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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 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]

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]