对材料统一强度参数的影响。在此基础上,对邓肯张双曲线模型进行改进,使得该模型能够反映复杂应力状态下的应力应变关系。采用粘土的平面应变试验进行验证,结果表明:在平面应变情况下,当b=0.4时,模型能够较好地反映粘土的应力应变关系,及其强度参数。分析了洛德参数以及中间主应力系数对模型的影响,进一步说明岩土材料存在主应力效应。该模型能够反映不同材料在复杂应力状态下的应力应变关系,有其更为广泛的适用性。     

Stress distribution in multilayered composites near loaded edges

The edge effect in layered composite material is studied using the piecewise-homogeneous body model and the exact equations of the theory of elasticity. It is assumed that continuously distributed normal forces act at the edges of the reinforcing layers. A plain strain state is considered and the stresses are expressed in terms of the solutions of a system of dual singular integral equations. The singularity of the stresses is determined by the solution procedure. The concentration of the reinforcing layers is assumed low and the interaction between them is not taken into account. A numerical algorithm is developed and numerical results on the stress distribution are presented Published in Prikladnaya Mekhanika, Vol. 44, No. 4, pp. 134–144, April 2008.     

Elastoplastic stress-strain state of flexible layered shells made of isotropic and transversely isotropic materials with different moduli and subjected to axisymmetric loading

The paper proposes a numerical technique for analysis of the elastoplastic stress-strain state of flexible layered shells of revolution under axisymmetric loading. It is assumed that the shells are made of isotropic and transversely isotropic materials with different moduli in tension and compression. The technique is based on a geometrically nonlinear theory of shells that takes into account the squared angles of rotation and the Kirchhoff-Love hypotheses for a layer stack. The deformation of isotropic materials is described using the theory of deformation along paths of small curvature. The deformation of transversely isotropic materials is described using the theory of elasticity with different moduli in tension and compression. The problem is solved by the method of successive approximations. A numerical example is given __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 11, pp. 31–42, November 2007.     

Mode III fracture problem of a cracked FGPM surface layer bonded to a cracked FGPM substrate

This work deals with the mode III fracture problem of a cracked functionally graded piezoelectric surface layer bonded to a cracked functionally graded piezoelectric substrate. The cracks are normal to the interface and the electro-elastic material properties are assumed to be varied along the crack direction. Potential and flux types of boundary condition are assigned on the edge of the surface layer. The problem under the assumptions of impermeable and permeable cracks can be formulated to the standard singular integral equations, which are solved by using the Gauss–Chebyshev technique. The effects of the boundary conditions, the material properties and crack interaction on the stress and electric displacement intensity factors are discussed.     

On the interaction between a dislocation and a crack in a material with a nonlinear stress-strain law

The problem of the interaction of a crack and a dislocation in a medium with a nonlinear stress-strain law is considered for the case of a semi-infinite crack in a displacement loaded strip under longitudinal shear deformation. A power law stress-strain relation is considered and the dislocation is assumed positioned so that the net effect of its interaction with the crack is to produce a zero stress intensity factor when combined with the effect of the applied displacements. Thus the Atkinson-Kay superdislocation model of a relaxed crack tip is extended to the situation where the material satisfies a power-law stress-strain relationship.