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The main results of research on some nonclassical problems of fracture/failure mechanics are analyzed. These results have been obtained by the author and his followers at the Department of Dynamics and Stability of Continua of the S. P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine (the NAS of Ukraine) during the last 50 years. The nonclassical problems of fracture/failure mechanics are problems to which the approaches and criteria of classical fracture mechanics are not applicable. A distinguishing feature of the results obtained by the author and his followers is application of three-dimensional theories of stability, dynamics, and statics of solid mechanics to study the nonclassical problems of fracture/failure mechanics. The majority of other researchers have been using various approximate theories of shells, plates, and rods as well as other approaches to studying the nonclassical problems of fracture/failure mechanics. The main scientific results of solving the eight nonclassical problems of fracture\failure mechanics obtained in the framework of the above mentioned approach (three-dimensional theories of solid mechanics) have been presented very briefly, with focus on the statement of problems, the analysis of corresponding experiments, the development of methods for their solution within the framework of approach under consideration, and the discussion of final results. The mathematical aspects of the methods for solving the mentioned problems and their computer-aided implementation have not been discussed in this review, with information on this subject briefly presented as annotation. The following eight nonclassical problems of fracture\failure mechanics (results by the author and his followers) are considered in this review: – first problem is fracture of composites compressed along the reinforcement; – second problem is short-fiber model in stability and fracture of composites under compression; – third problem is end-crush fracture of composites under compression along the reinforcement; – fourth problem is brittle fracture of cracked materials with initial (residual) stresses acting along the cracks; – fifth problem is shredding fracture of composites stretched or compressed along the reinforcement; – sixth problem is fracture of materials under compression along parallel cracks; – seventh problem is brittle fracture of cracked materials under dynamic loads (with contact interaction of the crack faces); – eighth problem is fracture of thin-walled cracked bodies under tension with prebuckling. About 523 monographs and papers published by the author and his followers on the eight nonclassical problems of fracture mechanics have been included in the references to this review. This review consists of three parts. The first part is General Problems; it is published in Prikladnaya Mekhanika (55, No. 2, 2019). The second part is Compressive Failure of Composite Materials; it is published in Prikladnaya Mekhanika (55, No. 3, 2019). The third part is Other Nonclassical Problems of Fracture/Failure Mechanics; it is published in Prikladnaya Mekhanika (55, No. 4, 2019). [ABSTRACT FROM AUTHOR]

The principal results of research on some nonclassical problems of fracture/failure mechanics have been analyzed. These results have been obtained by the author and his followers at the Department of Continuum Dynamics and Stability of the Tymoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine (the NAS of Ukraine) during the last 50 years. The nonclassical problems of fracture/failure mechanics are problems to which the approaches and criteria of classical fracture mechanics are not applicable. A distinguishing feature of the results obtained by the author and his followers is application of three-dimensional theories of stability, dynamics, and statics of solid mechanics to study the nonclassical problems of fracture/failure mechanics. The majority of other researchers have been using various approximate theories of shells, plates, and rods as well as other approaches to studying the nonclassical problems of fracture/failure mechanics. The main scientific results of solving the eight nonclassical problems of fracture\failure mechanics obtained in the framework of the above mentioned approach (three-dimensional theories of solid mechanics) have been presented very briefly, with focus on the statement of problems, the analysis of corresponding experiments, the development of methods for their solution within the framework of approach under consideration, and the discussion of final results. The mathematical aspects of the methods for solving the mentioned problems and their computer-aided implementation have not been discussed in this review, with information on this subject briefly presented as annotation. The following eight nonclassical problems of fracture\failure mechanics (results by the author and his followers) are considered in this review: – first problem is fracture of composites compressed along the reinforcement; – second problem is short-fiber model in stability and fracture of composites under compression; – third problem is end-crush fracture of composites under compression along the reinforcement; – fourth problem is brittle fracture of cracked materials with initial (residual) stresses acting along the cracks; – fifth problem is shredding fracture of composites stretched or compressed along the reinforcement; – sixth problem is fracture of materials under compression along parallel cracks; – seventh problem is brittle fracture of cracked materials under dynamic loads (with contact interaction of the crack faces); – eighth problem is fracture of thin-walled cracked bodies under tension with prebuckling. About 523 monographs and papers published by the author and his followers on the eight nonclassical problems of fracture mechanics have been included in the references to this review. This review consists of three parts. The first part is General Problems; it is published in Prikladnaya Mekhanika (55, No. 2, 2019). The second part is Compressive Failure of Composite Materials. The third part deals with other nonclassical problems of fracture mechanics. [ABSTRACT FROM AUTHOR]

A review of analytical models of the prefracture zone in the vicinity of the tip of an interfacial crack in a piecewise-homogeneous elastic-brittle body is given in connection with the study of crack rotation from the interface of the connected materials. They are based on a complex model of an interfacial crack, which assumes the presence in the vicinity of the crack tip of a contact area between the faces and a small-scale prefracture zone with a near-the-tip domain of material destruction. The main provisions of the analytical method for taking into account the small-scale prefracture zone near the tip of an interfacial crack are stated, they allow us to reduce the initial nonlinear problem of fracture mechanics to solving the boundary value problem of the elasticity theory about the displacement discontinuity line extending from the crack tip into a less crack-resistant material. The mathematical apparatus for analytically solving the boundary value problems of the analyzed models is the Wiener–Hopf method in combination with the Mellin integral transform. Variants of implementation of the complex model of an interfacial crack for the cases of predominant tension or shear are considered. A numerical analysis of the parameters of the prefracture zone and the area of face contact for different loading conditions was performed. The predictions of the model are compared with the experimental results of the study of interfacial crack rotation. The mechanism of opening of an initially closed crack due to the formation of the destruction zone is described. The results of an approximate analytical solution to the problem of a complex model of an interfacial crack under loads that provide commensurate zones of face contact and prefracture are analyzed. The mutual effect of the contact of the faces and the prefracture zone on their parameters and the angle of rotation of the crack was determined. [ABSTRACT FROM AUTHOR]

The paper establishes a correspondence between the solutions for rectilinear cracks located in a piezoceramic plane at a right angle to the polarization axis and smoothly (no friction) opened with rigid wedges and the solutions for cracks in a purely elastic isotropic plane. This correspondence can be used to calculate the SIFs for cracks in a piezoceramic plane from the expressions for cracks in an elastic isotropic plane, without the need to solve the electroelastic problem. The following problems are solved as examples: opening of a semi-infinite crack with a semi-infinite rounded wedge, a truncated wedge, and a wedge of constant thickness; opening of two semi-infinite cracks with hyperbolic wedges and wedges of constant thickness [ABSTRACT FROM AUTHOR]

The paper is concerned with the fracture process zone at the tip of a crack at the nonsmooth interface between isotropic elastic media. A plane symmetric problem is formulated. The zone is modeled by lines of discontinuity of the normal displacement at the interface. The exact solution of the elastic problem is found by the Wiener-Hopf method [ABSTRACT FROM AUTHOR]

The paper studies the stress rupture behavior of a reinforced viscoelastic composite through which a penny-shaped mode I crack propagates under a constant load. The composite has hexagonal symmetry and consists of elastic isotropic fibers and viscoelastic isotropic matrix. The material is modeled as a transversely isotropic homogeneous viscoelastic medium with effective characteristics. The crack is in the isotropy plane. The ring-shaped fracture process zone at the crack front is modeled by a modified Dugdale zone with time-dependent stresses. The viscoelastic properties of the matrix are characterized using a resolvent integral operator. Use is made of Volterra's principle, the method of operator continued fractions, and the theory of precritical crack growth in viscoelastic bodies. The problem is reduced to nonlinear integral equations. Numerical results are obtained for certain components of the composite, constant volume fractions, and different fracture strengths [ABSTRACT FROM AUTHOR]

This paper is concerned with dynamic problems in fracture mechanics for elastic solids having cracks with contacting faces. The contact problem for a penny-shaped crack with a nonzero initial opening under normally incident harmonic wave is solved by the method of boundary integral equations. The solutions are compared with those that neglect the contact interaction of the crack faces. Results are presented for different values of the initial crack opening [ABSTRACT FROM AUTHOR]

The paper proposes an approach to form (by special heat treatment) a structure and phase composition of martensitic steel that would enhance its ductility in the high-strength state. A correlation is experimentally established between the stability of fracture resistance and ductility in linear and plane stress states. The behavior of the scatterband of the ultimate strength with increase in the degree of ductility is analyzed. The possibility of predicting the ultimate strength from the lower edge of its scatterband is demonstrated with an example of a circular cylindrical shell [ABSTRACT FROM AUTHOR]

The paper discusses the scaled-boundary method as applied to electroelastic problems. As an example, the stress-intensity factor is calculated for a thin rectangular piezoelectric plate with an edge crack [ABSTRACT FROM AUTHOR]

The paper reports on the results from analysis of some nonclassical fracture problems that allow for stresses along cracks. The results have been obtained by the author and his collaborators at the Institute of Mechanics (Kiev) since 1980 [ABSTRACT FROM AUTHOR]

The Wiener–Hopf method is used to find the exact analytical solution of the problem of fracture mechanics for a piecewise-homogeneous isotropic elastic body with shear cracks at the corner point of the interface. The behavior of the stress concentration at the crack tip is established. The growth condition for the cracks is determined and the stability of their equilibrium is analyzed. [ABSTRACT FROM AUTHOR]

The general list of references to the monograph Aleksandr N. Guz, "Eight Non-classical Problems of Fracture Mechanics" Springer Nature, 2021, 390 pp. is presented. This monograph does not have a general list of references but each chapter has its local list of references. [ABSTRACT FROM AUTHOR]

Models in the theory of stability of multiwalled carbon nanotubes in a polymer matrix are justified. Some results on the fracture mechanics of nanocomposites are presented. New areas of research in mechanics suggested by a group of well-known scientists are discussed [ABSTRACT FROM AUTHOR]

An effective approach to the simulation of crack-type fracture is developed based on the semi-analytical finite element method. Algorithms for determining the parameters of fracture strength for elastic bodies of revolution and prismatic bodies under non-stationary force loading of different intensity and duration are proposed. The energy approach based on the application of a special prismatic and ring finite elements with crack under dynamic loading are used to calculate the fracture parameters. The efficiency of the algorithms is estimated. [ABSTRACT FROM AUTHOR]

The stress state of a piecewise-homogeneous isotropic elastic body near a small-scale mode I crack at the corner point of the interface of media is analyzed. The exact solution of the corresponding elasticity problem is obtained using the Wiener-Hopf method. [ABSTRACT FROM AUTHOR]

The long-term fracture of a plate made of an isotropic linear viscoelastic nanocomposite with a mode I crack is studied. A technique for experimental determination of the viscoelastic characteristics of a nanocomposite is employed. The efficiency of the approach proposed is validated considering data obtained in experiments with real composites. It is shown that the shape of kinetic curves and plate durability significantly depend on the fracture parameters and the concentration of nanoinclusions. [ABSTRACT FROM AUTHOR]

The results of solving spatial problems of the fracture of cracked materials under loads acting along cracks are reviewed. A combined approach based on the three-dimensional linearized solid mechanics is used to analyze two nonclassical brittle-fracture mechanisms: (i) fracture of materials with initial stresses acting along cracks and (ii) fracture of materials compressed along parallel cracks. The results of solving nonaxisymmetric and axisymmetric problems for the most typical cases of arrangement of cracks relative to each other and to the boundaries of prestressed bodies are generalized. In the linearized theory, stresses and displacements are expressed in terms of harmonic potential functions. The Hankel transform is used to reduce problems for interacting cracks to the Fredholm equations of the second kind. This approach allows solving problems in a universal general form for compressible or incompressible, isotropic or transversely isotropic homogeneous elastic bodies with an arbitrary elastic potential using the theories of finite and small initial deformations and specifying the material model only at the stage of numerical solution of the general governing equations. New mechanical effects associated with the influence of the initial stresses and crack interaction on the asymptotic distribution of stresses and displacements near the crack tips are analyzed. Resonant effects occurring as the initial compressive stresses tend to the level at which local buckling of the material occurs near the crack are detected. This allows using the combined approach to determine the critical loads for bodies compressed along cracks. Conclusions on the behavior of the stress intensity factors and critical compressive loads with variation in the geometrical and material parameters are drawn [ABSTRACT FROM AUTHOR]

The results of study of two nonclassical fracture mechanisms in composite materials are reported. They are the brittle fracture of bodies with initial (residual) stresses acting in parallel to crack planes and the fracture of bodies compressed along parallel cracks. A combined approach to the study of these mechanisms using linearized solid mechanics is proposed. Three-dimensional problems for prestressed composites with interacting circular cracks are mathematically formulated. Problems for an infinite body with two parallel coaxial cracks and for a half-space with a near-surface crack are solved. A few types of loading (normal, radial shear, torsion) on the crack faces are considered. The effect of prestresses on the stress intensity factors of certain composites is analyzed. The combined approach is used to determine the critical loads for composites compressed along interacting cracks. The effect of the geometrical and material characteristics on the critical loads is analyzed [ABSTRACT FROM AUTHOR]

Theoretical and experimental studies on the deformation and delayed fracture of viscoelastic bodies due to slow subcritical crack growth are reviewed. The focus of this review is on studies of subcritical growth of cracks with well-developed fracture process zones, the conditions that lead to their critical development, and all stages of slow crack growth from initiation to the onset of catastrophic growth. Models, criteria, and methods used to study the delayed fracture of viscoelastic bodies with through and internal cracks are analyzed. Experimental studies of the fracture process zones in polymers using physical and mechanical methods as well as theoretical studies of these zones using fracture mesomechanics models that take into account the structural and rheological features of polymers are reviewed. Particular attention is given to crack growth in anisotropic media, the effect of the aging of viscoelastic materials on their delayed fracture, safe external loads that do not cause cracks to propagate, the mechanism of multiple-flaw fracture of viscoelastic bodies with several cracks and, especially, processes causing cracks to coalesce into a main crack, which may result in a break of the body. Methods and results of solving two- and three-dimensional problems of the mechanics of delayed fracture of aging and non-aging viscoelastic bodies with cracks under constant and variable external loads, wedging, and biaxial loads are given [ABSTRACT FROM AUTHOR]

The transverse axisymmetric vibrations of an elastic stepped cylindrical shell with stable cracks in the inside corner of the steps are studied. The effect of the cracks on the vibrations of the shell is evaluated considering local flexibility and the compliance function, which is related to the stress intensity factor of linear fracture mechanics.Amatrix solution for an arbitrary number of cracks is found. The effect of the location and length of cracks on the transverse axisymmetric vibrations of elastic one- and two-step cylindrical shells is evaluated numerically. [ABSTRACT FROM AUTHOR]

The basic results of establishing the foundations of the mechanics of fracture of homogeneous materials compressed along cracks and inhomogeneous (composite) materials compressed along interface cracks are analyzed. These results were obtained using elastic, plastic, and viscoelastic material models. This review consists of three parts. The first part discusses the basic concept that the start (onset) of fracture is the mechanism of local instability near the cracks located in a single plane or parallel planes. The fracture criterion and the basic problems arising in this division of fracture mechanics are also formulated. Two basic approaches to establishing the foundations of the mechanics of fracture of materials compressed along cracks are outlined. One approach, so-called beam approximation, is based on various applied theories of stability of thin-walled systems (including the Bernoulli, Kirchhoff-Love, Timoshenko-type hypotheses, etc.). This approach is essentially approximate and introduces an irreducible error into the calculated stresses. The other approach is based on the basic equations and methods of the three-dimensional linearized theory of stability of deformable bodies for finite and small subcritical strains. This approach does not introduce major errors typical for the former approach and allows obtaining results with accuracy acceptable for mechanics. The second part offers a brief analysis of the basic results obtained with the first approach and a more detailed analysis of the basic results obtained with the second approach, including the consideration of the exact solutions for interacting cracks in a single plane and in parallel planes and results for some structural materials. The third part reports new results for interacting cracks in very closely spaced (or coinciding, as an asymptotic case) planes. These results may be considered a transition from the second approach (three-dimensional linearized theory of elastic stability) to the first approach (beam approximation). This is how the accuracy of results produced by the first approach is evaluated and the boundary conditions near the crack tip are established in the second approach. [ABSTRACT FROM AUTHOR]

A statistical model describing the coupled deformation and damage of composites with porous transversely isotropic and orthotropic components is proposed. The mechanism of microdamage of such composites is studied assuming that the microstrength of the material is inhomogeneous. A singlemicrodamage is modeled by an empty quasispherical pore forming in place of a microvolume damaged in accordance with the Huber-Mises failure criterion. The ultimate microstrength is assumed to be a random function of coordinates with Weibull one-point distribution density. The method of conditional moments, the damage balance equations, and the Newton-Raphson method are used to set up an algorithm to calculate the effective deformation characteristics of composite materials depending on macrostrains. The effect of the damage of the material on the macrostress-macrostrain relationship is established. The influence of the mechanical characteristics of the material, the volume fraction and porosity of its components, the geometrical parameters of its structure, and the distribution of microstrength on the damage and macrostress-macrostrain curves of the material is analyzed [ABSTRACT FROM AUTHOR]

Three-dimensional problems in the dynamic fracture mechanics of materials with interface cracks are considered as nonclassical problems of fracture mechanics. Physically correct results in fracture mechanics in the case where the interaction of the crack edges must be taken into account are analyzed. The linear (classical) and nonlinear (nonclassical) problems of dynamic fracture mechanics for materials with interface cracks are formulated using the above approaches. A method for solving three-dimensional linear dynamic problems based on boundary integral equations for piecewise-homogeneous materials and the boundary-element method is outlined. This method can be used for incremental solution of nonlinear problems. The method involves the regularization of hypersingular integrals. New classes of three-dimensional linear dynamic problems for circular and elliptic interface cracks are solved. Numerical values of stress intensity factors obtained with the linear problem formulation are the first step toward calculating them in the nonlinear formulation. The first results obtained in solving nonlinear dynamic problems for interface cracks with interacting faces are briefly analyzed [ABSTRACT FROM AUTHOR]

A symmetric problem of elasticity is solved to determine the initial fracture process zone at the corner point of a V-shaped interface in a piecewise-homogeneous isotropic body. The interface is a thin elastic layer joining two isotropic elastic materials. The initial fracture process zone is modeled by lines of discontinuity of normal displacement located at the interface. The exact solution of the problem of linear elasticity is found with the Wiener-Hopf method and then used to determine the length of the fracture process zone. The stress state near the corner point is examined [ABSTRACT FROM AUTHOR]

The role of the fracture process zone near the tip of a mode I crack in a nonlinear elastic body is studied. A boundary-value problem is solved numerically to examine the effect of the fracture process zone on the size and shape of the nonlinear zone near the crack tip [ABSTRACT FROM AUTHOR]

The radiowave photoelasticity method is developed and is justified for use in the fracture mechanics of dielectrics. The damage tensors of a material with microcracks are considered. The basic equations of the method are given. The time-dependence of microcrack density is analyzed. Numerical results are presented and analyzed [ABSTRACT FROM AUTHOR]

A mixed-mode (I + II) crack model with a plastic strip on its continuation under plane strain is proposed. The stress components within the strip are determined from the yield conditions, stress limitation, and relationship between the normal stress components defined via the principal stress state. The crack parameters are analyzed for the Mises yield condition. In the quasibrittle case, the governing system of equations includes stress intensity factors K, K, and T-stresses [ABSTRACT FROM AUTHOR]

Major results on the mechanics of crack propagation in materials with initial (residual) stresses are analyzed. The case of straight cracks of constant width that propagate at a constant speed in a material with initial (residual) stresses acting along the cracks is examined. The results were obtained, based on linearized solid mechanics, in a universal form for isotropic and orthotropic, compressible and incompressible elastic materials with an arbitrary elastic potential in the cases of finite (large) and small initial strains. The stresses and displacements in the linearized theory are expressed in terms of analytical functions of complex variables when solving dynamic plane and antiplane problems. These complex variables depend on the crack propagation rate and the material properties. The exact solutions analyzed were obtained for growing (mode I, II, III) cracks and the case of wedging by using methods of complex variable theory, such as Riemann-Hilbert problem methods and the Keldysh-Sedov formula. As the initial (residual) stresses tend to zero, these exact solutions of linearized solid mechanics transform into the respective exact solutions of classical linear solid mechanics based on the Muskhelishvili, Lekhnitskii, and Galin complex representations. New mechanical effects in the dynamic problems under consideration are analyzed. The influence of initial (residual) stresses and crack propagation rate is established. In addition, the following two related problems are briefly analyzed within the framework of linearized solid mechanics: growing cracks at the interface of two materials with initial (residual) stresses and brittle fracture under compression along cracks [ABSTRACT FROM AUTHOR]

The influence of longitudinal loading on the size and shape of the plastic zone near a crack in an anisotropic body is analyzed. A generalized plane stress state is considered. A relevant boundary-value problem is solved numerically to study the behavior of the main plastic zone at the crack tip, a new plastic zone above the crack, and an additional plastic zone on the lateral surface, which merge to form a single plastic zone [ABSTRACT FROM AUTHOR]

The problem of bifurcational instability of rectangular plates made of fibrous composite materials with reinforcement subject to long-term damage is formulated and solved [ABSTRACT FROM AUTHOR]

We solve a fracture-mechanics problem for a cracked material under polyharmonic loading (waves of various lengths propagating through an elastic material). The frictional contact interaction of the finite crack edges in a plane is analyzed for the case of normal incidence of two harmonic shear waves with different frequencies. The forces of contact interaction and displacement discontinuity are determined. The effect of the wave frequency on the stress intensity factor for different normalized wave numbers is examined [ABSTRACT FROM AUTHOR]

The problem of physically incorrect results due to neglecting the interaction of the crack edges in fracture mechanics is discussed. The cases of dynamic loading, interface cracks, and thermal loading in fracture mechanics are analyzed. The main conclusion is that the majority of results obtained in these areas of fracture mechanics are physically incorrect. [ABSTRACT FROM AUTHOR]

We will solve a fracture-mechanics problem for an elastic material with cracks subject to a polyharmonic load created by longitudinal waves with different wavelengths propagating through the material. The frictionless contact between the edges of a finite-length plane crack under the action of two normal harmonic tension/compression waves with different frequencies is studied. The forces of contact interaction and displacement discontinuity are analyzed. The effect of the wave frequency on the stress intensity factor is examined for different normalized wave numbers. [ABSTRACT FROM AUTHOR]

Linearized solid mechanics is used to solve an axisymmetric problem for an infinite body with a periodic set of coaxial cracks. Two nonclassical fracture mechanisms are considered: fracture of a body with initial stresses acting in parallel to crack planes and fracture of materials compressed along cracks. Numerical results are obtained for highly elastic materials described by the Bartenev–Khazanovich, Treloar, and harmonic elastic potentials. The dependence of the fracture parameters on the loading conditions, the physical and mechanical characteristics of the material, and the geometrical parameters is analyzed [ABSTRACT FROM AUTHOR]

The influence of the length of a mode I crack on the plastic zone in an anisotropic body under hard loading is studied. The case of a generalized plane stress state is examined. A boundary-value problem is solved numerically to study the behavior of the main plastic zone at the crack tip, the additional plastic zone on the lateral face of the body, and the merged plastic zone [ABSTRACT FROM AUTHOR]

A modified δc-model is used to study the limiting state of an orthotropic plate weakened by a periodic row of collinear cracks and satisfying a general failure criterion. The failure mechanism of the plate is analyzed.Astudy is made of the effects of the degree of orthotropy, the biaxiality of external loading, and the geometrical parameters on the fracture process zones at the crack tips and the limiting state of the plate. The safe loading of an orthotropic viscoelastic plate with a periodic row of collinear cracks is examined. The effect of the rheological parameters on the safe-load region is studied [ABSTRACT FROM AUTHOR]

A system of boundary integral equations that allows evaluating the displacement and stress fields for an interfacial crack under harmonic loading is presented. Expressions for the integral kernels are obtained. A numerical solution for a penny-shaped crack between steel and aluminum half-spaces under normally incident compression-rarefaction wave is given [ABSTRACT FROM AUTHOR]

The growth of a straight mode II crack in a viscoelastic orthotropic plate is examined. The plate material is modeled by a viscoelastic anisotropic medium. The shear displacement in the fracture process zone is determined as a function of time using the corresponding elastic solution, the Volterra principle, and the method of operator continued functions. The time dependence of the crack length is constructed as integral equations of three phases of stable growth. The solution of these equations gives kinetic curves [ABSTRACT FROM AUTHOR]

The plastic zone at a crack tip in a finite anisotropic body is studied. A boundary-value problem is formulated in terms of the components of the covariant displacement vector for small strains. Particular attention is given to the case of plain strain. In this case, a numerical solution is found for a long rectangular body with a central crack under tension. As a result, conditions for the occurrence and development of a plastic zone at the crack tip are established. A plastic zone on the lateral surface of the body is discovered. How both zones extend and coalesce is elucidated. The effect of anisotropy on the occurrence of a plastic zone is evaluated [ABSTRACT FROM AUTHOR]

The Wiener-Hopf method is used to find a solution to a symmetric problem that gives a criterion for the onset of growth of long shear cracks emanating from a corner point on the boundary of a hole and filled with a plastic material [ABSTRACT FROM AUTHOR]

The Wiener-Hopf method is used to study, under the conditions of plane strain, the direction of development of a thin fracture process zone at the tip of an interfacial crack in a piecewise homogeneous isotropic elastoplastic body. The zone is modeled by a straight line of tangential displacement discontinuity that emerges from the crack tip at an angle to the interface. The dependences of the zone length and the angle on the load and other parameters of the problem are investigated [ABSTRACT FROM AUTHOR]

The problem of contact interaction of the opposite faces of a linear crack under a normally incident harmonic tension-compression wave is numerically solved by the Galerkin method with piecewise-linear continuous elements. The dependence of the stress intensity factor (opening mode) on the wave number is investigated [ABSTRACT FROM AUTHOR]

The semianalytic finite-element method is used to develop a method for solving problems of creep and continuous fracture of complex spatial bodies. The method allows modeling the variation of the stress-strain state during creep, accompanying accumulation of dispersed microdamages, and development of macroscopic effects—continuous fracture process zones. The growth of a continuous fracture process zone is modeled. A criterion is formulated for determination of the applicability limits of continuum damage mechanics. The method is exemplified by the problem of deformation and continuous fracture of a gas turbine blade [ABSTRACT FROM AUTHOR]

The Dugdale crack model is generalized to the case of plane strain. The governing equations are set up to determine the stresses in the plastic zone. Numerical results from specific problems are analyzed and compared with those for plane stress state and other cases. A relationship between the crack model and KI- T theory is established in the case of small-scale yielding at the crack tip [ABSTRACT FROM AUTHOR]

A two-level fracture model of composites with cracks under compression is proposed. Fiber-reinforced laminated panels with a hole are considered. The panels are compressed along the fibers so that two cracks propagate from the hole boundary at a right angle to the loading direction. The fracture mechanism is analyzed at two levels. The first level is the compression-induced stress concentration at the tip of a finite-thickness crack filled with a fractured material. At this level, the theory of elasticity of linear orthotropic body is used. The second level is compression fracture at the crack tip. The analysis performed at this level involves the three-dimensional linearized theory of stability of solids, considering microcracks in the interface between the fractured and intact materials, and the exact solution describing the compression-induced instability of the cracked interface. The second level is where results obtained by the author are used. Thus, the approach proposed employs the theory of elasticity of linear orthotropic body and the three-dimensional linearized theory of stability of solids to analyze a specific mechanism of fracture [ABSTRACT FROM AUTHOR]

A new alternative approach to fracture problems for materials and structural elements with cracks is set out. It is based on the mechanism of local instability near defects. The approach is used to study the fracture of materials compressed along interacting cracks and the fracture of thin structural members with cracks under tension with allowance for local buckling. [ABSTRACT FROM AUTHOR]