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prof. dr hab. Victor Eremeev
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total: 129
Catalog Publications
Year 2021
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Experimental and Numerical Investigation of Tensile and Flexural Behavior of Nanoclay Wood-Plastic Composite
PublicationIn this study, the effect of wood powder and nanoclay particle content on composites’ mechanical behavior made with polyethylene matrix has been investigated. The wood flour as a reinforcer made of wood powder was at levels of 30, 40, and 50 wt.%, and additional reinforcement with nanoclay at 0, 1, 3, and 5 wt.%. Furthermore, to make a composite matrix, high-density polyethylene was used at levels of 70, 60, and 50% by weight....
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Flexomagnetic response of buckled piezomagnetic composite nanoplates
PublicationIn this paper, the equation governing the buckling of a magnetic composite plate under the influence of an in-plane one-dimensional magnetic field, assuming the concept of flexomagnetic and considering the resulting flexural force and moment, is investigated for the first time by different analytical boundary conditions. To determine the equation governing the stability of the plate, the nonlocal strain gradient theory has been...
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Investigation of Wood Flour Size, Aspect Ratios, and Injection Molding Temperature on Mechanical Properties of Wood Flour/Polyethylene Composites
PublicationIn the present research, wood flour reinforced polyethylene polymer composites with a coupling agent were prepared by injection molding. The effects of wood flour size, aspect ratios, and mold injection temperature on the composites’ mechanical properties were investigated. For the preparation of the polymer composites, five different formulations were created. The mechanical properties including tensile strength and the modulus,...
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Local material symmetry group for first- and second-order strain gradient fluids
PublicationUsing an unified approach based on the local material symmetry group introduced for general first- and second-order strain gradient elastic media, we analyze the constitutive equations of strain gradient fluids. For the strain gradient medium there exists a strain energy density dependent on first- and higher-order gradients of placement vector, whereas for fluids a strain energy depends on a current mass density and its gradients....
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Mechanical simulation of artificial gravity in torus-shaped and cylindrical spacecraft
PublicationLarge deformations and stress analyses in two types of space structures that are intended for people to live in space have been studied in this research. The structure under analysis is assumed to rotate around the central axis to create artificial gravitational acceleration equal to the gravity on the Earth's surface. The analysis is fully dynamic, which is formulated based on the energy method by using the first-order shear deformation...
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Nonlinear Free and Forced Vibrations of a Hyperelastic Micro/Nanobeam Considering Strain Stiffening Effect
PublicationIn recent years, the static and dynamic response of micro/nanobeams made of hyperelasticity materials received great attention. In the majority of studies in this area, the strain-stiffing effect that plays a major role in many hyperelastic materials has not been investigated deeply. Moreover, the influence of the size effect and large rotation for such a beam that is important for the large deformation was not addressed. This...
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Nonlinear resultant theory of shells accounting for thermodiffusion
PublicationThe complete nonlinear resultant 2D model of shell thermodiffusion is developed. All 2D balance laws and the entropy imbalance are formulated by direct through-the-thickness integration of respective 3D laws of continuum thermodiffusion. This leads to a more rich thermodynamic structure of our 2D model with several additional 2D fields not present in the 3D parent model. Constitutive equations of elastic thermodiffusive shells...
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On forced vibrations of piezo-flexomagnetic nano-actuator beams
PublicationThe effect of excitation frequency on the piezomagnetic Euler-Bernoulli nanobeam taking the flexomagnetic material phenomenon into consideration is investigated in this chapter. The magnetization with strain gradients creates flexomagneticity. We couple simultaneously the piezomagnetic and flexomagnetic properties in an inverse magnetization. Resemble the flexoelectricity, the flexomagneticity is also size-dependent. So, it has...
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On nonlinear dilatational strain gradient elasticity
PublicationWe call nonlinear dilatational strain gradient elasticity the theory in which the specific class of dilatational second gradient continua is considered: those whose deformation energy depends, in an objective way, on the gradient of placement and on the gradient of the determinant of the gradient of placement. It is an interesting particular case of complete Toupin–Mindlin nonlinear strain gradient elasticity: indeed, in it, the...
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On the generalized model of shell structures with functional cross-sections
PublicationIn the present study, a single general formulation has been presented for the analysis of various shell-shaped structures. The proposed model is comprehensive and a variety of theories can be used based on it. The cross-section of the shell structure can be arbitrarily analyzed with the presented equations. In other words, various types of shell structures, including cylindrical, conical, spherical, elliptical, hyperbolic, parabolic,...
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On the influence of a surface roughness on propagation of anti-plane short-length localized waves in a medium with surface coating
PublicationWe discuss the propagation of localized surface waves in the framework of the linear Gurtin–Murdoch surface elasticity and taking into account a roughness of a free boundary. We derive a boundary-value problem for anti-plane motions with curvilinear boundary and surface stresses. Using the asymptotic technique developed earlier, we obtain the form of a localized wave and analyze its amplitude evolution. As the main result we present...
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On thermal stability of piezo-flexomagnetic microbeams considering different temperature distributions
PublicationBy relying on the Euler–Bernoulli beam model and energy variational formula, we indicate critical temperature causes in the buckling of piezo-flexomagnetic microscale beams. The corresponding size-dependent approach is underlying as a second strain gradient theory. Small deformations of elastic solids are assessed, and the mathematical discussion is linear. Regardless of the pyromagnetic effects, the thermal loading of the thermal...
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On weak solutions of boundary value problems within the surface elasticity of Nth order
PublicationA study of existence and uniqueness of weak solutions to boundary value problems describing an elastic body with weakly nonlocal surface elasticity is presented. The chosen model incorporates the surface strain energy as a quadratic function of the surface strain tensor and the surface deformation gradients up to Nth order. The virtual work principle, extended for higher‐order strain gradient media, serves as a basis for defining...
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Strong ellipticity conditions and infinitesimal stability within nonlinear strain gradient elasticity
PublicationWe discuss connections between the strong ellipticity condition and the infinitesimal instability within the nonlinear strain gradient elasticity. The strong ellipticity (SE) condition describes the property of equations of statics whereas the infinitesimal stability is introduced as the positive definiteness of the second variation of an energy functional. Here we establish few implications which simplify the further analysis...
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Surface and interfacial anti-plane waves in micropolar solids with surface energy
PublicationIn this work, the propagation behaviour of a surface wave in a micropolar elastic half-space with surface strain and kinetic energies localized at the surface and the propagation behaviour of an interfacial anti-plane wave between two micropolar elastic half-spaces with interfacial strain and kinetic energies localized at the interface have been studied. The Gurtin–Murdoch model has been adopted for surface and interfacial elasticity....
Year 2020
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A continual model of a damaged medium used for analyzing fatigue life of polycrystalline structural alloys under thermal–mechanical loading
PublicationThe main physical laws of thermal–plastic deformation and fatigue damage accumulation processes in polycrystalline structural alloys under various regimes of cyclic thermal–mechanical loading are considered. Within the framework of mechanics of damaged media, a mathematical model is developed that describes thermal–plastic deformation and fatigue damage accumulation processes under low-cycle loading. The model consists of three...
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A new hyperbolic-polynomial higher-order elasticity theory for mechanics of thick FGM beams with imperfection in the material composition
PublicationA drawback to the material composition of thick functionally graded materials (FGM) beams is checked out in this research in conjunction with a novel hyperbolic‐polynomial higher‐order elasticity beam theory (HPET). The proposed beam model consists of a novel shape function for the distribution of shear stress deformation in the transverse coordinate. The beam theory also incorporates the stretching effect to present an indirect...
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Buckling analysis of a non-concentric double-walled carbon nanotube
PublicationOn the basis of a theoretical study, this research incorporates an eccentricity into a system of compressed double-walled carbon nanotubes (DWCNTs). In order to formulate the stability equations, a kinematic displacement with reference to the classical beam hypothesis is utilized. Furthermore, the influence of nanoscale size is taken into account with regard to the nonlocal approach of strain gradient and the van der Waals interaction...
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Characterization of the Functionally Graded Shear Modulus of a Half-Space
PublicationIn this article, a method is proposed for determining parameters of the exponentialy varying shear modulus of a functionally graded half-space. The method is based on the analytical solution of the problem of pure shear of an elastic functionally graded half-space by a strip punch. The half-space has the depth-wise exponential variation of its shear modulus, whose parameters are to be determined. The problem is reduced to an integral...
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Effect of Axial Porosities on Flexomagnetic Response of In-Plane Compressed Piezomagnetic Nanobeams
PublicationWe investigated the stability of an axially loaded Euler–Bernoulli porous nanobeam considering the flexomagnetic material properties. The flexomagneticity relates to the magnetization with strain gradients. Here we assume both piezomagnetic and flexomagnetic phenomena are coupled simultaneously with elastic relations in an inverse magnetization. Similar to flexoelectricity, the flexomagneticity is a size-dependent property. Therefore,...
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Enriched buckling for beam-lattice metamaterials
PublicationWe discuss two examples of beam-lattice metamaterials which show attractive mechanical properties concerning their enriched buckling. The first one considers pantographic beams and the nonlinear solution is traced out numerically on the base of a Hencky’s model and an algorithm based on Riks’ arc-length scheme. The second one concerns a beam-lattice with sliders and the nonlinear solution is discussed in analytic way and, finally,...
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Experimental analysis of wear resistance of compacts of fine-dispersed iron powder and tungsten monocarbide nanopowder produced by impulse pressing
PublicationThe paper presents the results of studying the structure and wear resistance of compacts produced from fine dispersed reduced iron powder (average particle size 3–mu m) with the addition of tungsten carbide (WC) nanopowder with the average particle size of 25–30 nm. The mass fraction of tungsten carbide (wolfram carbide) in the powder composition was 5% and 10% of the total mass. Impulse pressing was conducted using the modified...
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Flexoelectricity and apparent piezoelectricity of a pantographic micro-bar
PublicationWe discuss a homogenized model of a pantographic bar considering flexoelectricity. A pantographic bar consists of relatively stiff small bars connected by small soft flexoelectric pivots. As a result, an elongation of the bar relates almost to the torsion of pivots. Taking into account their flexoelectric properties we find the corresponding electric polarization. As a results, the homogenized pantographic bar demonstrates piezoelectric...
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Free Vibration of Flexomagnetic Nanostructured Tubes Based on Stress-driven Nonlocal Elasticity
PublicationA framework for the flexomagneticity influence is here considered extending the studies about this aspect on the small scale actuators. The developed model accommodates and composes linear Lagrangian strains, Euler-Bernoulli beam approach as well as an extended case of Hamilton’s principle. The nanostructured tube should subsume and incorporate size effect; however, for the sake of avoiding the staggering costs of experiments,...
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On Dynamic Extension of a Local Material Symmetry Group for Micropolar Media
PublicationFor micropolar media we present a new definition of the local material symmetry group considering invariant properties of the both kinetic energy and strain energy density under changes of a reference placement. Unlike simple (Cauchy) materials, micropolar media can be characterized through two kinematically independent fields, that are translation vector and orthogonal microrotation tensor. In other words, in micropolar continua...
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On Effective Bending Stiffness of a Laminate Nanoplate Considering Steigmann–Ogden Surface Elasticity
PublicationAs at the nanoscale the surface-to-volume ratio may be comparable with any characteristic length, while the material properties may essentially depend on surface/interface energy properties. In order to get effective material properties at the nanoscale, one can use various generalized models of continuum. In particular, within the framework of continuum mechanics, the surface elasticity is applied to the modelling of surface-related...
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On effective properties of beam-lattice structures made of flexoelectric materials
PublicationThe e-Workshop Advances in ELAstoDYNamics of architected materials and BIOmaterials International Research Project (IRP) Coss&Vita of the CNRS
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On instabilities and post-buckling of piezomagnetic and flexomagnetic nanostructures
PublicationWe focus on the mechanical strength of piezomagnetic beam-like nanosize sensors during post-buckling. An effective flexomagnetic property is also taken into account. The modelled sensor is selected to be a Euler-Bernoulli type beam. Long-range interactions between atoms result in a mathematical model based on the nonlocal strain gradient elasticity approach (NSGT). Due to possible large deformations within a post-buckling phenomenon,...
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On Nonlinear Bending Study of a Piezo-Flexomagnetic Nanobeam Based on an Analytical-Numerical Solution
PublicationAmong various magneto-elastic phenomena, flexomagnetic (FM) coupling can be defined as a dependence between strain gradient and magnetic polarization and, contrariwise, elastic strain and magnetic field gradient. This feature is a higher-order one than piezomagnetic, which is the magnetic response to strain. At the nanoscale, where large strain gradients are expected, the FM effect is significant and could be even dominant. In...
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On rotational instability within the nonlinear six-parameter shell theory
PublicationWithin the six-parameter nonlinear shell theory we analyzed the in-plane rotational instability which oc- curs under in-plane tensile loading. For plane deformations the considered shell model coincides up to notations with the geometrically nonlinear Cosserat continuum under plane stress conditions. So we con- sidered here both large translations and rotations. The constitutive relations contain some additional mi- cropolar parameters...
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On Solvability of Boundary Value Problems for Elastic Micropolar Shells with Rigid Inclusions
PublicationIn the framework of the linear theory of micropolar shells, existence and uniqueness theorems for weak solutions of boundary value problems describing small deformations of elastic micropolar shells connected to a system of absolutely rigid bodies are proved. The definition of a weak solution is based on the principle of virial movements. A feature of this problem is non-standard boundary conditions at the interface between the...
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On stress singularity near the tip of a crack with surface stresses
PublicationIn the framework of the simplified linear Gurtin–Murdoch surface elasticity we discuss a singularity of stresses and displacements in the vicinity of a mode III crack. We show that inhomogeneity in surface elastic properties may significantly affect the solution and to change the order of singularity. We also demonstrate that implicitly or explicitly assumed symmetry of the problem may also lead to changes in solutions. Considering...
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On Surface Kinetic Constitutive Relations
PublicationIn the framework of the strain gradient surface elasticity we discuss a consistent form of surface kinetic energy. This kinetic constitutive equation completes the statement of initial–boundary value problems. The proposed surface kinetic energy density is the most general function consistent with the constitutive relations in bulk. As the surface strain energy depends on the surface deformation gradient and its gradient, the kinetic...
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On the Dynamics of a Visco–Piezo–Flexoelectric Nanobeam
PublicationThe fundamental motivation of this research is to investigate the effect of flexoelectricity on a piezoelectric nanobeam for the first time involving internal viscoelasticity. To date, the effect of flexoelectricity on the mechanical behavior of nanobeams has been investigated extensively under various physical and environmental conditions. However, this effect as an internal property of materials has not been studied when the...
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On the effective properties of foams in the framework of the couple stress theory
PublicationIn the framework of the couple stress theory, we discuss the effective elastic properties of a metal open-cell foam. In this theory, we have the couple stress tensor, but the microrotations are fully described by displacements. To this end, we performed calculations for a representative volume element which give the matrices of elastic moduli relating stress and stress tensors with strain and microcurvature tensors.
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On the geometrically nonlinear vibration of a piezo-flexomagnetic nanotube
PublicationIn order to describe the behavior of thin elements used in MEMS and NEMS, it is essential to study a nonlinear free vibration of nanotubes under complicated external fields such as magnetic environment. In this regard, the magnetic force applied to the conductive nanotube with piezo-flexomagnetic elastic wall is considered. By the inclusion of Euler-Bernoulli beam and using Hamilton’s principle, the equations governing the system...
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On the non-linear dynamics of torus-shaped and cylindrical shell structures
PublicationIn this study, the non-linear dynamic analysis of torus-shaped and cylindrical shell-like structures has been studied. The applied material is assumed as the functionally graded material (FGM). The structures are considered to be used for important machines such as wind turbines. The effects of some environmental factors on the analysis like temperature and humidity have been considered. The strain field has been calculated in...
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On the well posedness of static boundary value problem within the linear dilatational strain gradient elasticity
PublicationIn this paper, it is proven an existence and uniqueness theorem for weak solutions of the equilibrium problem for linear isotropic dilatational strain gradient elasticity. Considered elastic bodies have as deformation energy the classical one due to Lamé but augmented with an additive term that depends on the norm of the gradient of dilatation: only one extra second gradient elastic coefficient is introduced. The studied class...
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Post-critical buckling of truncated conical carbon nanotubes considering surface effects embedding in a nonlinear Winkler substrate using the Rayleigh-Ritz method
PublicationThis research predicts theoretically post-critical axial buckling behavior of truncated conical carbon nanotubes (CCNTs) with several boundary conditions by assuming a nonlinear Winkler matrix. The post-buckling of CCNTs has been studied based on the Euler-Bernoulli beam model, Hamilton’s principle, Lagrangian strains, and nonlocal strain gradient theory. Both stiffness-hardening and stiffness-softening properties of the nanostructure...
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Surface effects of network materials based on strain gradient homogenized media
PublicationThe asymptotic homogenization of periodic network materials modeled as beam networks is pursued in this contribution, accounting for surface effects arising from the presence of a thin coating on the surface of the structural beam elements of the network. Cauchy and second gradient effective continua are considered and enhanced by the consideration of surface effects. The asymptotic homogenization technique is here extended to...
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Torsional stability capacity of a nano-composite shell based on a nonlocal strain gradient shell model under a three-dimensional magnetic field
PublicationThis paper considers a single-walled composite nano-shell (SWCNS) exposed in a torsional critical stability situation. As the magnetic field affects remarkably nanostructures in the small size, a three-dimensional magnetic field is assessed which contains magnetic effects along the circumferential, radial and axial coordinates system. Based on the results of the nonlocal model of strain gradient small-scale approach and the first-order...
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Transverse surface waves on a cylindrical surface with coating
PublicationWe discuss the propagation of transverse surface waves that are so-called whispering-gallery waves along a surface of an elastic cylinder with coating. The coating is modelled in the framework of linearized Gurtin–Murdoch surface elasticity. Other interpretations of the surface shear modulus are given and relations to so-called stiff interface and stiff skin model are discussed. The dispersion relations are obtained and analyzed.
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Weak Solutions within the Gradient-Incomplete Strain-Gradient Elasticity
PublicationIn this paper we consider existence and uniqueness of the three-dimensional static boundary-value problems in the framework of so-called gradient-incomplete strain-gradient elasticity. We call the strain-gradient elasticity model gradient-incomplete such model where the considered strain energy density depends on displacements and only on some specific partial derivatives of displacements of first- and second-order. Such models...
Year 2019
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A Generalized Framework Towards Structural Mechanics of Three-layered Composite Structures
PublicationThree-layered composite structures find a broad application. Increasingly, composites are being used whose layer thicknesses and material properties diverge strongly. In the perspective of structural mechanics, classical approaches to analysis fail at such extraordinary composites. Therefore, emphasis of the present approach is on arbitrary transverse shear rigidities and structural thicknesses of the individual layers. Therewith...
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Adaptation of the arbitrary Lagrange–Euler approach to fluid–solid interaction on an example of high velocity flow over thin platelet
PublicationThe aim of this study is to analyse the behaviour of a thin plate with air flow velocities of 0.3–0.9 Ma. Data from the experiment and numerical tools were used for the analysis. For fluid–solid interaction calculations, the arbitrary Lagrange–Euler approach was used. The results of the measurements are twofold. The first one is the measurement of the flow before and after vibrating plate, i.e. pure flow plate, and the second consists...
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Anti-plane surface waves in media with surface structure: Discrete vs. continuum model
PublicationWe present a comparison of the dispersion relations derived for anti-plane surface waves using the two distinct approaches of the surface elasticity vis-a-vis the lattice dynamics. We consider an elastic half-space with surface stresses described within the Gurtin–Murdoch model, and present a formulation of its discrete counterpart that is a square lattice half-plane with surface row of particles having mass and elastic bonds different...
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Assessment of dynamic characteristics of thin cylindrical sandwich panels with magnetorheological core
PublicationBased on the equivalent single-layer linear theory for laminated shells, free and forced vibrations of thin cylindrical sandwich panels with magnetorheological core are studied. Five variants of available magnetorheological elastomers differing in their composition and physical properties are considered for smart viscoelastic core. Coupled differential equations in terms of displacements based on the generalized kinematic hypotheses...
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Comparison of anti-plane surface waves in strain-gradient materials and materials with surface stresses
PublicationHere we discuss the similarities and differences in anti-plane surface wave propagation in an elastic half-space within the framework of the theories of Gurtin–Murdoch surface elasticity and Toupin–Mindlin strain-gradient elasticity. The qualitative behaviour of the dispersion curves and the decay of the obtained solutions are quite similar. On the other hand, we show that the solutions relating to the surface elasticity model...
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Identification of Shear Modulus Parameters of Half-space Inhomogeneous by Depth
PublicationThe paper propose a method for determining of the parameters of the exponential shear modulus of a functionally graded half-space based on the solution of the problem of a pure shear of an elastic functionally graded half-space by a strip punch. The solution of the integral equation of the contact problem is constructed by asymptotic methods with respect to the dimensionless parameter. The dependence of contact stresses on the...
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Nonlinear finite element modeling of vibration control of plane rod-type structural members with integrated piezoelectric patches
PublicationThis paper addresses modeling and finite element analysis of the transient large-amplitude vibration response of thin rod-type structures (e.g., plane curved beams, arches, ring shells) and its control by integrated piezoelectric layers. A geometrically nonlinear finite beam element for the analysis of piezolaminated structures is developed that is based on the Bernoulli hypothesis and the assumptions of small strains and finite...
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