The viscoplastic deformation of a granular nickel alloy during isothermal rolling under high temperature conditions is considered. The stress state of the alloy during rolling is inhomogeneous and multiaxial during repeated deformation with a variable deformation rate. The diagrams of the viscoplastic deformation of the alloy at high temperatures and various deformation rates have a falling (softening) section up to destruction, which is due to a short-term creep during powerful softening. Mathematical modeling of the viscoplastic behavior of the alloy under such conditions is proposed to be carried out on the basis of a variant of the theory of thermoviscoplasticity based on the theory of flow under combined hardening. A variant of the theory of thermoviscoplasticity is generalized to non-isothermal loading and to dependence of the violation process on the deformation rate. The main provisions and equations of the variant of the theory of thermoviscoplasticity are presented. The material parameters that close the version of the theory, the basic experiment and the method of obtaining material parameters are determined. The material parameters of the granular nickel alloy at high temperatures and various deformation rates are obtained. The results of experiments on uniaxial stretching of cylindrical samples made of granular nickel alloy at high temperatures and different deformation rates are presented. Tests with unloading and subsequent loading are also considered. Mathematical modeling of tests of a granular nickel alloy is carried out on the basis of a numerical solution of the Cauchy problem by the Runge-Kutta method of the 4th order of accuracy of the system of equations for a uniaxial stress state under rigid loading obtained on the basis of general equations of a variant of the theory of thermoviscoplasticity. The obtained calculated diagrams of viscoplastic deformation are compared with experimental ones. There is a reliable correspondence between the calculated and experimental results, which indicates the adequacy of the developed version of the theory of thermoviscoplasticity and the method of identification of material parameters.

Previously, the authors of this article formulated a physically and geometrically nonlinear formulation of the problem of porous fluid-saturated medium deformation during fluid filtration (consolidation problem) in terms of the rate of solid phase displacement and the change in pore pressure in differential and variational forms. The developed consolidation model takes into account changes in the porosity and permeability of the medium during deformation. Deformation-type constitutive relations are used in the model. The developed consolidation model can be used to simulate non-stationary processes in the soil, for example, the formation of ruts and unevenness of dirt roads, as well as to calculate the uneven settlement of engineering structures. This work is devoted to the experimental determination of the deformation and strength properties of water-saturated sandy soils, which is the next stage in the consolidation process simulation. The results of the experimental determination of the bulk and shear properties of sandy soil using the ASIS automated complex (OOO NPP “Geotek”) are presented. The studies were carried out on three quartz sands of various grain sizes. To determine the volumetric moduli of dry and water-saturated sandy soils, compression tests were carried out under a continuously growing vertical load at a constant strain rate. The experiments were carried out for various strain rates in the range from 3·10–6 to 3·10–3 s–1. According to the experimental results, the bulk properties do not depend on the strain rate in the specified range. Deformation and strength shear characteristics of sandy soils were determined by the method of multiplanar shear, approximating a simple shear. The tests were carried out under a kinematically applied shear load with a given constant strain rate according to the scheme of consolidated-drained shear. The dependences of the deformation and strength properties of coarse and fine quartz sands on the shear strain rate in the range from 2·10–4 tо 4·10–3 s–1 were studied. Increasing, decreasing and nonmonotonic dependences of the internal friction angle on the shear strain rate were obtained for dry and water-saturated sands of various grain sizes. For water-saturated sands, the maximum spread in the values of the internal friction angle for different strain rates does not exceed 7 %. A technique has been developed for recalculating the obtained properties and experimental dependences into the parameters of the proposed sandy soil consolidation model.

Among modern combined laser and electron-beam technologies, special attention is paid to those in which composition formation takes place directly in the process of product creation or coating synthesis. In the present work, a coupled model of coating synthesis on a substrate is constructed. When building the model, a sequential transition was carried out from a three-dimensional model of the coating synthesis process on the substrate to a one-dimensional model, which is useful for qualitative analysis. The one-dimensional model takes into account the main physical features of the physical and chemical processes during the synthesis, as well as the coupled nature of the heat transfer and deformation at the same time taking into account the differences in thermophysical and mechanical properties of different materials. When constructing the intermediate analytical solution, it is assumed that the system "substrate-coating" is in a plane stress state. As a result, explicit expressions for the components of stress and strain tensors connected with changes in temperature and composition are obtained. With the help of the obtained analytical solution, the thermokinetic part of the problem is modified and reduced to a more convenient form. Further, the experience accumulated in the field of macrokinetics is used, which allows us to model the processes of creating new materials (e.g., intermetallic or metal matrix composites) in modern technologies from the point of view of controlling the processes of phase formation in the reaction zone by a moving external source. The transition to dimensionless variables revealed complexes and parameters representing relations of characteristic scales of different processes. The parametric study of the model allowed us to establish interesting qualitative effects. It is demonstrated that the quasi-stationary regime is accompanied by physical and chemical processes in the region, which the laser beam had left, due to the heat accumulated in the materials. It is shown that the coupled nature of different processes significantly affects the dynamics of synthesis and the parameters of the quasi-stationary regime.

This paper proposes a mathematical model for a disk-type pulsed electrodynamic transducer operating in the low-frequency range. A well-known architecture of an electromagnetic acoustic radiator with a helical coil and a conducting disk is studied. In the work, the equations of the electromechanical system in the form of the Lagrange-Maxwell equations are built with the use of the Green's functions of a plane axisymmetric acoustic problem to estimate the reaction force of the fluid. A comparison is made between the results of a numerical solution of the obtained equations and direct numerical calculation in the COMSOL finite element analysis software. The resulting model shows good qualitative agreement with the results of finite element calculations while allowing calculations with a variation for all main model parameters required to design the transducer.

A systematic analytical study of the mathematical properties of the nonlinear shear flow model of thixotropic viscoelastic-plastic media is continued. It takes into account the mutual influence of а deformation process and structure evolution (the kinetics of the formation and destruction of intermolecular bonds and associates of macromolecules). The model is reduced to the system of two nonlinear differential equations for the dimensionless stress and the degree of structuredness (i.e. cross-links density and so on). Assuming six material parameters and an (increasing) material function governing the model are arbitrary, the phase portrait of the system is analytically studied in the vicinity of its single equilibrium point. Basic properties of flow curves and stress-strain curves with constant shear rate generated by the model are examined. Thus, the analysis of the model ability to describe the behavior of both liquid-like media and solid-like (thickening, hardening, solidifying) viscoelastic-plastic media has been started: the effects of strain-rate and strain hardening, relaxation, creep, recovery, etc. The stress-strain curves dependence on the shear deformation (monotonicity, convexity, instantaneous modulus, tangent modulus evolution), on the shear rate and initial structuredness and on the material parameters and function of the model (in particular, the parameters that control the effect of structuredness on viscosity and shear modulus and the influence stress on the rate of destruction of the structure) has been studied. It is proved that stress-strain curves can be both increasing and have sections of decrease, resembling a yield-drop, and damped oscillations; that all stress-strain curves have horizontal asymptotes (steady flow stress), monotonically dependent on shear rate, and the flow stress strictly increases with increasing shear rate; that their instantaneous shear modulus, on the contrary, depends on the initial structuredness, but does not depend on shear rate. Under certain restrictions on the material parameters, the model is also capable to provide a bilinear form of stress-strain curves, which is intrinsic for an ideal elastoplastic model, but with strain rate sensitivity. It has been established that the family of stress-strain curves does not have to be increasing function of initial structuredness or shear rate: in a certain range of shear rates, in which the equilibrium point is a “mature” focus and pronounced oscillations of stress-strain curves are observed, it is possible that stress-strain curves with different shear rates may interweave with each other. It is studied how structuredness changes in the process of deformation depending on shear rate, stress, material parameters and material function of the model. The initial structuredness affects only the initial arc of stress-strain curves, but does not affect their asymptotes and the steady value of the structuredness, which monotonically decreases with increasing shear rate. A variety of scenarios of structuredness behavior over time (in particular, the observed sharp collapse of the structuredness when critical stress values are reached) generates a number of unusual effects (unusual properties) in comparison with typical properties stress-strain curves of structurally stable materials.