137 results on '"Eremeyev, Victor A."'
Search Results
2. Strong Ellipticity and Infinitesimal Stability within N th-Order Gradient Elasticity.
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Eremeyev, Victor A.
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ELASTICITY , *NONLINEAR differential equations , *PARTIAL differential equations , *STRAINS & stresses (Mechanics) , *BOUNDARY value problems - Abstract
We formulate a series of strong ellipticity inequalities for equilibrium equations of the gradient elasticity up to the Nth order. Within this model of a continuum, there exists a deformation energy introduced as an objective function of deformation gradients up to the Nth order. As a result, the equilibrium equations constitute a system of 2 N -order nonlinear partial differential equations (PDEs). Using these inequalities for a boundary-value problem with the Dirichlet boundary conditions, we prove the positive definiteness of the second variation of the functional of the total energy. In other words, we establish sufficient conditions for infinitesimal instability. Here, we restrict ourselves to a particular class of deformations which includes affine deformations. [ABSTRACT FROM AUTHOR]
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- 2023
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3. Ellipticity in couple-stress elasticity.
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Eremeyev, Victor A., Scerrato, Daria, and Konopińska-Zmysłowska, Violetta
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MICROPOLAR elasticity , *STRAINS & stresses (Mechanics) , *ELASTICITY , *ENERGY density - Abstract
We discuss ellipticity property within the linear couple-stress elasticity. In this theory, there exists a deformation energy density introduced as a function of strains and gradient of macrorotations, where the latter are expressed through displacements. So the couple-stress theory could be treated as a particular class of strain gradient elasticity. Within the micropolar elasticity, the model is called Cosserat pseudocontinuum or medium with constrained rotations. Applying the classic definitions of ordinary ellipticity and strong ellipticity to static equations of the couple-stress theory, we conclude that these equations are neither elliptic nor strongly elliptic. As a result, one should be aware of extending properties of full strain gradient models such as Toupin–Mindlin strain gradient elasticity to models with incomplete set of second derivatives. [ABSTRACT FROM AUTHOR]
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- 2023
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4. On dynamic modeling of piezomagnetic/flexomagnetic microstructures based on Lord–Shulman thermoelastic model.
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Malikan, Mohammad and Eremeyev, Victor A.
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STRAINS & stresses (Mechanics) , *THERMOELASTICITY , *FREE vibration , *DYNAMIC models , *ELASTIC deformation , *MICROSTRUCTURE - Abstract
We study a time-dependent thermoelastic coupling within free vibrations of piezomagnetic (PM) microbeams considering the flexomagnetic (FM) phenomenon. The flexomagneticity relates to a magnetic field with a gradient of strains. Here, we use the generalized thermoelasticity theory of Lord–Shulman to analyze the interaction between elastic deformation and thermal conductivity. The uniform magnetic field is permeated in line with the transverse axis. Using the strain gradient approach, the beam yields microstructural properties. The analytical solving process has been gotten via applying sine Fourier technique on displacements. Graphical illustrations are assigned to shape numerical examples concerning variations in essential physical quantities. It was observed that the flexomagnetic effect could be extraordinary if the thermal conductivity of the material is higher or the thermal relaxation time of the heat source is lesser. This theoretical study will provide the way of starting studies on magneto-thermoelastic small-scale piezo-flexomagnetic structures based on the heat conduction models. [ABSTRACT FROM AUTHOR]
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- 2023
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5. Minimal surfaces and conservation laws for bidimensional structures.
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Eremeyev, Victor A
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MINIMAL surfaces , *CONSERVATION laws (Physics) , *MICROPOLAR elasticity , *FRACTURE mechanics , *CONSERVATION laws (Mathematics) , *SURFACES (Technology) , *ELASTICITY - Abstract
We discuss conservation laws for thin structures which could be modeled as a material minimal surface, i.e., a surface with zero mean curvatures. The models of an elastic membrane and micropolar (six-parameter) shell undergoing finite deformations are considered. We show that for a minimal surface, it is possible to formulate a conservation law similar to three-dimensional non-linear elasticity. It brings us a path-independent J -integral which could be used in mechanics of fracture. So, the class of minimal surfaces extends significantly a possible geometry of two-dimensional structures which possess conservation laws. [ABSTRACT FROM AUTHOR]
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- 2023
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6. On solvability of initial boundary-value problems of micropolar elastic shells with rigid inclusions.
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Eremeyev, Victor A, Lebedev, Leonid P, and Konopińska-Zmysłowska, Violetta
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ELASTIC plates & shells , *BOUNDARY value problems , *ORDINARY differential equations , *PARTIAL differential equations , *EXISTENCE theorems - Abstract
The problem of dynamics of a linear micropolar shell with a finite set of rigid inclusions is considered. The equations of motion consist of the system of partial differential equations (PDEs) describing small deformations of an elastic shell and ordinary differential equations (ODEs) describing the motions of inclusions. Few types of the contact of the shell with inclusions are considered. The weak setup of the problem is formulated and studied. It is proved a theorem of existence and uniqueness of a weak solution for the problem under consideration. [ABSTRACT FROM AUTHOR]
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- 2022
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7. Workshop "Micropolar continua and beyond".
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Müller, Wolfgang H. and Eremeyev, Victor A.
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STRAINS & stresses (Mechanics) - Abstract
We present a review of the recent workshop "Micropolar Continua and beyond" which held in March 28–31, 2023, at Technische University of Berlin, Germany. [ABSTRACT FROM AUTHOR]
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- 2024
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8. On weak solutions of the boundary value problem within linear dilatational strain gradient elasticity for polyhedral Lipschitz domains.
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Eremeyev, Victor A. and dell'Isola, Francesco
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STRAINS & stresses (Mechanics) , *BOUNDARY value problems , *ELASTICITY , *NUMERICAL solutions to differential equations , *FINITE element method - Abstract
We provide the proof of an existence and uniqueness theorem for weak solutions of the equilibrium problem in linear dilatational strain gradient elasticity for bodies occupying, in the reference configuration, Lipschitz domains with edges. The considered elastic model belongs to the class of so-called incomplete strain gradient continua whose potential energy density depends quadratically on linear strains and on the gradient of dilatation only. Such a model has many applications, e.g., to describe phenomena of interest in poroelasticity or in some situations where media with scalar microstructure are necessary. We present an extension of the previous results by Eremeyev et al. (2020 Z angew Math Phys 71 (6): 1–16) to the case of domains with edges and when external line forces are applied. Let us note that the interest paid to Lipschitz polyhedra-type domains is at least twofold. First, it is known that geometrical singularity of the boundary may essentially influence singularity of solutions. On the other hand, the analysis of weak solutions in polyhedral domains is of great significance for design of optimal computations using a finite-element method and for the analysis of convergence of numerical solutions. [ABSTRACT FROM AUTHOR]
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- 2022
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9. On nonlinear rheology of masonries and granular media.
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Reccia, Emanuele and Eremeyev, Victor A.
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MASONRY , *BRICKS , *DEFORMATIONS (Mechanics) - Abstract
We introduce a new rheological nonlinear model for some granular media such as masonries. The latter may demonstrate a rather complex behaviour. In fact, considering a masonry one can see that relative rotations of bricks are most important in comparison with deformation of bricks themselves. As a result, one gets stresses and couple stresses as static characteristics of such a medium. Using the Cosserat point approach for modelling of orientational interactions between masonry elements we provide a deformation energy for such a medium which takes into account both material and geometrical nonlinearity. [ABSTRACT FROM AUTHOR]
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- 2024
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10. Flexomagneticity in buckled shear deformable hard-magnetic soft structures.
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Malikan, Mohammad and Eremeyev, Victor A.
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SHEAR (Mechanics) , *STRAINS & stresses (Mechanics) , *ATOMIC structure , *ANALYTICAL solutions , *MAGNETIZATION - Abstract
This research work performs the first time exploring and addressing the flexomagnetic property in a shear deformable piezomagnetic structure. The strain gradient reveals flexomagneticity in a magnetization phenomenon of structures regardless of their atomic lattice is symmetrical or asymmetrical. It is assumed that a synchronous converse magnetization couples both piezomagnetic and flexomagnetic features into the material structure. The mathematical modeling begins with the Timoshenko beam model to find the governing equations and non-classical boundary conditions based on shear deformations. Flexomagneticity evolves at a small scale and dominant at micro/nanosize structures. Meanwhile, the well-known Eringen's-type model of nonlocal strain gradient elasticity is integrated with the mathematical process to fulfill the scaling behavior. From the viewpoint of the solution, the displacement of the physical model after deformation is carried out as the analytical solution of the Galerkin weighted residual method (GWRM), helping us obtain the numerical outcomes on the basis of the simple end conditions. The best of our achievements display that considering shear deformation is essential for nanobeams with larger values of strain gradient parameter and small amounts of the nonlocal coefficient. Furthermore, we showed that the flexomagnetic (FM) effect brings about more noticeable shear deformations' influence. [ABSTRACT FROM AUTHOR]
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- 2022
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11. Local material symmetry group for first- and second-order strain gradient fluids.
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Eremeyev, Victor A.
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STRAINS & stresses (Mechanics) , *SYMMETRY groups , *MASS density gradients , *STRAIN energy , *FLUIDS - Abstract
Using 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. Both models found applications to modeling of materials with complex inner structure such as beam-lattice metamaterials and fluids at small scales. The local material symmetry group is formed through such transformations of a reference placement which cannot be experimentally detected within the considered material model. We show that considering maximal symmetry group, i.e. material with strain energy that is independent of the choice of a reference placement, one comes to the constitutive equations of gradient fluids introduced independently on general strain gradient continua. [ABSTRACT FROM AUTHOR]
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- 2021
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12. On nonlinear dilatational strain gradient elasticity.
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Eremeyev, Victor A., Cazzani, Antonio, and dell'Isola, Francesco
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STRAINS & stresses (Mechanics) , *EULER-Lagrange equations , *ELASTIC deformation , *POROELASTICITY , *THEORY of wave motion , *ELASTICITY , *MICROSTRUCTURE - Abstract
We 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 only second gradient effects are due to the inhomogeneous dilatation state of the considered deformable body. The dilatational second gradient continua are strictly related to other generalized models with scalar (one-dimensional) microstructure as those considered in poroelasticity. They could be also regarded to be the result of a kind of "solidification" of the strain gradient fluids known as Korteweg or Cahn–Hilliard fluids. Using the variational approach we derive, for dilatational second gradient continua the Euler–Lagrange equilibrium conditions in both Lagrangian and Eulerian descriptions. In particular, we show that the considered continua can support contact forces concentrated on edges but also on surface curves in the faces of piecewise orientable contact surfaces. The conditions characterizing the possible externally applicable double forces and curve forces are found and examined in detail. As a result of linearization the case of small deformations is also presented. The peculiarities of the model is illustrated through axial deformations of a thick-walled elastic tube and the propagation of dilatational waves. [ABSTRACT FROM AUTHOR]
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- 2021
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13. Nonlinear resultant theory of shells accounting for thermodiffusion.
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Eremeyev, Victor A. and Pietraszkiewicz, Wojciech
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THERMOPHORESIS , *NONLINEAR theories , *ELASTIC plates & shells , *ENTROPY - Abstract
The 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 are discussed in more detail. They are formulated from restrictions imposed by the resultant 2D entropy imbalance according to Coleman–Noll procedure extended by a set of 2D constitutive equations based on heuristic assumptions. [ABSTRACT FROM AUTHOR]
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- 2021
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14. Surface and interfacial anti-plane waves in micropolar solids with surface energy.
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Chaki, Mriganka Shekhar, Eremeyev, Victor A, and Singh, Abhishek K
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SURFACE waves (Fluids) , *SURFACE energy , *ACOUSTIC surface waves , *PLANE wavefronts , *MICROPOLAR elasticity , *SURFACE strains , *SURFACE coatings - Abstract
In 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. Dispersion equations for both models have been obtained in algebraic form for two types of anti-plane wave, i.e. a Love-type wave and a new type of surface wave (due to micropolarity). The angular frequency and phase velocity of anti-plane waves have been analysed through a numerical study within cut-off frequencies. The obtained results may find suitable applications in thin film technology, non-destructive analysis or biomechanics, where the models discussed here may serve as theoretical frameworks for similar types of phenomena. [ABSTRACT FROM AUTHOR]
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- 2021
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15. Surface finite viscoelasticity and surface anti-plane waves.
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Eremeyev, Victor A.
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ACOUSTIC surface waves , *DISPERSION relations , *RELAXATION phenomena , *VISCOELASTICITY , *STRESS relaxation (Mechanics) - Abstract
We introduce the surface viscoelasticity under finite deformations. The theory is straightforward generalization of the Gurtin–Murdoch model to materials with fading memory. Surface viscoelasticity may reflect some surface related creep/stress relaxation phenomena observed at small scales. Discussed model could also describe thin inelastic coatings or thin interfacial layers. The constitutive equations for surface stresses are proposed. As an example we discuss propagation shear (anti-plane) waves in media with surface stresses taking into account viscoelastic effects. Here we analysed surface waves in an elastic half-space with viscoelastic coatings. Dispersion relations were derived. [ABSTRACT FROM AUTHOR]
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- 2024
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16. M-integral for finite anti-plane shear of a nonlinear elastic matrix with rigid inclusions.
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Eremeyev, Victor A. and Naumenko, Konstantin
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SHEAR (Mechanics) , *SHEARING force - Abstract
The path-independent M-integral plays an important role in analysis of solids with inhomogeneities. However, the available applications are almost limited to linear-elastic or physically non-linear power law type materials under the assumption of infinitesimal strains. In this paper we formulate the M-integral for a class of hyperelastic solids undergoing finite anti-plane shear deformation. As an application we consider the problem of rigid inclusions embedded in a Mooney–Rivlin matrix material. With the derived M-integral we compute weighted averages of the shear stress acting on the inclusion surface. Furthermore, we prove that a system of rigid inclusions can be replaced by one effective inclusion. [ABSTRACT FROM AUTHOR]
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- 2024
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17. On weak solutions of boundary value problems within the surface elasticity of Nth order.
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Eremeyev, Victor A., Lebedev, Leonid P., and Cloud, Michael J.
- Abstract
A 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 the weak solution. In order to characterize the smoothness of such solutions, certain energy functional spaces of Sobolev type are introduced. Compared with the solutions obtained in classical linear elasticity, weak solutions for solids with surface stresses are smoother on the boundary; more precisely, a weak solution belongs to H1(V)∩HN(Ss) where Ss⊂S≡∂V and V⊂R3. A 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 the weak solution..... [ABSTRACT FROM AUTHOR]
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- 2021
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18. On rotary inertia of microstuctured beams and variations thereof.
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Eremeyev, Victor A. and Elishakoff, Isaac
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METAMATERIALS , *MICROSTRUCTURE , *KINEMATICS , *DEFORMATIONS (Mechanics) , *ROTATIONAL motion - Abstract
We discuss the classic rotary inertia notion and extend it for microstructured beams introducing new microinertia parameters as an additional dynamic response to microstructure changes. Slender structures made of beam- or platelet-lattice metamaterials may exhibit not only large translations and rotations but also general deformations of inner structure. Here we considered a few examples of beam-like structures and derive their inertia properties which include effective mass density, rotary inertia and microinertia. Extended dynamic characteristics related to enhanced kinematics may be crucial for description of origami-like structures or other beam-lattice metamaterials. • Rotary inertia and its extensions for a few microstructured beams was discussed. • Rotary inertia and microinertia maybe dominant for some microstructures. • Rotary and microinertia may essentially depend on deformations. • Correspondence to other generalized models of slender structures and media is given. [ABSTRACT FROM AUTHOR]
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- 2024
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19. Buckling analysis of a non-concentric double-walled carbon nanotube.
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Malikan, Mohammad, Eremeyev, Victor A., and Sedighi, Hamid M.
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DOUBLE walled carbon nanotubes , *STRAINS & stresses (Mechanics) , *CARBON nanotubes , *CARBON , *ECCENTRICS (Machinery) , *TUBES - Abstract
On 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 for both inner and outer tubes is also considered based on the Lennard–Jones model. Galerkin decomposition is employed to numerically deal with the governing equations. It is evidently demonstrated that the geometrical eccentricity remarkably affects the stability threshold and its impact is to increase the static stability of DWCNTs. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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20. On the effective properties of foams in the framework of the couple stress theory.
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Skrzat, Andrzej and Eremeyev, Victor A.
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FOAM , *ELASTIC properties of metals , *STRAIN tensors , *METAL foams , *ELASTIC modulus , *COUPLES - Abstract
In 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. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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21. Can we really solve an arch stability problem?
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Chróścielewski, Jacek and Eremeyev, Victor A.
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ARCHES , *NONLINEAR equations , *BOUNDARY value problems , *PROBLEM solving - Abstract
We bring attention to the problem of solving nonlinear boundary-value problems for elastic structures such as arches and shells. Here we discuss a classical problem of a shear-deformable arch postbuckling. Considering a postbuckling behaviour of a circular arch we discuss the possibility to find numerically a solution for highly nonlinear regimes. The main attention is paid to the problem of determination of all solutions. The main conclusion that there is no guarantee to find all solutions, in general. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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22. On dynamics of origami-inspired rod.
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Berinskii, Igor and Eremeyev, Victor A.
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DISPERSION relations , *NONDESTRUCTIVE testing , *EQUATIONS of motion , *THEORY of wave motion , *ORIGAMI , *MOTION - Abstract
We discuss the dynamics of a relatively simple origami-inspired structure considering discrete and continuum models. The latter was derived as a certain limit of the discrete model. Here we analyze small in-plane deformations and related equations of infinitesimal motions. For both models, dispersion relations were derived and compared. The comparison of the dispersion relations showed that the continuum model can capture the behavior of origami structures, which can be helpful in the materials properties determination and nondestructive evaluation. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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23. Two- and three-dimensional elastic networks with rigid junctions: modeling within the theory of micropolar shells and solids.
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Eremeyev, Victor A.
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MICROPOLAR elasticity , *MODEL theory , *ORDINARY differential equations - Abstract
For two- and three-dimensional elastic structures made of families of flexible elastic fibers undergoing finite deformations, we propose homogenized models within the micropolar elasticity. Here we restrict ourselves to networks with rigid connections between fibers. In other words, we assume that the fibers keep their orthogonality during deformation. Starting from a fiber as the basic structured element modeled by the Cosserat curve beam model, we get 2D and 3D semi-discrete models. These models consist of systems of ordinary differential equations describing the statics of a collection of fibers with certain geometrical constraints. Using a specific homogenization technique, we introduce two- and three-dimensional equivalent continuum models which correspond to the six-parameter shell model and the micropolar continuum, respectively. We call two models equivalent if their approximations coincide with each other up to certain accuracy. The two- and three-dimensional constitutive equations of the networks are derived and discussed within the micropolar continua theory. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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24. On existence and uniqueness of weak solutions for linear pantographic beam lattices models.
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Eremeyev, Victor A., Alzahrani, Faris Saeed, Cazzani, Antonio, dell'Isola, Francesco, Hayat, Tasawar, Turco, Emilio, and Konopińska-Zmysłowska, Violetta
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SOBOLEV spaces , *ELLIPTIC operators , *DEFORMATION of surfaces , *DIFFERENTIAL operators , *STRAIN energy , *FUNCTION spaces , *ENERGY density - Abstract
In this paper, we discuss well-posedness of the boundary-value problems arising in some "gradient-incomplete" strain-gradient elasticity models, which appear in the study of homogenized models for a large class of metamaterials whose microstructures can be regarded as beam lattices constrained with internal pivots. We use the attribute "gradient-incomplete" strain-gradient elasticity for a model in which the considered strain energy density depends on displacements and only on some specific partial derivatives among those constituting displacements first and second gradients. So, unlike to the models of strain-gradient elasticity considered up-to-now, the strain energy density which we consider here is in a sense degenerated, since it does not contain the full set of second derivatives of the displacement field. Such mathematical problem was motivated by a recently introduced new class of metamaterials (whose microstructure is constituted by the so-called pantographic beam lattices) and by woven fabrics. Indeed, as from the physical point of view such materials are strongly anisotropic, it is not surprising that the mathematical models to be introduced must reflect such property also by considering an expression for deformation energy involving only some among the higher partial derivatives of displacement fields. As a consequence, the differential operators considered here, in the framework of introduced models, are neither elliptic nor strong elliptic as, in general, they belong to the class so-called hypoelliptic operators. Following (Eremeyev et al. in J Elast 132:175–196, 2018. 10.1007/s10659-017-9660-3) we present well-posedness results in the case of the boundary-value problems for small (linearized) spatial deformations of pantographic sheets, i.e., 2D continua, when deforming in 3D space. In order to prove the existence and uniqueness of weak solutions, we introduce a class of subsets of anisotropic Sobolev's space defined as the energy space E relative to specifically assigned boundary conditions. As introduced by Sergey M. Nikolskii, an anisotropic Sobolev space consists of functions having different differential properties in different coordinate directions. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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25. On the correspondence between two- and three-dimensional Eshelby tensors.
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Eremeyev, Victor A. and Konopińska-Zmysłowska, Violetta
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NONLINEAR equations , *CHEMICAL potential , *LETTERS , *ELASTICITY - Abstract
We consider both three-dimensional (3D) and two-dimensional (2D) Eshelby tensors known also as energy–momentum tensors or chemical potential tensors, which are introduced within the nonlinear elasticity and the resultant nonlinear shell theory, respectively. We demonstrate that 2D Eshelby tensor is introduced earlier directly using 2D constitutive equations of nonlinear shells and can be derived also using the through-the-thickness procedure applied to a 3D shell-like body. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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26. Comparison of anti-plane surface waves in strain-gradient materials and materials with surface stresses.
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Eremeyev, Victor A, Rosi, Giuseppe, and Naili, Salah
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ACOUSTIC surface waves , *SURFACES (Technology) , *ELASTIC wave propagation , *FREE surfaces , *SURFACE waves (Seismic waves) - Abstract
Here 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 are more localised near the free surface. For the strain-gradient elasticity model there is a range of wavenumbers where the amplitude of displacements decays very slowly. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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27. Foreword.
- Author
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Aßmus, Marcus, Eremeyev, Victor A., and Öchsner, Andreas
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CONTINUUM damage mechanics , *CONTINUUM mechanics - Published
- 2021
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28. Advances in Micro- and Nanomechanics.
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Eremeyev, Victor A.
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STRAINS & stresses (Mechanics) , *ATOMIC force microscopy techniques - Abstract
It is worth mentioning stress and strain gradient elasticity, surface elasticity, media with internal degrees of freedom, and nonlocal continua among others. 32967152 10 Tocci Monaco G., Fantuzzi N., Fabbrocino F., Luciano R. Critical temperatures for vibrations and buckling of magneto-electro-elastic nonlocal strain gradient plates. Recent advances in technologies of design, manufacturing and further studies of new materials and structures result in an essential extension of classic models of continuum and structural mechanics. [Extracted from the article]
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- 2022
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29. Anti-plane surface waves in media with surface structure: Discrete vs. continuum model.
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Eremeyev, Victor A. and Sharma, Basant Lal
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SURFACE structure - Abstract
We 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 from the ones in the bulk. As both models possess anti-plane surface waves we discuss similarities between the continuum and discrete viewpoint. In particular, in the context of the behaviour of phase velocity, we discuss the possible characterization of the surface shear modulus through the parameters involved in lattice formulation. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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30. On the material symmetry group for micromorphic media with applications to granular materials.
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Eremeyev, Victor A.
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GRANULAR materials , *CONTINUUM mechanics , *FLUID dynamics , *NONLINEAR systems , *ELASTICITY - Abstract
Highlights • New definition of the local material symmetry group within the nonlinear micromorphic continuum. • Definitions of micromorphic solids, fluids and subfluids. • Granular material as a micromorphic subfluid. Abstract Within the framework of the theory of nonlinear elastic micromorphic continua we introduce the new definition of the local material symmetry group. The group consists of ordered triples of second- and third-order tensors describing such changes of a reference placement that cannot be recognized with any experiment. Using the definition we characterize the micromorphic isotropic media, micromorphic fluids, solids and special intermediate cases called micromorphic subfluids or micromorphic liquid crystals. We demonstrate that some typical behaviour of such complex media as granular materials can be described within the micromorphic subfluids mechanics. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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31. Acceleration waves in the nonlinear micromorphic continuum.
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Eremeyev, Victor A., Lebedev, Leonid P., and Cloud, Michael J.
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ACCELERATION waves , *ELASTICITY , *NONLINEAR mechanics , *TENSOR products , *ENGINEERING - Abstract
Highlights • Acceleration waves in the nonlinear micromorphic medium are studied. • The formulas for the acoustic tensors are derived. • For the relaxed micromorphic continuum, the strong ellipticity condition is violated. Abstract Within the framework of the nonlinear elastic theory of micromorphic continua we derive the conditions for propagation of acceleration waves. An acceleration wave, also called a wave of weak discontinuity of order two, can be treated as a propagating nonmaterial surface across which the second derivatives of the placement vector and micro-distortion tensor may undergo jump discontinuities. Here we obtain the acoustic tensor for the micromorphic medium and formulate the conditions for existence of acceleration waves. As examples we consider these conditions for the linear micromorphic medium and for the relaxed micromorphic model. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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32. Virtual spring damper method for nonholonomic robotic swarm self-organization and leader following.
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Wiech, Jakub, Eremeyev, Victor A., and Giorgio, Ivan
- Subjects
- *
NONHOLONOMIC dynamical systems , *ROBOTICS - Abstract
In this paper, we demonstrate a method for self-organization and leader following of nonholonomic robotic swarm based on spring damper mesh. By self-organization of swarm robots we mean the emergence of order in a swarm as the result of interactions among the single robots. In other words the self-organization of swarm robots mimics some natural behavior of social animals like ants among others. The dynamics of two-wheel robot is derived, and a relation between virtual forces and robot control inputs is defined in order to establish stable swarm formation. Two cases of swarm control are analyzed. In the first case the swarm cohesion is achieved by virtual spring damper mesh connecting nearest neighboring robots without designated leader. In the second case we introduce a swarm leader interacting with nearest and second neighbors allowing the swarm to follow the leader. The paper ends with numeric simulation for performance evaluation of the proposed control method. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
33. Ellipticity of gradient poroelasticity.
- Author
-
Eremeyev, Victor A.
- Subjects
- *
STRAINS & stresses (Mechanics) , *ELLIPTIC equations , *ELASTICITY , *ENERGY density , *EQUILIBRIUM , *POROELASTICITY - Abstract
We discuss the ellipticity properties of an enhanced model of poroelastic continua called dilatational strain gradient elasticity. Within the theory there exists a deformation energy density given as a function of strains and gradient of dilatation. We show that the equilibrium equations are elliptic in the sense of Douglis–Nirenberg. These conditions are more general than the ordinary and strong ellipticity but keep almost all necessary properties of equilibrium equations. In particular, the loss of the ellipticity could be considered as a criterion of a strain localization or material instability. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
34. A layer-wise theory of shallow shells with thin soft core for laminated glass and photovoltaic applications.
- Author
-
Naumenko, Konstantin and Eremeyev, Victor A.
- Subjects
- *
PHOTOVOLTAIC cells , *LAMINATED glass , *THIN films , *DIFFERENTIAL equations , *GLASS construction - Abstract
The aim of this paper is to develop a robust layer-wise theory for structural analysis of curved glass and photovoltaic panels. By the analogy to the existing theories of plates, governing equations for doubly curved layers including kinematic relations, equilibrium conditions and constitutive equations are introduced. Applying assumptions of shear rigidity of skin layers and moments-free core layer as well as approximations of thin shallow shell, a reduced form of governing differential equations is proposed. Compared to the classical theories of shells the derived system includes an additional second order differential equation. As a result, additional boundary conditions should be satisfied for any edge of the shell. The importance of these extensions is demonstrated for long cylindrical panel with for two examples of simple supports: one with free edges, where relative in-plane displacements of skins are allowed, and one with framed edges, where cross-section rotations of all layers are assumed the same. For both cases closed-form analytical solutions related to a shell strip approximation are presented. Displacement bounds in monolithic and layered cases are derived, and the dependence of deformation and stress characteristics on the radius of curvature and types of supports are illustrated. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
35. Generalized continua with applications.
- Author
-
Altenbach, Holm and Eremeyev, Victor A.
- Subjects
- *
STRAINS & stresses (Mechanics) , *MICROPOLAR elasticity , *CONTINUUM mechanics , *SOLID mechanics , *FUNCTIONALLY gradient materials , *FRACTURE mechanics - Published
- 2022
- Full Text
- View/download PDF
36. On Finite Element Computations of Contact Problems in Micropolar Elasticity.
- Author
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Eremeyev, Victor A., Skrzat, Andrzej, and Stachowicz, Feliks
- Subjects
- *
MICROPOLAR elasticity , *POLYMERIC composites , *CONTACT mechanics , *SUBSTRATES (Materials science) , *FINITE element method - Abstract
Within the linear micropolar elasticity we discuss the development of new finite element and its implementation in commercial software. Here we implement the developed 8-node hybrid isoparametric element into ABAQUS and perform solutions of contact problems. We consider the contact of polymeric stamp modelled within the micropolar elasticity with an elastic substrate. The peculiarities of modelling of contact problems with a user defined finite element in ABAQUS are discussed. The provided comparison of solutions obtained within the micropolar and classical elasticity shows the influence of micropolar properties on stress concentration in the vicinity of contact area. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
37. The effect of shear deformations' rotary inertia on the vibrating response of multi-physic composite beam-like actuators.
- Author
-
Malikan, Mohammad and Eremeyev, Victor A.
- Subjects
- *
SHEAR (Mechanics) , *COMPOSITE construction , *ACTUATORS , *LAXATIVES , *ELASTICITY - Abstract
In the present work, the flexomagnetic (FM) behaviour of a vibrating squared multi-physic beam in finite dimensions. It is assumed that the bending and shear deformations cause rotary inertia. In the standard type of the Timoshenko beam the rotary inertia originated from shear deformations has been typically omitted. It means the rotary inertia resulting from shear deformation is a new concept considered here. Thus, the novelty in this work is that the effect of shear deformation's rotary inertia (SDRI) on the FM response will be considered in detail. When it comes to nanosize, the well-posed nonlocal elasticity assumption of Eringen can be worth choosing. In this study, the weak form (differential) of strain-driven nonlocal theory is taken into hand for easiness. The procedure of solution will be in regard to the advantage of the Galerkin weighted residual technique based on an analytical flow for the meta beam located at simply-simply supported ends. Several separate studies will show how SDRI and FM can influence each other. The observations give some new achievements in the series of studies on FM. It has been earned that the SDRI can directly impress the flexomagnetic feature of small-scale actuators. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
38. Nonlinear strain gradient and micromorphic one-dimensional elastic continua: Comparison through strong ellipticity conditions.
- Author
-
Eremeyev, Victor A. and Reccia, Emanuele
- Subjects
- *
STRAINS & stresses (Mechanics) , *ELASTICITY - Abstract
We discuss the strong ellipticity (SE) conditions for strain gradient and micromorphic continua considering them as an enhancement of a simple nonlinearly elastic material called in the following primary material. Recently both models are widely used for description of material behavior of beam-lattice metamaterials which may possess various types of material instabilities. We analyze how a possible loss of SE results in the behavior of enhanced models. We shown that SE conditions for a micromorphic medium is more restrictive than for its gradient counterpart. On the other hand we see that a violation of SE for a primary material affects solutions within enhanced models even if the SE conditions are fulfilled for them. • Strong ellipticity (SE) conditions are compared for nonlinear strain gradient (SG) and micromorphic (MM) elasticity. • Relations between SE of enhanced models and of simple nonlinear elastic (primary) material are clarified. • SE within SG approach is independent on SE of primary material, whereas SE of MM model elasticity inherits it partially. • Both models regularize primary material behavior, so non-existence of solutions is avoided. • SE conditions bring information on material instabilities within enhanced models of continua. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
39. Strong ellipticity within the Toupin–Mindlin first strain gradient elasticity theory.
- Author
-
Eremeyev, Victor A. and Lazar, Markus
- Subjects
- *
STRAINS & stresses (Mechanics) , *ELASTICITY , *BOUNDARY value problems - Abstract
We discuss the strong ellipticity (SE) condition within the Toupin–Mindlin first strain gradient elasticity theory. SE condition is closely related to certain material instabilities and describes mathematical properties of corresponding boundary-value problems. For isotropic solids, SE condition transforms into two inequalities in terms of five gradient-elastic moduli. • Strong ellipticity (SE) conditions within Toupin–Mindlin first strain gradient elasticity are formulated. • For an isotropic material, SE conditions transform into two inequalities in terms gradient-elastic moduli. • SE conditions and uniqueness of solutions were discussed. • SE conditions and characteristic lengths for a few materials are provided. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
40. Surface/interfacial anti-plane waves in solids with surface energy.
- Author
-
Eremeyev, Victor A., Rosi, Giuseppe, and Naili, Salah
- Subjects
- *
SURFACE energy , *PLANE wavefronts , *SOLIDS , *ELASTICITY , *STRAINS & stresses (Mechanics) , *KINETIC energy - Abstract
In this paper we discuss new type of surface anti-plane waves localized near the surface an elastic half-space and in the vicinity of plane interface between two half-spaces, when considering surface strain and kinetic energies. We also consider the case of non-perfect interface, i.e. when a jump of displacement or of its gradient, with the aim of modelling lacking of adhesion between solids. The phase velocity profiles and dispersion relations of surface waves are presented and several different material parameters are considered. Among the results, we observe an anomalous dispersion when the surface/interface is stiffer than the bulk material. These results can be exploited for the nondestructive characterization and the analysis of thin inter-phases between two solids, and can find several engineering applications. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
41. Mathematical study of boundary-value problems within the framework of Steigmann-Ogden model of surface elasticity.
- Author
-
Eremeyev, Victor and Lebedev, Leonid
- Subjects
- *
BOUNDARY value problems , *ELASTICITY , *NANOMECHANICS , *STRAINS & stresses (Mechanics) , *FUNCTIONAL analysis - Abstract
Mathematical questions pertaining to linear problems of equilibrium dynamics and vibrations of elastic bodies with surface stresses are studied. We extend our earlier results on existence of weak solutions within the Gurtin-Murdoch model to the Steigmann-Ogden model of surface elasticity using techniques from the theory of Sobolev's spaces and methods of functional analysis. The Steigmann-Ogden model accounts for the bending stiffness of the surface film; it is a generalization of the Gurtin-Murdoch model. Weak setups of the problems, based on variational principles formulated, are employed. Some uniqueness-existence theorems for weak solutions of static and dynamic problems are proved in energy spaces via functional analytic methods. On the boundary surface, solutions to the problems under consideration are smoother than those for the corresponding problems of classical linear elasticity and those described by the Gurtin-Murdoch model. The weak setups of eigenvalue problems for elastic bodies with surface stresses are based on the Rayleigh and Courant variational principles. For the problems based on the Steigmann-Ogden model, certain spectral properties are established. In particular, bounds are placed on the eigenfrequencies of an elastic body with surface stresses; these demonstrate the increase in the body rigidity and the eigenfrequencies compared with the situation where the surface stresses are neglected. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
42. Material symmetry group and constitutive equations of micropolar anisotropic elastic solids.
- Author
-
Eremeyev, Victor A. and Pietraszkiewicz, Wojciech
- Subjects
- *
MICROPOLAR elasticity , *STRAIN energy , *ENERGY density , *SYMMETRY , *CURVATURE - Abstract
We discuss the material symmetry group of the micropolar continuum and related consistently simplified constitutive equations. Following Eremeyev and Pietraszkiewicz (Int J Solid Struct 2012; 49: 1993–2005; Generalized continua as models for materials, Heidelberg: Springer, 2013, 77–90) we extend the definition of the group proposed by Eringen and Kafadar (Continuum physics, vol. 4, New York, NY: Academic Press, 1976, 1–75) by taking into account the microstructure curvature tensor as well as different transformation properties of polar (true) and axial (pseudo) tensors. Our material symmetry group consists of ordered triples of tensors which make the strain energy density of the micropolar continuum invariant under change of the reference placement. Within micropolar solids we discuss the isotropic, hemitropic, orthotropic, transversely isotropic and clinotropic materials and give explicitly the consistently reduced representations of the strain energy density. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
43. On effective properties of materials at the nano- and microscales considering surface effects.
- Author
-
Eremeyev, Victor
- Subjects
- *
NANOSTRUCTURED materials , *MECHANICAL behavior of materials , *ELASTICITY , *SURFACE properties , *SURFACE coatings - Abstract
In the last years, the rapid increase in the technical capability to control and design materials at the nanoscale has pushed toward an intensive exploitation of new possibilities concerning optical, chemical, thermoelectrical and electronic applications. As a result, new materials have been developed to obtain specific physical properties and performances. In this general picture, it was natural that the attention toward mechanical characterization of the new structures was left, in a sense, behind. Anyway, once the theoretically designed objects proceed toward concrete manufacturing and applications, an accurate and general description of their mechanical properties becomes more and more scientifically relevant. The aim of the paper is therefore to discuss new methods and techniques for modeling the behavior of nanostructured materials considering surface/interface properties, which are responsible for the main differences between nano- and macroscale, and to determine their actual material properties at the macroscale. Our approach is intended to study the mechanical properties of materials taking into account surface properties including possible complex inner microstructure of surface coatings. We use the Gurtin-Murdoch model of surface elasticity. We consider the inner regular and irregular surface thin coatings (i.e., ordered or disordered nanofibers arrays) and present few examples of averaged 2D properties of them. Since the actual 2D properties depend not only on the mechanical properties of fibers or other elements of a coating, but also on the interaction forces between them, the analysis also includes information on the geometry of the microstructure of the coating, on mechanical properties of elements and on interaction forces. Further we use the obtained 2D properties to derive the effective properties of solids and structures at the macroscale, such as the bending stiffness or Young's modulus. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
44. On the use of the first order shear deformation plate theory for the analysis of three-layer plates with thin soft core layer.
- Author
-
Altenbach, Holm, Eremeyev, Victor A., and Naumenko, Konstantin
- Subjects
- *
DEFORMATIONS (Mechanics) , *SHEAR (Mechanics) , *LAMINATED materials , *PHOTOVOLTAIC cells , *FIRST-order phase transitions - Abstract
Three-layer laminates with thin soft core layer can be found in many engineering applications. Examples include laminated glasses and photovoltaic panels. For such structures high contrast in the mechanical properties of faces and core requires the use of advanced methods to determine effective material properties of the laminate. In this paper we address the application of the first order shear deformation plate theory to the analysis of laminates with thin and soft core layer. In particular, transverse shear stiffness parameters for three-layered plates with different symmetric configurations are analyzed. For classical sandwiches with thick core layer the result coincides with the Reissner's formula. For the case of thin and compliant core layer the new expression for the effective shear stiffness is derived. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
45. On free oscillations of an elastic solids with ordered arrays of nano-sized objects.
- Author
-
Eremeyev, Victor, Ivanova, Elena, and Morozov, Nikita
- Subjects
- *
OSCILLATIONS , *ELASTIC solids , *NANOPARTICLES , *ELASTIC structures (Mechanics) , *EIGENFREQUENCIES - Abstract
We discuss free oscillations of some elastic structures consisting of an elastic substrate and an ordered array of aligned nano-sized objects. Considering various shapes of nano-objects such as beams, tubes, and spheres, we investigate the spectrum of eigenfrequencies of these structures in comparison with the spectra of one nano-object and of the substrate. As a result, we find the correspondence between the spectrum of whole structure and the spectrum of one nano-object, which gives the possibility to determine few first eigenfrequencies of nano-sized objects. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
46. The Rayleigh and Courant variational principles in the six-parameter shell theory.
- Author
-
Eremeyev, Victor A., Lebedev, Leonid P., and Cloud, Michael J.
- Subjects
- *
RAYLEIGH scattering , *MICROPOLAR elasticity , *EIGENFREQUENCIES , *EIGENVALUES , *EIGENVECTORS - Abstract
Courant’s minimax variational principle is considered in application to the six-parameter theory of prestressed shells. The equations of a prestressed micropolar shell are deduced in detail. Courant’s principle is used to study the dependence of the least and higher eigenfrequencies on shell parameters and boundary conditions. Cases involving boundary reinforcements and shell junctions are also treated. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
47. Fluid–solid interaction on a thin platelet with high-velocity flow: vibration modelling and experiment.
- Author
-
Ziółkowski, Piotr J., Ochrymiuk, Tomasz, and Eremeyev, Victor A.
- Subjects
- *
MACH number , *FINITE volume method , *FLUID dynamics , *FINITE element method , *FLOW velocity - Abstract
The paper concerns the nonlinear behaviour of a thin platelet that is streamlined in an aerodynamic tunnel. The air velocity in the aerodynamic tunnel was at 858.9 km/h or 0.7 Ma (Ma—Mach number is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound). This experiment was numerically simulated using FSI (fluid–solid interaction) tools, namely the coupling between the strength and flow code. The strength code uses the finite element method, while the flow code is based on the finite volume method. The coupling between the codes was made by means of an interface that transmitted the relevant data and results between the two codes. The paper discusses the methodology of this coupling. The study also highlights the phenomena occurring during the interaction of flow with the plate with emphasis on their nonlinear character. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
48. On time-dependent nonlinear dynamic response of micro-elastic solids.
- Author
-
Malikan, Mohammad and Eremeyev, Victor A.
- Subjects
- *
STRAINS & stresses (Mechanics) , *NONLINEAR equations , *NONLINEAR analysis - Abstract
• A microbeam based on the thin beam model has been assumed. • A dynamic extension of modified couple stress theory has been presented including micro-mass inertia. • A two-step solution technique is performed to solve nonlinear equations; Galerkin decomposition, and Homotopy perturbation methods. • Time-dependent large amplitude frequency has been investigated. A new approach to the mechanical response of micro-mechanic problems is presented using the modified couple stress theory. This model captured micro-turns due to micro-particles' rotations which could be essential for microstructural materials and/or at small scales. In a micro media based on the small rotations, sub-particles can also turn except the whole domain rotation. However, this framework is competent for a static medium. In terms of dynamic investigations of micro materials, it is required to involve micro-rotations' mass inertias. This fact persuades us to pay particular attention to the micro mechanics' samples and directed us to re-derive the modified couple stress model to propose and represent a new micro-mechanic approach which is well-deserved, especially for dynamic studies of microstructures. In carrying out this job, the classical beam has provided the basic form of formulation procedure. The continuum medium has been limited to a square flat non-porous beam deducing a homogeneous isotropic micromaterial. As long as the time-dependent results are concerned due to studying micro-mass inertia in time history, there would be two solution steps. The Galerkin decomposition technique is imposed in accord with an analytical postulate to issue the algebraic problem distributing time-dependent equations. The latter, the Homotopy perturbation method delivers time-dependent outcomes. The solution methods have been validated by building numerical models in Abaqus software. On the new achievements of this study, one can declare that both static and dynamic length scale parameters are very effective in order to study vibrations of microstructures. If the values of these characteristic lengths are considerable, the nonlinear frequency analysis will be essential. Furthermore, the stiffness of the structure will be higher if the values of both length scale parameters increase. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
49. Electrodynamics from the viewpoint of modern continuum theory—A review.
- Author
-
Müller, Wolfgang H., Vilchevskaya, Elena N., and Eremeyev, Victor A.
- Subjects
- *
ELECTROMAGNETIC fields , *MAXWELL equations , *ELECTRIC flux , *ELECTRODYNAMICS , *MATHEMATICAL continuum , *ELECTRIC charge - Abstract
This paper wants to draw attention to several issues in electrodynamic field theory and to make way for a rational continuum approach to the subject. The starting point are the balances for magnetic flux and electric charge, both in a very general formulation for volumes and for open surfaces, all of which can deform and be immaterial or material. The spatial point‐of‐view for the description of fields is favored and its advantages in comparison to the concept of material particles is explained. A straightforward answer to the question of how to choose units for the electromagnetic fields most suitably is also presented. The transformation properties of the electromagnetic fields are addressed by rewriting the balances in space–time notation. Special attention is paid to the connection between the two sets of electromagnetic fields through the so‐called Maxwell–Lorentz–æther relations. The paper ends with an outlook into constitutive theory of matter under the influence of electromagnetic fields and a discussion on curious developments in context with Maxwell's equations. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
50. A layer-wise theory for laminated glass and photovoltaic panels.
- Author
-
Naumenko, Konstantin and Eremeyev, Victor A.
- Subjects
- *
LAMINATED glass , *CIVIL engineering , *SOLAR cells , *CONSTRAINTS (Physics) , *SYMMETRY (Physics) , *SHEAR (Mechanics) - Abstract
Abstract: Laminated plates with glass skin layers and a core layer from soft polymers are widely used in the civil engineering. Photovoltaic panels currently available on the market are composed from stiff front and back layers and a solar cell layer embedded in a soft polymeric encapsulant. In this paper a layer-wise theory for the structural analysis of glass and photovoltaic laminates is developed. Starting from governing equations for individual layers, kinematical constraints and appropriate interaction forces, a twelfth order system of partial differential equations is derived. The primary variables in the theory include the Airy stress function, the deflection function and the vector of relative in-plane displacements of skin layers. For symmetric laminates a system of uncoupled differential equations with respect to scalar potentials is presented. Three of them correspond to the first order shear deformation plate. The new additional second order differential equation provides a correction function according to the layer-wise theory. Closed form analytical solutions for a plate strip are derived to illustrate the essential influence of this correction for laminates with soft core layer. The importance of additional boundary conditions is shown for examples of free and framed plate edges. [Copyright &y& Elsevier]
- Published
- 2014
- Full Text
- View/download PDF
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