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Results of theoretical and experimental investigations of physical and mechanical properties of a heterogeneous material based on the TiB ceramics and VT-6 metallic alloy obtained by means of controlled laser processing are reported. Elastic properties of the heterogeneous structure under analysis are described by the method of conditional moments. Young's modulus of the created heterogeneous material cased on the titanium alloy and titanium boride is measured. The experimental data are found to be in good agreement with the numerical predictions.

Results of the analysis of elastoplastic deformation of a rotating solid cylinder with fixed end faces under monotonic loading by centrifugal forces are reported. The theory of small elastoplastic strains is used in formulating the problem. The general piecewise-linear condition of plasticity and the associated law of the flow are used for calculating the plastic component of the strain. The chosen plasticity condition depends on the parameter that can be considered as a material characteristic. An exact solution of the governing system of equations is derived. Regular features of plastic flow development are found. It is demonstrated that six plasticity domains are formed in the cylinder in the general case; these domains correspond to different ribs and faces of the surface defined by the general piecewise-linear condition. The dependence of the critical velocity of cylinder rotation on the parameter included into the plasticity condition is derived.

A method is proposed to control the properties of thin ferroelectric films under forced deformation due to the size mismatch of the crystalline lattices of film and substrate materials and due to the difference of their thermal expansion coefficients. Control is based on additional mechanical deformation of the substrate. A model of a single-crystal Ba_xSr_1-xTiO₃ film is studied within the framework of phenomenological theory using the Landau potential. It is shown that additional uniaxial deformation of the substrate in a Ba_xSr_1-xTiO₃ film changes the material constants of the film. Abnormal change occurs at deformation values close to the values at which the phase state of the film changes. The generation of surface acoustic waves is studied. The results of modeling simulations indicate the possibility of controlling the excitation of surface acoustic waves in the film-silicon substrate heterostructure.

A mathematical model of large deformations is used to solve a coupled boundary-value problem about the deformation of an elastic-viscoplastic material in a cylindrical viscometer with account for its heating due to wall friction. The deformation of a material enclosed between rigid surfaces due to the rotation of an inner cylindrical surface at a variable velocity is investigated. It is taken into account that a yield point depends on temperature. The motion of elastoplastic boundaries is described. Stresses, strains, and temperature in a thermoelastic deformation region and in a flow region both during the development of the flow and during its deceleration, including stopping, unloading, and cooling, are calculated. Residual stresses and deformations are determined.

A model of dynamic deformation and fracture of composite materials is been developed. This model accounts for the significant nonlinearity of shock loading diagrams with hardening, which depends on strain rate. An approach is used in which the dependence of ultimate strength on damage parameters and their variation rate is introduced in the form of constitutive relations. The proposed relations are similar to those of the Johnson-Cook model, but stresses are expressed via damage parameters and their variation rate rather than in terms of plastic deformations and the variation rate of plastic deformations. On the basis of the developed model, the impact fracture of a tubular profile made of a composite material based on carbon fiber and a polymer binder are numerically simulated. The influence of the orientation of unidirectional layers of a composite on specific absorption energy is investigated.

A problem of the projectile impact onto a membrane is studied under the following assumptions: the armor shell is a membrane with a zero flexural stiffness and a large Young's modulus under tension; the frontal part of the projectile is shaped as a paraboloid; the projectile impact onto the membrane is considered in a quasi-static formulation; the membrane is broken when a certain limiting surface tension is reached at the paraboloid vertex. It is found that the armor shell ensures safety if the kinetic energy of the projectile does not exceed some maximum value for this armor determined theoretically or experimentally.

We have investigated a class of materials whose experimental stress-strain behavior does not allow them to be considered plastic or elastic. They are not elastic since unloading occurs along a curve significantly different from the loading curve; nor are they plastic since in a full loading-unloading cycle, residual deformations are absent. As such materials we investigate so-called metal rubbers - materials made from twisted wire pressed into an almost homogeneous body. The propagation of shock waves in these materials is studied using a one-dimensional model.

A stress-strain state arising under dynamic tension of a homogeneous rod made of an incompressible ideally rigid-plastic material that satisfies the Mises-Hencky criterion is investigated. The possibility of thickening or thinning of the rod along its length is taken into account in an axisymmetric formulation, which makes it possible to simulate the formation and development of a neck. Three dimensionless time functions are introduced, one of which is a small geometric parameter, namely the ratio of an average radius to half the rod length. The ratios of the orders of smallness of the other two dimensionless functions to the small geometric parameter determine the influence of inertial terms in equations of motion on the stress and strain rate distribution. These ratios may vary at different time intervals, which determines one or another dynamic tension regimes. Two such characteristic regimes are revealed: one of them depends on a velocity at which the end sections move away from each other, and the other one depends on their acceleration. For the second regime, an asymptotic integration based analysis makes it possible to find the stress-strain state parameters, in which case this state is an “inertial correction”' with respect to a quasistatic state in the rod with a cylindrical lateral surface.

Results of solutions to problems of determining the parameters of anisogrid lattice structures of spacecraft bodies are presented. These problems include analyzing the deformability of a body loaded with transverse inertial forces, determining the fundamental frequency of transverse vibrations of a cantilevered body, studying the deformability of a body loaded with axial compressive force, and analyzing the deformability of a body with an internal fuel tank loaded with transverse inertial forces. The problems under consideration are solved using a continuous model of the lattice structure of a cylindrical body and the finite-element method.

A method is proposed for constructing variational models of continuous media for reversible and irreversible processes based on the generalized Hamilton-Ostrogradskii principle, which reduces to the principle of steadiness for a non-integrable variational form of a spatial-temporal continuum. For dissipative processes, the corresponding linear variational form is constructed as a sum of variation of the Lagrangian of the reversible part and a linear combination of dissipation channels of physically nonlinear processes. Examples of using the variational approach to the description of hydrodynamic models are considered. The corresponding variational models of the Darcy hydrodynamics, linear Navier-Stokes hydrodynamics, Brinkman hydrodynamics, gradient hydrodynamics, and some generalization of the classical nonlinear Navier-Stokes hydrodynamics are constructed. For modeling irreversible processes of hydrodynamics with allowance for coupling of deformation with the associated physical processes of heat transfer, it is proposed to use variational formalism for the spatial-temporal continuum, where the spatial and temporal processes are considered simultaneously and consistently because the normalized time is a coordinate.