Heorhiy Sulym

• Doctor of Science
• Bialystok University of Technology

The paper proposes a transparent and compact form of constitutive and equilibrium relations for the plane thermoelasticity of quasicrystal solids. The symmetry and positive definiteness of the obtained extended tensors of material constants are studied. An extension of the Stroh formalism is proposed for solving plane problems of thermoelasticity f...

An analytical–numerical method for solving the class of problems of determining mechanical fields in composite structures with interfacial ribbon-like deformable multilayer physically nonlinear inhomogeneities under combined force and dislocation loading is proposed. The mathematical model of thin inclusion of material with arbitrary mechanical pro...

By using the principle of coupling of continua of different dimensions, we propose an approach to the mathematical modeling of deformable thread-like inhomogeneities. The proposed approach is based on the conditional partition of the analyzed problem into three partially coupled subproblems: a) external for a medium with conditionally given (a prio...

This study provides a mathematical method for the analysis of plane phonon-phason thermomechanical fields in quasi-crystalline bodies, which was developed based on the complex variable calculus and the Stroh formalism. Constitutive and balance equations of thermoelasticity of quasicrystal solids are written in a generalized form using extended phon...

By the method of direct cutting-out, the problems of longitudinal shear of an orthotropic half space, a layer, and a wedge with thin elastic orthotropic inclusions are reduced to the basic problem of interaction of thin inhomogeneities in the orthotropic space. We establish the conditions of interaction of loaded elastic anisotropic inclusions with...

The paper presents a solid boundary element approach for analysis of time-harmonic elastodynamic problems for isotropic and anisotropic solids containing rigid shell-like inhomogeneities of finite mass (movable inclusions). It presents a novel approach to derivation of the integral formulae and boundary integral equations, which is based on the par...

The effect of a functional gradient in the cross-section material (FGM) of a thin ribbon-like interfacial deformable inclusion on the stress–strain state of a piecewise homogeneous linear–elastic matrix under longitudinal shear conditions is considered. Based on the equations of elasticity theory, a mathematical model of such an FGM inclusion is co...

The effect of a functional gradient in the cross-section material (FGM) of a thin ribbon-like interfacial deformable inclusion on the stress–strain state of a piecewise homogeneous linear–elastic matrix under longitudinal shear conditions is considered. Based on the equations of elasticity theory, a mathematical model of such an FGM inclusion is co...

This work studies the problem of thermomagnetoelectroelastic anisotropic bimaterial with imperfect high-temperature conducting coherent interface, whose components contain thin inclusions. Using the extended Stroh formalism and complex variable calculus, the Somigliana-type integral formulae and the corresponding boundary integral equations for the...

The paper presents a novel approach for analysis of thermoelasticity problems for solids with deformable thread-like (wired, textile) inhomogeneities. It is proposed to model a thread-like inclusion with a spatial curve, with appropriate influence functions set on it. The mathematical models of heat conduction and thermoelasticity of thread-like in...

In the present paper, we propose a method aimed at the mathematical simulation of deformable threadlike (wire) inclusions based on the replacement of their influence on the elastic medium by tensile/compressive forces distributed along their axes. We construct a regularized integral equation of the problem external with respect to the inhomogeneity...

: Within the framework of the concept of deformable solid mechanics, an analytical-numerical method to the problem of determining the mechanical fields in the composite structures with interphase ribbon-like deformable multilayered inhomogeneities under combined force and dislocation loading has been proposed. Based on the general relations of line...

Within the framework of the concept of deformable solid mechanics, an analytical numerical method to the problem of determining the mechanical fields in the composite structures with interphase ribbon-like deformable multilayered inhomogeneities under combined force and dislocation loading has been proposed. Based on the general relations of linear...

УДК 517.968.23: 539.3 Запропоновано спосіб математичного моделювання деформівних ниткових включень на підставі заміни їхнього впливу на пружне середовище розподіленими вздовж їхньої осі зусиллями розтягу-стиску. Побудовано регуляризоване інтегральне рівняння зовнішньої щодо неоднорідності задачі, а також математичні моделі неоднорідності, що з урах...

A numerical–analytical approach to the problem of determining the stress–strain state of bimaterial structures with interphase ribbon-like deformable inhomogeneities under combined force and dislocation loading has been proposed. The possibility of delamination along a part of the interface between the inclusion and the matrix, where sliding with d...

A numerical–analytical approach to the problem of determining the stress–strain state of bimaterial structures with interphase ribbon-like deformable inhomogeneities under combined force and dislocation loading has been proposed. The possibility of delamination along a part of the interface between the inclusion and the matrix, where sliding with d...

The paper presents a novel approach for analytic modeling and numerical analysis of spatial problems of thermoelasticity for isotropic solids containing thread-like nondeformable inhomogeneities. The inhomogeneity is removed from consideration as a geometric object, and its influence on the continuum is replaced by sought functions (of heat flux an...

An incremental approach to solving the antiplane problem for bimaterial media with a thin, physically nonlinear inclusion placed on the materials interface is discussed. Using the jump functions method and the coupling problem of boundary values of the analytical functions method we reduce the problem to the system of singular integral equations (S...

Increasing machining productivity causes the cutting forces acting on tools or workpieces to grow and requires extra clamping forces for their fixation reliably. In the research, a mathematical model of the operation of the clamping mechanism for fixating cylindrical objects on the spindle of machine tools at the stage of tension is presented. The...

In the earlier developed method of direct cutting-out, we take into account the anisotropy of material. This method is based on the procedure of modeling of finite or bounded bodies with thin structural defects of any type and boundary conditions on its contour by an infinite space with the same inhomogeneities as in the original problem and additi...

The research is devoted to the problem of determining the efficiency of the workpiece fixing mechanism operation. Improving characteristics of workpiece fixing is one of the required conditions to increase the cutting modes, which may help to enhance the machining productivity. The study investigates the main characteristics and general features of...

We present a survey of investigations aimed at the analysis of thermally, magnetically, and electrically stressed states of the bodies containing thin inclusions and systems of inclusions, as well as at the analysis of their stress-strain states.

The chapter presents analytical research of the joining process of the AA2519/AA1050/Ti6Al4V laminate layers produced by the explosive method. The proposed model allows determining the influence of connection parameters on the shape and quality of the connection zone. The analytical research uses the theory of the elastodynamic character of materia...

Using the methods of solving dynamic problems for inhomogeneous centers and boundary elements for the study of geometrically complex and physically heterogeneous and nonlinear finite-dimensional bodies, the dynamic problem of linear elastic theory for a thin rectangular plate, loaded on opposite sides with evenly distributed stresses, has been solv...

The influence of impulse load applied for different duration on the distribution of normalised dynamic radial stresses in positive and negative Poisson’s ratio medium was investigated in this study. For solving the non-stationary problem in the case of plane deformation for structurally inhomogeneous materials, the model of Cosserat continuum was a...

This work studies the problem of a thermomagnetoelectroelastic anisotropic bimaterial with imperfect high temperature-conducting coherent interface, which components contain thin inclusions. Using the extended Stroh formalism and complex variable calculus the Somigliana type integral formulae and corresponding boundary integral equations for the an...

The paper presents boundary element models of anisotropic thermoelastic medium containing partially debonded shell-like rigid inclusions, which possess high rates of heat conduction. Boundary integral equations are derived, which account for partial debonding of a shell-like inclusion at one of its faces. Special attention is paid to full debonding...

The paper derives integral equations of heat conduction and thermoelasticity of isotropic solids with non-deformable perfectly thermally conducting thread-like inclusions. It is observed that, in spite of the order of singularity, the integral equations obtained are hypersingular due to the symmetry of the kernels. Non-integral terms of these equat...

The paper presents a novel approach for the analysis of steady-state heat conduction of solids containing perfectly conductive thread-like inhomogeneities. Modelling of a thread-like heat conductive inhomogeneity is reduced to determination of density of heat distributed along a spatial curve, which replaces the inclusion. Corresponding boundary in...

The paper presents a rigorous and straightforward approach for obtaining the 2D boundary integral equations for a thermoelastic half-space containing holes, cracks and thin foreign inclusions. It starts from the Cauchy integral formula and the extended Stroh formalism which allows writing the general solution of thermoelastic problems in terms of c...

The paper presents a novel approach in derivation and solution of boundary integral equations of anisotropic elasticity of solids containing thin rigid wires (thread-like inclusions). It proposes to model rigid thread-like inclusions as spatial curves, which can rotate as a rigid one and possess certain rigid displacement. Somigliana identity is wr...

This paper contains an analytical description of the deformation of the upper layer AA2519/AA1050/Ti6Al4V laminate produced by an explosive bonding method. The basic parameters of the explosive welding process that influence the quality of the bonding are the detonation velocity of the explosive, the explosion energy, and the impact angle of the co...

The paper presents general boundary element approach for analysis of thermomagnetoelectroelastic solids containing shell‐like electrically conducting inclusions with high magnetic permittivity. The latter are modeled with opened surfaces with certain boundary conditions on their faces. Rigid displacement and rotation, along with constant electric a...

The earlier developed method of direct cutting-out is extended to the class of problems of elastic equilibrium of piecewise homogeneous bodies with internal and interface crack-like defects under antiplane deformation. This method is based on modeling of the initial problem for a body with thin inclusions (in particular, cracks) by a simpler proble...

The problem of longitudinal shear of bimaterial with thin nonlinear elastic inclusion at the interface of matrix materials is considered. Solution of the problem is constructed using the boundary value problem of combining analytical functions and jump functions method. The model of the thin inclusion with nonlinear resilient parameters is built. S...

The paper presents studies on the application of the boundary integral equation method for investigation of dynamic stress state of foam media with tunnel cavities in Cosserat continuum. For the solution of the non-stationary problem, the Fourier transform for time variable was used. The potential representations of Fourier transform displacements...

The paper presents general boundary element approach for analysis of thermoelectroelas- tic (pyroelectric) solids containing shell-like electricity conducting permittive inclusions. The latter are modeled with opened surfaces with certain boundary conditions on their faces. Rigid displacement and rotation, along with constant electric potential of...

We develop a model of thin inclusion with nonlinear anisotropic mechanical properties of the general form. By using this model and the methods of the problem of conjugation of the limit values of analytic and jump functions, we construct a system of singular integral equations with variable coefficients (functions). The solution of the system enabl...

The paper presents novel boundary element technique for analysis of anisotropic thermomagnetoelectroelastic solids containing cracks and thin shell-like soft inclusions. Dual boundary integral equations of heat conduction and thermomagnetoelectroelasticity are derived, which do not contain volume integrals in the absence of distributed body heat an...

This paper proposes the novel technique for analysis of dynamic stress state of multi-connected infinite plates under the action of weak shock waves. For solution of the problem it uses the integral and discrete Fourier transforms. Calculation of transformed dynamic stresses at the incisions of plates is held using the boundary-integral equation me...

We use the extended Stroh formalism and the theory of functions of complex variable to construct Somigliana-type integral relations and the corresponding equations for thermoelastic anisotropic bimaterial solids with imperfect thermal contact on the rectilinear interface between their components. Applying the mathematical model of thin deformable t...

The paper presents studies on the Green’s function for thermomagnetoelectroelastic medium and its reduction to the contour integral. Based on the previous studies the thermomagnetoelectroelastic Green’s function is presented as a surface integral over a half-sphere. The latter is then reduced to the double integral, which inner integral is evaluate...

By using the Laguerre and Fourier integral transformations, we construct the solution of a plane quasistatic problem of thermoelasticity for a half strip with coating heated by a heat flow acting upon its ends and cooled through the surfaces of the coatings that are free of loads. The results of numerical analyses of the dependence of the thermal s...

The paper presents a general boundary element approach for analysis of 3D cracks in anisotropic thermomagnetoelectroelastic solids. Dual boundary integral equations are derived, which kernels are explicitly written. These equations do not contain volume integrals in the absence of distributed body heat and extended body forces, which is advantageou...

The work describes the process of joining the explosive layered materials. It will be presented attempt analytical process of connecting the wave and its impact on the effects of combining explosive. The calculations will be chosen for the base materials AA2519 and Ti6Al4V. Verification tests will be through the execution and evaluation of metallog...

Based on the combined application of the Stroh formalism and the theory of functions of complex variable, we deduce dual integral equations for a magnetoelectroelastic bimaterial. For the first time, we construct the integral representations of the Stroh complex potentials and the explicit expressions for all kernels in terms of the parameters and...

We propose a model of multiple cracking of specimens under the combined action of thermal and mechanical cyclic loads. In view of the complexity of computations required for the solution of the problems of interaction of stochastically arranged cracks, it is proposed to treat them as doubly periodic systems of branched cracks capable of modeling th...

Based on the relations of elastodynamics this paper models the typical wave initiation and wave-shaped structure of the substrate surface due to the explosion welding. Herewith, the substrate is modeled as a half-plane, and the contact interaction of specimens is reduced to the local traction loading, which moves with a constant subsonic velocity a...

We construct an analytical solution to the anti-plane problem of an inhomogeneous bi- -material medium with the interfacial crack considering sliding friction. The medium is exposed to an arbitrary normal and shear loading in the longitudinal direction. Using the jump function method, the problem is reduced to a solution to singular integral equati...

The paper derives Somigliana type boundary integral equations for 3D thermomagnetoelectroelasticity of anisotropic solids. In the absence of distributed volume heat and body forces these equations contain only boundary integrals. Besides all of the obtained terms of integral equations are to be calculated in the real domain, which is advantageous t...

This paper studies a thermoelastic anisotropic bimaterial with thermally imperfect interface and internal inhomogeneities. Based on the complex variable calculus and the extended Stroh formalism a new approach is proposed for obtaining the Somigliana type integral formulae and corresponding boundary integral equations for a thermoelastic bimaterial...

We study the problem of antiplane deformation of an isotropic medium containing a thin elastic curved inhomogeneity. The methods used for the solution of this problem are based on the application of the method of jump functions and the conditions of interaction of the matrix containing a thin curvilinear inclusion and the solution of the resultant...

On the basis of the general integral equations of thermoelectroelasticity deduced earlier for bodies with thin heterogeneities, we construct an analytic solution of the plane problem for a pyroelectric body containing a crack whose faces are kept at a constant temperature under the action of a concentrated heat source lying on the continuation of i...

The paper presents the exact solution of the antiplane problem for an inhomogeneous bimaterial with the interface crack exposed to the normal load and cyclic loading by a concentrated force in the longitudinal direction. Using discontinuity function method the problem is reduced to the solution of singular integral equations for the displacement an...

This paper proposes the novel technique for analysis of dynamic stress state of multi-connected infinite plates under the action of oscillating forces. Calculation of dynamic stresses at the incisions of plates is held using the boundary-integral equation method and the theory of complex variable functions. The numerical implementation of the devel...

This paper utilizes the Stroh formalism and the complex variable approach to derive the integral formulae and boundary integral equations of anisotropic thermoelectroelasticity for a bimaterial solid with Kapitza-type interface. Obtained integral formulae and boundary integral equations do not contain domain integrals, thus, the boundary element ap...

The paper presents the exact analytic solution to the antiplane problem for a non-homogeneous bimaterial medium containing closed interfacial cracks, which faces can move relatively to each other with dry friction. The medium is subjected to the action of normal and arbitrary single loading in a longitudinal direction. Based on the discontinuity fu...

The extended Somigliana identity for thermomagnetoelectroelastic anisotropic dielectric solids is deduced. This identity does not impose restrictions on the dimensionality of the problem. The volume integral caused by the interaction of physical fields (internal temperature field and electric and magnetic loads) is reduced to the surface integral....

The paper considers dynamic problem of coupled thermoelasticity for a rectangular plate. The problem approximately models the technological process of high intensity deformation of structural materials. The solution of the problem is derived as a series of Laguerre polynomials, which coefficients are determined based on the obtained recurrent depen...

The paper presents complex variable integral formulae and singular boundary integral equations for doubly periodic cracks in anisotropic elastic medium. It utilizes the numerical solution procedure, which accounts for the contact of crack faces and produce accurate results for SIF evaluation. It is shown that the account of contact effects signific...

This paper presents a comprehensive study on the 2D boundary integral equations, Green׳s functions and boundary element method for thermoelectroelastic bimaterials containing cracks and thin inclusions. Based on the extended Stroh formalism, complex variable approach and the Cauchy integral formula, the paper derives integral formulae for the Stroh...

The purpose of this paper is to analyze the interaction of thin elastic inclusions with globular defects in a solid structural element and develop technique to determine fracture parameters when the elastic inclusion of the structure is close to a circular hole and/or to its bonding layers. Procedures for determination of fracture parameters are ba...

By using the Laguerre and Hankel integral transformations, we construct the solution of an axisymmetric quasistatic problem of thermoelasticity for a half space with coating. We present some results of the numerical analysis of thermal stressed state depending on the relative geometric and thermomechanical properties of the coating and the half spa...

The integral equations of antiplane shear deformation of anisotropic solids with periodic sets of thin ribbonlike inclusions are constructed. A modified boundary-element method is used to obtain the numerical solutions of specific problems. We compute the stress intensity factors for anisotropic bodies with one, two, or three columns of parallel de...

The paper derives the equations, which should be satisfied by the temperature field that does not induce stress and electric displacement in an anisotropic thermoelectroelastic solid. It is shown that these equations are satisfied identically only if the pyroelectric solid is heated or cooled by a constant temperature. Due to the tertiary pyroelect...

The paper presents a complex variable approach for obtaining of the integral formulae and integral equations for plane thermoelectroelasticity of an anisotropic bimaterial with thermally insulated interface. Obtained relations do not contain domain integrals and incorporate only physical boundary functions such as temperature, heat flux, extended d...

The paper presents a rigorous and straightforward approach for obtaining the 2D boundary integral equations for a thermoelectroelastic half-space containing holes, cracks and thin foreign inclusions. It starts from the Cauchy integral formula and Stroh orthogonality relations to obtain the integral formulae for the Stroh complex functions, which ar...

We apply methods of the theory of thermoelastic deformation of bodies with thin inclusions to study magnetoelectroelastic media with thin inhomogeneities. We construct the integral equations of the problem and propose an efficient numerical procedure of the boundary-element method for their solution. It is established that the fields of mechanical...

We propose two approaches to the solution of problems of antiplane deformation of bounded bodies with thin-walled defects by concentrated factors. The first is a numerical approach based on the boundary element method, in which the Volterra approach was developed to take into account the action of screw dislocations, and special tip boundary elemen...

On the basis of pure physical reasoning, we deduce the relationship between the stresses acting at the tip of a defect and the coefficients of root singularity of the stress field, i.e., the generalized stress intensity factors. We propose approximate relations for the evaluation of the generalized stress intensity factors. The efficiency of the pr...

This paper considers the doubly periodic problem of elasticity for anisotropic solids containing regular sets of thin branched inclusions. A coupling principle for continua of different dimension is utilized for modeling of thin inhomogeneities and the boundary element technique is adopted for numerical solution of the problem. The branches of the...

This paper develops Somigliana type boundary integral equations for 2D thermoelectroelasticity of anisotropic solids with cracks and thin inclusions. Two approaches for obtaining of these equations are proposed, which validate each other. Derived boundary integral equations contain domain integrals only if the body forces or distributed heat source...

This paper presents a novel approach for obtaining boundary integral equations of 2D anisotropic magnetoelectroelasticity. This approach is based on the holomorphy theorems and the Stroh formalism and allows developing of the integral equations for the aperiodic, singly and doubly periodic problems of magnetoelectroelasticity. Obtained equations co...

This paper considers a dynamic problem of elasticity for a rectangular plate under time-dependent tensile load, and uses it in modeling of transient stress-strain state of experimental samples under high-speed dynamic overloading. The solution of the problem is obtained using the integral transform approach. Based on this solution the paper studie...

We investigate the stress-strain state of an infinite isotropic plate with a crack the faces of which are free of external loading. The plate is under the action of concentrated bending moments. It is assumed that the crack faces are in a smooth contact along the entire length of the crack in the two-dimensional zone of constant width near the uppe...

We have constructed the fundamental system of solutions of the axially symmetric problem of the theory of elasticity for an unbounded body with a sheet of volume forces, normal to a chosen plane, and moment dipoles, which is a mathematical model of the internal boundary layer of a certain type. With the help of such layers, one succeeds in formulat...

The method of direct cutting-out consists of modeling of a finite body, in particular, with thin heterogeneities, using a much simpler problem for a bounded or a partially bounded body with thin heterogeneities located in the same manner and the presence of additional cracks or absolutely rigid inclusions of fairy large length, which are modeled by...

We have proposed to apply the dual boundary element method in problems of the theory of thin inclusions. The contact conditions on the boundary of a thin inclusion are considered as jumps of displacements and stresses in the body on the median surface of this defect. Thus, the relations between the unknown discontinuities and average values of the...

By the methods of singular integral equations, we construct a mathematical model of the antiplane deformation of a body containing thin ribbonlike elastic inclusions. In the model, we take into account the possibility of longitudinal deformation of the inclusion in two mutually perpendicular planes and deduce equations for the description of thin e...

We propose a method for the nondestructive evaluation of the ultimate strength and fracture toughness KIc of structural steels based on the high-precision data on strains and stresses obtained as a result of the improved numerical solution of the problem of plane strained state in the nonstationary elastoplastic formulation. The developed method sa...

The mathematical models, integral equations and the corresponding numerical schemes, required for the study of the stress state of plates containing thin crooked defects are considered and explicitly written. The results obtained using the proposed line model for a circular arc inclusion are in good agreement with those obtained by the direct appro...

We have ascertained the limits of reasonable application of the classical boundary element method for the solution of the antiplane problem of the theory of elasticity in the study of bodies with thin-walled elements of structure and geometry. We have proposed an approach for the regularization of singular and quasisingular integrals, which appear...

Novel self-regular (and continuous to the boundarystress integral equations are obtained. Singular and hypersingular integrals are both regularized using the imposition of simple polynomial solution. For determination of generalized stress intensity factors a number of techniques are proposed. Two of them are based on the energy integrals approach,...

The stress hypersingular integral equations of axisymmetric elasticity are considered. The singular and hypersingular integrals are regularized using the imposition of auxiliary polynomial solution, and self-regular integral equations are obtained for bounded and unbounded domains. The presented numerical examples show high efficiency of the propos...

We use the J-integral for the investigation of generalized stress intensity factors near the tips of thin curvilinear inclusions. The dependence of the generalized stress intensity factor on the relative stiffness of an elastic inclusion along a circular arc is investigated. It is shown that the a priori tip constants used by the other authors give...

For determination of a limit state of elastic solids with thin-walled elastic inclusions of arbitrary rigidity the use of the J-integral is proposed. The relationship between the J-integral and GSIFs for all three modes of deformation is determined. It is shown with the help of a method of dominating GSIF that the J-integral (energy release rate) i...

The limiting equilibrium and type of fracture of an orthotropic body containing a linear rigid inclusion in tension at infinity along the axis of the inclusion is studied under the conditions of plane problem. Localized process zones (of weakened contact) develop along the boundary of the inclusion from its ends to the central part. The analytic so...