Mechanics of Solids最新文献

The article studies the limit state of rods made of ideal rigid-plastic nonuniform material under the action of variable external pressure linearly changing along the generatrix of the rod. The main relations describing the limit state of nonuniform rods are considered. The characteristics of the studied relations and relations along the characteristics are determined. Integrals of the main relations have been obtained under various conditions of the limiting state of the rod. The problem of the limit state of a nonuniform prismatic rod with a rectangular cross-section under external pressure is considered under the assumption that the yield strength depends linearly on the ordinate of the point.

The properties of metamaterials with negative and positive Poisson’s ratio (with an auxetic structure based on a cell in the form of a concave hexagon or a conventional honeycomb structure of convex hexagons) to resist penetration by a rigid spherical striker along the normal have been experimentally studied. Samples of metamaterials, including those with a chiral structure, are made of e‑PLA plastic using a 3D printer. Auxetic and non-auxetic samples, approximately equal in mass, have been compared by their ability to reduce the kinetic energy of penetrating strikers in conditions of cells filled with air and gelatin. We have established a fact of a significant increase in penetration resistance when auxetic chiral samples are filled with gelatin compared to those filled with chiral non-auxetics. In experiments with chiral metamaterials filled with gelatin, a deviation of the striker motion direction after leaving the sample being penetrated from the approach direction (normal to the side surface) has been recorded.

The paper presents a mathematical model of oscillations of a preheated orthotropic plate reinforced with stiffeners. The paper is based on a continuum model of a geometrically irregular plate. Equations, boundary and initial conditions are derived from the Ostrogradsky-Hamilton variational principle. The kinematic hypothesis of S.P. Timoshenko is used. The analysis of the natural frequencies of plate oscillations is performed for various geometric and thermomechanical parameters.

Many research groups are studying the strength properties of cancellous bone in uniaxial compression experiments. The effective modulus of elasticity is determined by the linear section of the diagram under the assumption that the specimen is in a uniaxial stress state. Obviously, this is correct only in the case of compression of long specimens, whose length in the direction of load application is significantly greater than the transverse dimensions. Most researchers compress short cubic or cylindrical specimens with an aspect ratio of 2 to 1. It is also noted that under uniaxial compression, tissue in the grip area is damaged, which leads to an underestimation of the calculated effective modulus of elasticity by 20–40%. It is believed that errors in measuring the effective modulus of elasticity can be avoided if the deformation is not measured directly, evaluating only the displacement of the movable crosshead, but a contact or contactless extensometer is used or the ends of the specimens are protected from destruction using end caps. At the first stage of the work, the influence of the relative height of the specimen on the effective modulus of elasticity of the spongy bone of cattle calculated according to the rod theory was studied (a total of 90 bone specimens were tested). At the second stage, the modulus was assessed with direct application of load to the specimen, as well as with gluing plastic and aluminum plugs to its end (a total of 75 bone samples were tested). Regression dependencies were constructed linking the mineral density of the bone and its modulus of elasticity.

It was revealed that when the relative height of the specimen is not less than 5 units, it ceases to affect the modulus of elasticity. It was shown that during uniaxial compression of such long specimen, the method of their loading does not affect the modulus of elasticity. It was found that the relationship between the effective modulus of elasticity and mineral density does not depend on the method of loading the specimen, provided that its relative height is not less than 5 units.

In this article, a step was made to develop a standard for conducting uniaxial experiments on bone tissue compression aimed at calculating the effective modulus of elasticity. It is shown that when planning such experiments, it is necessary to prepare specimen with a relative height of at least 5 units. This allows for the correct calculation of the effective modulus of elasticity of cancellous bone according to the rod theory, using data on the displacement of the upper grip of the testing machine.

The paper considers the problem of longitudinal and transverse bending of the multilayered concrete rods of constant cross section under the quasi-static loads. It is assumed that concretes are deformed linearly at deformations below the elastic limit, and nonlinearly quasi-elastically above it. In the area of nonlinear deformation, the correlations between strain and deformation are taken in the form of the second-order polynomials with different coefficients for different grades of concrete. It is supposed that there is a uniaxial strain condition, and in the compression area all layers of the rod are elastically deformed, while in the tension area the layers can be in the areas of elastic, nonlinear quasi-elastic deformation and include the boundary of these two areas. The presented analytical correlations are obtained to determine the distribution of displacements, deformations, forces, and the position of the neutral line in the case of a statically determinable problem of transverse bending of a hinged rod. An algorithm to determine the possible external loads is given for each of the possible deformation configurations in the rod layers.

The present study deals with the construction of an asymptotic model of propagation of non-stationary waves in thin shells of revolution under the action of end impact loads of the bending type. The developed asymptotic methods for solving boundary value problems for the components of the stress-strain state that are the main ones for the considered type of waves, namely the bending component according to the Kirchhoff-Love theory and the hyperbolic boundary layer, are described. The asymptotic methods are based on various types of expansions in power series in a small parameter of thinness of the wall depending on the values of the indices of variability and dynamicity. In this case, integral Laplace transforms in time and Fourier transforms in the spatial coordinate, methods of frontal asymptotics, expansions in special functions are used. Calculations performed on the example of a spherical shell have shown the efficiency of the developed methods.

The article considers the application of a singular fractional-power rheological model in modeling creep and long-term failure of a composite tensile rod in an active medium. The singular fractional-power model contains a natural mechanical characteristic – the short-term strength limit at the corresponding temperature. A rod of rectangular cross-section consists of three parts symmetrically located along the width and connected to each other with ideal adhesion without slipping. An additional factor affecting the studied rod system is the influence of the active medium, and a non-classical diffusion process is considered, taking into account the presence of the medium in the material in both free and bound states. Based on the kinetic theory of  Yu.N. Rabotnov with two structural parameters, the resulting system of equations for determining the dependences of stresses and damage on time during creep is obtained. A criterial assessment is proposed for determining the time to failure of both individual parts and the entire considered rod system as a whole.

The quasi-static behavior of an elastically reinforced ingomogeneous plate under compression is investigated. The problem of the existence of a quasi-static deformation process is considered based on the solution of an extremal problem. A condition is obtained, upon violation of which, it is not necessary to study the plate bending based on the selected mathematical model. For two particular cases of changes in the material properties, an analysis of the influence of non-homogeneity parameters on the region of quasi-static deformation described by the solution of a variational problem is carried out.

The influence of stresses on diffusion is recognized, along with diffusion’s role in the viscous deformation of solids. The interconnection between interdiffusion and deformations in metallic alloys and steels significantly affects the durability of machine components exposed to harsh conditions with substantial temperature and force. In such instances, diffusion facilitates the transportation of alloying elements from the surface layer, impacting the intensity of corrosion and corrosion cracking. Laws correlating diffusion flows to chemical potential gradients can be related to various diffusion reference frames, determined by the base experiment used or the convenience of establishing the boundary value problem. In the related equations of interdiffusion in a deformable solid, we must consider that diffusion happens in a local material volume transported by the convective velocity, and that diffusion is described in a local diffusion frame of reference moving relative to the material. A decision must be made regarding convective velocity and diffusion reference frame (decomposing the material motion into convective and diffusive parts). Within the linear thermodynamics of irreversible processes, a related system of equations is set for a multicomponent medium, where balance equations for composition variables are considered, and stress and strain tensors are introduced for the medium on the whole. Two diffusion descriptions are considered: one assumes a diffusion reference frame frozen into a local material volume, and the other involves a system of markers, small inert particles, moving relative to the material due to unbalanced diffusion flows. Both methods are employed in basic diffusion pair experiments to determine diffusion coefficients. For each of the diffusion descriptions – “material” and “marker” – within the process coupled with viscoelastic deformation, the thermodynamically resolved relations are derived for two-component and three-component metallic alloys. To compare the associated models, a one-dimensional problem is proposed. The perturbation method is applied, yielding the dependency of the relaxation time spectrum on the perturbation wavelength. The values of the effective interdiffusion coefficients align with the inclined asymptotes of these dependencies, and the effective viscosity coefficients match the horizontal ones. The dependency of these effective coefficients on the diffusion and viscoelastic properties for an austenitic alloy Fe65-Cr20-Ni15 at high temperature is examined. Overall, the marker description of interdiffusion provides more information and it is more convenient for setting boundary value problems with boundary diffusion of components.

The present paper deals with problems of propagation of coupled time-harmonic waves of temperature increment, translational and spinor displacements in a semi-isotropic thermoelastic solid. The governing couple partial differential equations of semi-isotropic thermoelastic solids are revisited. Dispersion equations for the wavenumbers of plane harmonic coupled thermoelastic longitudinal waves (bicubic equation) and transverse wave (biquartic equation) are obtained and solved. The roots of mentioned algebraic equations are calculated and normal wavenumbers are discriminated. The spatial polarizations of coupled time-harmonic thermoelastic waves have been studied. It is shown that the transverse plane wave carrying the two spatial polarizations in fact does not exist and can not be observed in semi-isotropic micropolar media due to existence of direct and mirror wavemodes.