Based on an elastoplastic model with a second-order gradient, the nonlinear dynamics and collapse of deformation of a one-dimensional rod under tension are considered. In fracture mechanics, interest in collapses is associated with the possibility of modeling material fracture (rupture) without involving empirical laws. Sufficient conditions for wave collapse are obtained for localized and periodic waves on the ascending branch of the material diagram σ(ε) in the quadratic approximation σ(ε) = Eε + κε² – βε′, where the homogeneous state of the rod is stable with respect to linear perturbations. On the descending branch of the diagram, which corresponds to deformation softening, dispersion instability occurs in the linear approximation. For this case, sufficient conditions for collapse for localized and periodic waves are also obtained in the quadratic approximation. A sufficient condition for the existence of wave collapse of deformation for an arbitrary form of the diagram σ(ε) is obtained. The conditions for the existence of collapse for all the listed cases include the condition of non-positivity of the energy integral, H ≤ 0. For this case, an exact solution describing the deformation collapse is constructed in the quadratic approximation for σ(ε). The solution describes a strongly inhomogeneous non-stationary structure of the deformation localization region that arises from an initially smooth perturbation with negative energy H and ends with collapse. The resulting singularity is non-integrable.

The creation of large sealed structures in Earth orbit for crew is the next logical step in space exploration. As it seems now, the most realistic way to create such structures is to prepare a prepreg with a long storage life on Earth, compactly pack such a prepreg in a container and send it into orbit. In orbit, the prepreg is deployed and the curing reaction is initiated. After the completion of the prepreg curing reaction, a durable sealed body is obtained, which can be filled with air at atmospheric pressure and used for the crew. This paper considers the creation of a large (100 m long and 10 m radius) thin-walled structure by inflating a prepreg with an uncured epoxy matrix in low Earth equatorial orbit and subsequent curing of the prepreg under solar heating. The calculation of the curing reaction kinetics is made on the example of four possible types of binders: Barnes, Gurit, EDT-10 and Narmco 5208 with different curing rates and temperature ranges. The model takes into account the reflective/absorptive properties of the outer surface of the structure, orientation to the Sun, heat capacity of the material, heat transfer through the shell and re-radiation through the internal cavity of the structure. Temperature fields in the structure wall as a function of time in orbit after inflation are obtained. Dependencies of the curing reaction kinetics on the surface of the structure in flight are obtained. It is shown that for certain flight conditions and material properties, it is possible to select types of binders that can cure within a reasonable flight time in orbit.

Within the framework of refined bending theory, a coupled problem of thermomechanical inelastic behavior of flexible reinforced shallow shells under dynamic loading is formulated. Geometric nonlinearity is taken into account in the Karman approximation. The deformation of the composite phase materials is described by a viscoelastic-viscoplastic body model under thermal influence. In the transverse direction of curved panels, the tangential displacements of their points and temperature are approximated by high-order polynomials. The solution of the essentially nonlinear problem is constructed using an explicit numerical scheme. The isothermal and non-isothermal viscoelastoplastic and viscoelastic-viscoplastic bending behavior of fiberglass cylindrical panels having a rectangular elongated shape in plan is analyzed. The thermomechanical behavior of shallow shells with orthogonal 2D reinforcement structure and with spatial 4D structure is compared. The structures are transversely loaded with high-intensity pressure for a short time. It is shown that to perform adequate calculations of the inelastic dynamics of curved panels and to determine their residual deformed state, the refined bending theory should be used, rather than the traditional non-classical Ambartsumyan theory. It is demonstrated that the calculation of the residual deformed state of fiberglass panels must be carried out taking into account the thermal response in them. It is shown that neglecting the sensitivity of the plastic properties of composite materials leads to a significant (even several times) overestimation of the intensity of residual deformations of the composite components, as well as to a significant distortion of the shape and magnitude of residual deflections. It is demonstrated that even in relatively thin shallow shells, replacing the cross-ply structure with a spatial reinforcement structure with the same fiber consumption can lead to a decrease in the residual deformed state of the composite phases and the magnitude of residual deflection. It is shown that after the attenuation of transverse vibrations, shallow shells acquire a corrugated shape; the resulting folds are oriented in the longitudinal direction.

Problems of rational design of reusable power actuators with a working body in the form of a rod made of shape memory alloy and a displacement body in the form of an elastic rod or coil spring are considered. The main attention is paid to the limitations imposed on the material and shape of the displacement body, its linear-elastic behavior, and the requirement of controllability of the power actuator operation by changing the temperature of the working body without any other mechanical influences. The latter condition is associated with the need to implement a closed two-way shape memory effect in the power actuator at the working and idle stroke stages. Through a qualitative study of the system consisting of differential and algebraic equations describing the idle stroke of the power actuator, it is established that the controllability condition reduces to a unique continuous monotonically decreasing dependence of the initial phase-structural deformation of the working body on the ratio of the elastic stiffnesses of the working body in the austenitic state and the displacement body. Analytical expressions are found for the minimum value of the ratio of the longitudinal dimensions of the displacement rod or coil spring to the length of the working rod made of SMA; the minimum value of the ratio of the cross-sectional areas of the working SMA rod and the displacement rod; the minimum value of the ratio of the volumes of the displacement body (rod or coil spring) and the working SMA rod. It is established that in the case of a working rod made of titanium nickelide and a displacement body made of structural metals or alloys, the minimum possible values of the above ratios are too large to correspond to rational design of the power actuator. It is proposed to switch to manufacturing displacement bodies from elastomers, polymers, or composites with a polymer matrix.

The Biot parameter is included in the formula for calculating effective stresses and shows what part of the pore pressure should be taken into account when calculating stresses in the soil skeleton. Therefore, when assessing the stress-strain state of a water-saturated rock mass, it is necessary to use adequate values of the Biot coefficient. The literature widely presents experimental methods for determining the Biot coefficient, both static and dynamic. Experimental methods, as a rule, are used under the assumption of isotropy of rocks or structural anisotropy caused by the geometry of voids. In this case, the material of the soil skeleton is homogeneous and isotropic. The computational method developed by the authors of this article for determining the tensor Biot parameter, based on asymptotic averaging of the equilibrium equation of a fluid-saturated porous medium within the framework of linear elasticity theory, can be practically useful. The computational method can be applied to inhomogeneous and anisotropic soils in which the skeleton material is inhomogeneous. A mathematical justification of the methodology for calculating the Biot tensor and elastic moduli of porous materials is presented. The computational methodology is applied to calculations of the Biot parameter and elastic moduli of various types of rock soils — limestone, dolomite, hyaloclastite, basalt. 3D models of real structures of rock samples built from X-ray computed tomography images were used for the calculations. A comparison of the results of 3D calculations of the Biot coefficient and Young’s modulus with the results of experimental determinations of these properties by the ultrasonic method is presented. The calculation and experimental results coincided with good accuracy. A study of the dependence of the Biot coefficient and Young’s modulus on porosity, pore shape and elastic properties of the skeleton material is conducted. These dependencies can be used in numerical modeling of deformation of water-saturated porous soils under load or during fluid pumping.

A mechanical-mathematical model of deformation of a five-layer plate asymmetric in thickness is proposed. The formulation of the boundary value problem for bending of this plate under the action of a uniformly distributed load is presented. The central and outer layers are assumed to be load-bearing, thin, and of increased stiffness. They bear the main part of the force load. The deformation of the load-bearing layers is described by Kirchhoff’s hypotheses. Two relatively thick rigid cores are used to connect them. The cores provide redistribution of forces between the layers and are used for protection against undesirable external influences — temperature, radiation. The deformation of the cores is described by Timoshenko’s hypotheses, i.e., relative shear — additional rotation of the normal to the middle surface of the layer — and the work of tangential stresses are taken into account. The plate is incompressible in thickness. Using the Lagrange variational method, a system of four ordinary differential equilibrium equations of the considered five-layer plate is obtained. The sought functions are: plate deflection, radial displacement of the middle plane of the central load-bearing layer, and two relative shears in the cores. The system is transformed into one fourth-order inhomogeneous differential equation for the shear in the upper core. The solution of the corresponding homogeneous equation is reduced to solving two modified second-order Bessel equations. The general solution of the inhomogeneous equation is written in final form for the case of a uniformly distributed load. Formulas for calculating the required displacements and relative shears under boundary conditions of rigid clamping of the plate contour are presented. The dependence of displacements on the thickness asymmetry of the load-bearing layers and cores in a plate made of D16-T — fluoroplastic — D16-T — fluoroplastic — D16-T materials is numerically investigated.

The main goal of this work is to study the vibration-absorbing properties of barriers in the form of homogeneous plates placed in an elastic medium simulating ground motion and subjected to plane harmonic waves. The method of compensating loads, which ensures correct consideration of various variants of plate fixation, is applied to solve the problem. The solution to the problem of motion of an infinite barrier in the ground is found, and then the boundary conditions at given points are satisfied using compensating loads. This approach allows obtaining plate displacements and determining the vibration absorption coefficient depending on the frequency of the incident wave. As examples, various methods of fixing the barrier are considered, such as hinged support on both sides, rigid clamping and their various combinations, as well as a variant with rigid clamping and a free edge. Special attention is paid to parametric analysis, including the study of the influence of plate thickness and mechanical properties of various materials on the efficiency of vibration absorption. As examples, both traditional materials (steel, aluminum) and modern alloys with enhanced dissipative characteristics, for example, steel 01Yu5T, are considered. The obtained dependencies allow identifying optimal combinations of thickness and material to achieve minimum values of vibration accelerations in the ground medium after interaction with the barrier. The research results can be used in the design of engineering structures and protective screens designed to reduce the negative impact of vibrations from transport, industrial and natural sources. The developed approach provides a theoretical basis for choosing effective design solutions in vibration and seismic protection problems.

Cylindrical and spherical capsules are used in autonomous crack healing processes in composite materials as containers containing the healing agent. In the shells of such capsules, significant stress concentration occurs under loading. Using the finite element method, dependences of the stress concentration factor on the relative elastic modulus of the capsule material for cylindrical and spherical capsules are obtained. With an increase in the relative elastic modulus of the capsule shell, the stress concentration factor on the inner surface of the shell increases, while on the surface of the cavity containing the capsule, it decreases significantly. An assessment of the influence of the healing agent filler of the capsule on the stress concentration factor is performed. For capsules filled with healing agent, with an increase in the relative elastic modulus of the capsule shell, the stress concentration factor on the cavity surface in the matrix also decreases. An increase in the relative elastic modulus of the shell of a filled capsule leads to a significant decrease in the stress concentration factor on the inner surface of the capsule. For a cylindrical capsule, the influence of a change in the elastic modulus of the healing filler on the stress concentration factor in the capsule and matrix is investigated. The analysis of mutual influence of capsules is performed on a characteristic cell containing two capsules, with variation of the distance between the centers of the capsules. For both types of capsules, calculations are performed under uniaxial tension parallel to the axial line connecting the centers of the capsules. At a small distance between the centers of the capsules, the stress concentration factor decreases and increases with increasing distance between the centers of the capsules to a value corresponding to a single capsule. For cylindrical capsules, tension in the direction perpendicular to the axial line is also considered. The mutual influence of capsules in this case leads to significantly higher stress concentration factor values on the inner surface of the capsule than for a single capsule. Estimates of the volume concentration of healing capsules in the material are obtained. The stress concentration when using spherical capsules is lower than when using cylindrical ones, which can lead to a decrease in the efficiency of capsule rupture during crack healing.