We consider the associated non-stationary problem of propagation of axisymmetric disturbances from a spherical cavity in electromagnetoelastic space. It is assumed that the medium is a homogeneous isotropic conductor. Linear equations of motion of an elastic medium are used taking into account the linearized Lorentz forces, as well as Maxwell's equations, together with the linearized generalized law. The initial conditions are zero, at the boundary of the cavity defined displacement and the tangential component of the electric field. The desired functions are arranged in series of Legendre and Gegenbauer polynomials, as well as in series according to a small parameter characterizing the connection of mechanical and electromagnetic fields. Apart from that the applicable Laplace transform in time is used. The result is a recurrence of the small parameter sequence of boundary value problems, the solution of which is represented in the integral form with kernels in the form of volume and surface Green's functions. Images of Green's functions are found in an explicit manner. Their "elastic" part due to the relation between the modified Bessel functions and elementary functions is reduced to the sum of products of rational functions of the parameter of the Laplace transform to the exponent that lets you find exactly the originals using the corresponding theorems of operational calculus. The “Electromagnetic” part of the Green's function is being constructed in a quasi-static approximation. As a result, in the space of the original resolution of the system is became possible to build recurrence equations which allows finding and moving all the components of the electromagnetic field. In calculating its constituent integrals quadrature formulas are used. The examples of computations are provided. The numerical study of the convergence of series in the small parameter is presented.

Flexible fittings with corrugated surfaces are traditionally used to improve the bond and minimize its debonding with concrete. But rigid I-beam reinforcements, the type required for heavy load bearing, are not corrugated. The onset of the debonding process that occurs when rigid I-beam reinforcement was pressed into concrete was established through comprehensive calculations and experimentation. The aim of the paper was to define the parameters and types of fractures in the “steel-concrete” contact zone. The Cohesive Zone Material Model (CZM), provided by ANSYS Workbench software, was used with the bilinear behavior law on the contact layer and described the separation of “steel-concrete" surfaces. A mathematical model of the contact boundary problem was solved by the finite element method. A comparison of calculations and experimentation confirmed that the bond for smooth rigid reinforcement for B35 class concrete is provided by adhesion; and it is best described by the CZM model. Distribution patterns of contact pressure in the contact zone and of shear stresses on the concrete faces and surfaces adjacent to the I-beam were revealed. The relative displacement of concrete when impacted by an external force was measured. Results of this investigation indicate that the mathematical model is consistent and reflects the experimental data.

The problem of determining the penetration resistance of the flat end projectile into dry and water-saturated sandy soils with the use of the reversed experiment technique is studied in the paper. In the experiment, the container with soil strikes the end of the measuring rod, and the resistance force is determined based on the strain gauge readings on the surface of the rod at a distance from its end. The propagation of pulse compression resulting from the impact of the rod flat end against the container with the water-saturated and dry sandy soils. The compressibility of the soil is described with Hugoniots, and the shear properties of the soil are described with a rational dependence of yield strength of the pressure. Hugoniots of the soils with different water saturation were obtained with the use of a multi-component model of the medium. The dependences of the resistance force of the cylindrical projectile on the time in dry, wet and water-saturated sandy soils were obtained numerically. In wet soils, the the non-stationary phase of power pulse was shorter than in dry soils. The analysis of errors was carried out in determining the forces acting on the projectile, from the values of the strain pulse on the surface of the rod. The effect of geometric dispersion during propagation along the rod pulse compression with a wavelength comparable to the radius of the cylinder was numerically shown. In order to restore the pulse at the end of the rod according to its values on the surface at a distance from the load point, the modified techniques were used after adjusting for variance and with an additional view of the uneven deformation distribution over the cross section of the rod. The distortions of the restored pulse were pointed out, the dependence of errors in determining the maximum value of the duration on the non-stationary part of the initial pulse was received. The accuracy of determining the quasi-stationary value of the resistance implementation after the introduction of amendments related to the dispersion both in dry and in water-saturated soils.

Magneto-electro-elastic materials have drawn increasing attention due to their magnetic-electric-mechanical coupling effect. They have the ability to convert the energy from one type to another and have a wide range of technical applications. This paper presents a Laplace domain direct boundary element formulation for static and transient dynamic problems of three-dimensional linear magneto-electro-elasticity. The standard contracted notation is used to express the coupled problem in the elastic-like fashion. The formulation is based on the displacement boundary integral equation. The Laplace transformed generalized fundamental solution is represented as a sum of singular and regular parts. Dynamic part is expressed as the surface integral over a half of a unit sphere and singular static part as an integral over a unit circumference. Classical collocation scheme is employed along with the mixed boundary elements for spatial discretization. The boundary is discretized with quadratic quadrilateral elements. Generalized displacements and tractions are approximated by linear and constant shape functions in each boundary element. In order to accelerate the integration process, regular dynamic parts of the fundamental solutions and their spatial derivatives are interpolated over a boundary element. Time domain solutions are retrieved via a numerical inversion technique. Two numerical examples are presented: static behaviour of the rectangular prism under prescribed tension and transient response of the unit cube under uniform uniaxial impact loading. A convergence study is presented for the dynamic problem and excellent agreement with the analytical solution is achieved for the static problem.

A method is developed for determining the load-bearing capacity of weakened ice plates, which are modeled by an ideal rigid-plastic plate located on an incompressible foundation. The plate is simply supported or clamped on arbitrary piece-wise smooth curvilinear external contour. The central part of the plate contains a free opening with an arbitrary contour. The thickness of the plate decreases when approaching the boundary of the opening. The plate is subject to a load distributed locally around the opening in the region of an arbitrary shape. The load is an arbitrary function of coordinates. The property of ice with different a resistance in tension and compression is taken into account. The solution is made based on the principle of virtual work. Two variants of kinematically admissible deformations are considered in dependence on the geometric parameters of the plate. In both deformation schemes, the central part of the plate (under loading) moves in the direction of the load; while the area near the external contour (due to the foundation incompressibility) moves in the opposite direction. An orthogonal curvilinear coordinate system associated with curvilinear external contour of the plate is considered. In this system, it is convenient to calculate double integrals describing the solution of the problem. Analytical expressions for the limit loads are obtained. Two integral characteristics of the load are determined; and it is shown that in case the plate is affected by differently distributed surface loads (in which these two characteristics coincide) the plate will have the same limit load. А simply supported and clamped plate shaped as an ellipse with a linear function of thickness under the action of several types of local surface loads is considered as an example. The proposed method allows calculating the load-bearing capacity of weakened curvilinear ice plates on an incompressible foundation and estimating the possibility to increase the load-bearing capacity by increasing the loaded area and by redistributing the load on the area of loading.

Describing structurally inhomogeneous materials as complex hierarchical systems allows deriving a consistent pattern of stress-strain state related to history dependence of damage evolution. In this work we use a random microstructure subvolume to describe a methodology of a numerical study of stress-strain response evolution of a structurally inhomogeneous material subjected to uniaxial tension and compression. The study involves micro- and macrolevel and takes both internal structure and rheological properties of material constituents into account. We use a particle reinforced metal matrix composite with a 99.8% pure aluminum matrix and silicon carbide reinforcing particles. Particles are considered to have an irregular prism shape. The geometric structure of a composite subvolume on the microlevel is modeled by the piecewise-homogenous medium. The medium consists of particle model volumes surrounded by a matrix model volume. To take a surrounding material into account, we introduce an additional buffer layer with averaged macromechanical properties of the composite. A microlevel computational model based on the above assumptions complies to the macrolevel representative volume of the composite with the microstructure fragment in the geometric center. Simulating the model loading behavior allows studying a stress-strain evolution of the random microstructure subvolume and describing it. Boundary conditions in the microlevel model are imposed in the way to represent the macrolevel strain in a point of material. The strain is obtained from macrolevel simulations. A buffer layer is used to improve accuracy of transferring the stress strain state from the macrolevel to the microlevel. The rheological properties of a matrix and buffer layer are taken into account by assigning experimentally obtained strain-hardening curves of the pure aluminum and composite. The matrix material is modeled by an elastoplastic medium with isotropic hardening. The buffer layer is assigned to have isotropic elastoviscoplastic properties. The silicon carbide particle material is considered to be isotropic linear elastic. A finite element discretization is generated with the aid of an in-house software. The software implements special techniques to generate three-dimensional model volumes of inhomogeneous materials with a complex internal structure. The numerical simulation allowed obtaining data on the evolution of the stress tensor components and strain increment tensor components in finite element mesh nodes. Contrary to homogenous macrolevel stress and strain fields emerging in loading simulations with the quasi-homogenous model of the composite material, computations yield peculiar heterogeneous stress-strain state of the microstructure subvolume. We describe features of the stress concentration area emergence and the local plastic strain regions development. We depict strain dependence of stress stiffness coefficient fields and Lode-Nadai coefficient fields. The statistical sampling of such microstructure subvolumes followed by a numerical study adhering to the computational model allows generalizing modeling results and deriving general laws of the stress-strain state evolution of the material on the microlevel.

Elements of structures which work in real conditions are quite often affected by variable temperatures and loadings. Nowadays the growth of interest related to the asymptotic behavior of inelastic structures subjected to cyclic loading leads to development of direct and incremental methods of stabilized state determining. If loadings vary and the body deforms elastically, then its durability is defined by fatigue characteristics of materials; destruction comes after a large number of cycles. If the body experiences elasto-plastic deformation, at loadings below the limit, the achievement of a dangerous state at a rather small number of cycles is possible. Thus it is necessary to distinguish two cases. The first case occurs when destruction comes due to the alternation of plastic deformations with different signs (for example, after plastic stretching there is plastic compression, etc.); it is cyclic plasticity (plastic or low-cyclic fatigue). The second case occurs when plastic deformations do notchange signs, but grow with each cycle (the progressing deformation - ratcheting). It leads to the inadmissible accumulation of plastic deformations. Thestudy results present finite-element (FEM) calculations of the asymptotical behavior of an elastoplastic plate with the central elliptic hole under the biaxial cyclic loading for three different materials. Incremental cyclic loading of the sample with the stress concentrator (the elliptic central hole) is performed in the multifunctional finite-element package SIMULIA Abaqus. The ranges of loads found for the shakedown, cyclic plasticity and ratcheting are presented. The obtained results are generalized and analyzed. Convenient normalization is suggested. At the expense of the chosen normalization all computed results corresponding to separate materials stay within one common curve with a minimum scattering of points. The convenience of the generalized chart consists of a possibility to receive the asymptotical behavior of the inelastic structure for those materials which computer calculations were not made.

The work is dedicated to the development and implementation of numerical-experimental method of evaluation of the stress and strain components on the base of infrared thermography. The infrared thermography is a non-contact method of visualization and measurement of temperature fields of objects. It could be used as a method of non-destructive testing. A program complex which could be used for the evaluation of the individual components of stress and strain is developed on the base of the solution of the boundary value problem and data of the sample temperature change caused by the thermoelastic effect. In order to verify the proposed method, a series of experiments on quasi-static tensile of specimens from structural steel 8X18H10 and titanium alloy VT1-0 with the stress concentrators were carried out. As a result, it is shown that in contrast to the similar approaches (e.g., TSA-Thermal Stress Analysis) the method allows us to obtain additional information about stress-deformed state of the material and to conduct a more detailed assessment of the degree of the critical state of the structure. The methodology of the proposed method is based on the experimental measurement of the first invariant of the stress tensor using the infrared scanning technique and its subsequent recalculation to determine boundary conditions. This allows us to identify all stress components at any point in the considered area of specimens or construction on the base of the numerical solution of the corresponding boundary value problem. Special feature of the developed approach is a small computational cost for the determination of the stress components, which allows using this technique in the analysis of a wide class of engineering structures in real time.

The problem of evaluating strength and service life of critical engineering facilities, whose operating properties are characterized by multi-parametric non-stationary thermomechanical effects is discussed in the paper. The main degradation mechanisms of structural materials (metals and alloys) specific to these objects are considered. The main requirements to the mathematical models of fatigue damage accumulation are formulated. The basic physical laws of complex thermoplastic deformation and fatigue damage accumulation in structural materials (metals and their alloys) for various modes of combined thermomechanical loading and their main difference from isothermal fatigue processes are considered. In the modern mechanics of damaged media (MDM), a mathematical model is developed which describes the processes of thermoplastic cyclic deformation and fatigue damage accumulation in structural alloys under multiaxial disproportionate modes of combined thermomechanical loading. A MDM model consists of three interrelated parts: defining relations of thermal plasticity accounting for their dependence on failure process, evolution equations of fatigue damage accumulation and a strength criterion of damaged material. It is shown that for certain parameters of equations of cyclic thermal plasticity, using a single point on the experimental fatigue curve, the parameters of evolution equations of damage accumulation can be determined which are used for a high-accuracy computational reconstruction of low-cycle fatigue curves for various complex deformation trajectories. The results of numerical modeling of thermoplastic cyclic deformation and fatigue damage accumulation in heat-resistant alloys (Haynes188) under combined thermomechanical loading are presented. Particular attention is paid to the issues of modeling the process of thermoplastic cyclic deformation and fatigue damage accumulation for complex processes of deformation accompanied by the rotation of the main sites of stress and strain tensors.