A B S T R A C TOne of the problems of fracture mechanics is the prediction of the propagation of cracks in solids. Thepresent paper deals mainly with linear fracture mechanics which owes its origin to the works erA. A. Griffith [1,2] and studies the development of cracks under sufficiently low loads when the behaviour of the material within a region sufficiently remote from the edges of cracks may he regarded as linearly elasti~ At present, linear fracture mechanics [3] is restricted mainly to special kinds of loading geometry, with the crack extending rectilinearly (in a plane case) or in its plane (in a three-dimensional case). The main problem here is to establish a relationship between the dimensions of cracks and the loads applied. Within the framework of linear fracture mechanics the fracture itself and other non-linear phenomena that precede it are assumed to take place only within local regions which are small compared to the dimensions of cracks. The possibility that such a situation exists is associated with the fact that when the crack dimensions are sufficiently large the characteristic dimension of the end region is fully determined by a certain intrinsic dimension of the material structure. Therefore, if the material does not exhibit time dependency, the state of the end region at the moment of rupture becomes fully independent of the loads applied and the geometry of the solid, i.e. autonomous. The notion of autonomy [4] leads to the formulation of this theory as one of limit equilibrium.If the conditions of rectilinear extension of the crack (or those of the crack extension in its plane) are disturbed, there arises a problem of determining not only the dimensions of the crack, but also the path of the crack extension under such conditions of loading that a slow, quasi-static crack development is possible. This problem can be actually subdivided into two: (1) Criteria for the determination of the dimensions and paths of the crack extension, and (2) Expressions for the characteristics of the stress-strain state which are constituents of these criteria through the geometry of solid with cracks and the loads applied.As regards (1), there have been many assertions, and the connections between them are not quite clear, at present. The first of the suggested criteria, namely that of local symmetry for the plane problem formulated by Barenblatt and Cherepanov [5,6] and by Erdogan and Sih [7] can be within certain limits substantiated and generalized for the threedimensional case. The guiding principle here is the treatment of the theory of cracks from the standpoint of the method of inner and outer expansions or that of singular perturbations [8]. The concept of the stress intensity factor which is basic in linear fracture mechanics is decisive in matching inner and outer expansions to find the main term of the asymptotic solution of the complete problem. Actually the construction of the theory of equilibrium cracks [4] implicitly employs this technique for a certain specific model. More explicit indicat...
Two‐parameter analysis of auxetics among the cubic crystals is proposed. A brief analysis of the equivalence of this two‐parameter consideration and other approaches is given. The main result of this paper is the classification of partial auxetics with a single dimensionless complex, which is composed of the crystals elastic compliances. The auxetic surface separates the regions with negative and positive Poisson's ratio. The character of its changes with change of the dimensionless complex is determined. The critical value of the complex where a topological rearrangement of the auxetic surface occurs is obtained. The distribution of partial auxetics in zones with different values of the dimensionless complex was found. The sign of another dimensionless parameter influences the location of a region with negative Poisson's ratio relative to the auxetic surface.
View of the auxetic boundary for a cubic crystal when the dimensionless elastic parameter is close to the critical value Πnormalc≈0.745.
A problem of parameters identification for embedded defects in a linear elastic body using results of static tests is considered. A method, based on the use of invariant integrals is developed for solving this problem. A problem on identification the spherical inclusion parameters is considered as an example of the proposed approach application. It is shown that the radius, elastic moduli and coordinates of a spherical inclusion center are determined from one uniaxial tension (compression) test. The explicit formulae expressing the spherical inclusion parameters by means of the values of corresponding invariant integrals are obtained for the case when a spherical defect is located in an infinite elastic solid. If the defect is located in a bounded elastic body, the formulae can be considered as approximate ones. The values of the invariant integrals can be calculated from the experimental data if both applied loads and displacements are measured on the surface of the body in the static test. A numerical analysis of the obtained explicit formulae is fulfilled. It is shown that the formulae give a good approximation of the spherical inclusion parameters even in the case when the inclusion is located close enough to the surface of the body.
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