Mechanics of Solids最新文献

An review of the temperature dependences of the elasticity characteristics of cubic crystals of simple substances is presented. It is shown that the general trend is a decrease in elastic moduli E, G, and B with temperature due to the weakening of interatomic bonds caused by thermal expansion of the crystal lattice. However, there are also anomalous dependencies, such as an increase in the shear modulus G with temperature, observed for BCC crystals of vanadium V, niobium Nb, tantalum Ta, and FCC crystals of palladium Pd, platinum Pt. A common feature for the cubic crystals considered, except for BCC chromium Cr, is an increase in Poisson’s ratio ν with temperature. The factor of elastic anisotropy A also shows a general upward trend, but for some crystals, BCC V, Nb, Ta, and FCC Al, local minima are observed, and for BCC Cr and FCC Pd, maxima are observed.

The paper presents fundamental principles of the mathematical theory of plasticity for spatial states, corresponding to an edge of the Coulomb–Tresca prism, when the flow of a body is governed by generalized associated flow rule. A detailed analysis is provided for the relations resulting from the generalized flow rule for an isotropic body, associated with the Tresca yield condition, and restricting the freedom of plastic flow to the minimum extent for the specified states. It has been shown that the spatial relations of plasticity theory formulated by A.Yu. Ishlinskii in 1946 follow from the generalized version of the flow theory. It has been established that the constitutive relations of Ishlinskii for the states on the edge of the Coulomb–Tresca prism express the commutativity of the stress and plastic strain increment tensors. An additional tensor symmetry relation is obtained by applying this commutativity relation.

On the basis of one- and two-parameter failure criteria of mixed mode loading of I+II crack-like defect of adhesive layer, the critical value of J-integral under normal compression is estimated. The additive decomposition of the J-integral into energy densities and consideration of the sign of hydrostatic pressure are assumed to be valid. It is shown that when the critical value of the J-integral of mode II exceeds significantly the critical value of the J-integral at normal rupture, the critical value of the J-integral at normal compression is much inferior to the analogous characteristic at compression.

The evolution of temperature stresses under the conditions of the assembly process operation of hot fitting a thin disk onto a round shaft is calculated within the framework of the theory of temperature stresses. The materials of the mating assembly parts are considered elastic-plastic with a yield strength dependent on temperature. The moments of time and places of origin of viscoplastic flows in the materials of the assembly elements, the features of the development of plastic regions, their attenuation and collapse are tracked. The level and distribution of residual stresses over the assembly parts are calculated.

The technologies of construction and major repairs of main pipelines provide for the replacement of pipes with anchor devices and reinforced concrete weights with three-layer pipes consisting of a steel pipe, an outer continuous weighting reinforced concrete coating and an insulating layer located between them. This three-layer pipe is designated as a concrete-coated pipe in scientific and technical literature. When such pipes are used in difficult natural and climatic conditions, they float. Floating sections of the gas pipeline are classified as emergency and are taken out of operation. In this article, the problem of the stress-strain state (SSS) of a gas pipeline section in a swamp is stated and solved using the finite element method after the following changes were made to its design: pipes with reinforced concrete weights are replaced with concrete-coated pipes; G-shaped compensators are installed at the ends of the gas pipeline section in the swamp. For a section of the gas pipeline in a swamp, at the ends of which compensators have not yet been installed, the limit values of the operating parameters were found that determine the change in the shape of the pipe bend, in which the deflection arrow becomes directed upwards, and it can lead to the gas pipeline floating up. In the flooded underwater part of the gas pipeline section in a swamp with compensators installed at its ends, when the pipe bends, the deflection arrow remains directed downwards, there are no prerequisites for its floating up. The gas pipeline along the entire length of the section is stretched in the longitudinal direction, while in the flooded underwater part there is a uniform stretching of the pipe. At the ends of the calculated section, the values of the tensile-compressive stresses of the pipe in the longitudinal direction are determined from the longitudinal forces specified by the boundary conditions.

Using the example of the matrix of elastic constants of an isotropic material, it is shown that the Young’s modulus, shear modulus, volume modulus, and Poisson’s ratio can take any real values. In this case, the positive definiteness of the matrix of elastic constants is not mandatory, as is traditionally assumed. The positivity of the specific strain energy also occurs when the matrix of elastic constants is not positive definite. It is sufficient for the invertibility of the relations of Hooke’s law to require the non-degeneracy of the matrix of elasticity constants. Graphs of Young’s modules, volume and Poisson’s ratio depending on the ratio of Lame constants are given.

The paper presents the results of a comprehensive study of fracture, filtration and sand production processes in weakly cemented reservoirs of one of the gas condensate fields of the Arctic shelf of Russia. A modified multidisciplinary scientific method was developed and implemented to solve the problems of ensuring safe operation of wells, validating effective modes of their operation and reducing the risks of sand production. The research methods are based on multilateral study of core material properties by means of geomechanical modeling of mechanical and filtration processes in the vicinity of wells, Thick-walled cylinder type tests to study sand production processes in wells, scanning electron microscopy, micromineralogy, computed tomography and digital core analysis. Special emphasis was placed on the analysis of changes in reservoir structure as a result of sand production processes, taking into account the mineral composition of the matrix and the dislodged sand. Experimental results allowed to determine for the considered field: a) evolution of deformation and filtration properties of rocks in the near-wellbore zone; b) values of critical stresses leading to wellbore wall failure; c) type and nature of rock failure; d) parameters of sand production processes and mechanisms of associated reservoir matrix failure; e) reservoir properties of rocks. Based on the research results, the optimal parameters for safe and efficient well operation have been determined, including allowable drawdown to reduce the sand production risks and maintain wellbore stability; the nature of well contour failure and the risks of damage to downhole equipment; and the optimal characteristics of downhole filters. The results of this research are intended to contribute to the development of technologies for creating new solutions aimed at improving the efficiency of hydrocarbon production, reducing the risks of sand production and wellbore wall failure, deterioration and breakdown of downhole equipment.

The excitation of a harmonic wave in a semi–infinite incompressible hyperelastic one-dimensional rod (material according to the Mooney-Rivlin model) leads to the formation and propagation of shock wave fronts arising between half-waves of the initial harmonic wave moving at different speeds. Shock wave fronts lead to the absorption of slow-moving parts by faster ones and, consequently, reduce both kinetic energy and elastic deformation energy with the corresponding release of heat. The explicit Lax–Wendroff difference scheme in combination with the finite element method is used to solve geometrically and physically nonlinear equations of motion.

Currently, there are two theories of metal plasticity in solid mechanics: the classical mathematical theory of plasticity [1, 2] and the physical and mathematical theory of plasticity [3]. Both theories are used to solve applied problems of plasticity, in particular, in the development and improvement of technological processes of metal pressure treatment [5–7]. This paper examines the relationship between the above-mentioned theories. Based on the analysis of the initial postulates and principles, the disadvantages and advantages of the theories for solving problems of theoretical design of technological processes of metal pressure treatment are identified. The analysis allows us to assert that the physical and mathematical theory of plasticity is a more general theory, which includes the mathematical theory of plasticity as a special case and which does not have the disadvantages of the latter. It follows from this that the physical and mathematical theory of metal plasticity is an important scientific achievement in solid mechanics.

A procedure for regularization of the Stieltjes integral in the case of a common breaking point for integrand functions is described. Using this procedure, it is possible to determine the Stieltjes integral, which represents mechanical work in accordance with the law of conservation of energy. The physical validity of the obtained results is confirmed by a number of examples. In particular, the regularization procedure makes it possible to calculate the energy dissipated during an instantaneous change in the state of the elastic suspension.