Search results for: STRAIN GRADIENT ELASTICITY

A Note on Reduced Strain Gradient Elasticity
PublicationWe discuss the particular class of straingradient elastic material models which we called the reduced or degenerated straingradient elasticity. For this class the strain energy density depends on functions which have different differential properties in different spatial directions. As an example of such media we consider the continual models of pantographic beam lattices and smectic and columnar liquid crystals.

Weak Solutions within the GradientIncomplete StrainGradient Elasticity
PublicationIn this paper we consider existence and uniqueness of the threedimensional static boundaryvalue problems in the framework of socalled gradientincomplete straingradient elasticity. We call the straingradient elasticity model gradientincomplete such model where the considered strain energy density depends on displacements and only on some specific partial derivatives of displacements of first and secondorder. Such models...

On Dynamic Boundary Conditions Within the Linear SteigmannOgden Model of Surface Elasticity and Strain Gradient Elasticity
PublicationWithin the strain gradient elasticity we discuss the dynamic boundary conditions taking into account surface stresses described by the Steigmann–Ogden model. The variational approach is applied with the use of the least action functional. The functional is represented as a sum of surface and volume integrals. The surface strain and kinetic energy densities are introduced. The Toupin–Mindlin formulation of the strain gradient elasticity...

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...

Analysis of strain localization in reinforced concrete elements with explicit secondgradient strain damage approach
PublicationArtykuł omawia obliczanie elementów żelbetowych przy zastosowaniu modelu zniszczeniowego z degradacją sztywności z uwzględnieniem lokalizacji odkształceń. Obliczenia wykonano dla belek żelbetowych.

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...

Electromagnetic forced vibrations of composite nanoplates using nonlocal strain gradient theory
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Comparison of antiplane surface waves in straingradient materials and materials with surface stresses
PublicationHere we discuss the similarities and differences in antiplane surface wave propagation in an elastic halfspace within the framework of the theories of Gurtin–Murdoch surface elasticity and Toupin–Mindlin straingradient 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...

Stability analysis of nanobeams in hygrothermal environment based on a nonlocal strain gradient Timoshenko beam model under nonlinear thermal field
PublicationThis article is dedicated to analyzing the buckling behavior of nanobeam subjected to hygrothermal environments based on the principle of the Timoshenko beam theory. The hygroscopic environment has been considered as a linear stress field model, while the thermal environment is assumed to be a nonlinear stress field based on the Murnaghan model. The sizedependent effect of the nanobeam is captured by the nonlocal strain gradient...

Torsional stability capacity of a nanocomposite shell based on a nonlocal strain gradient shell model under a threedimensional magnetic field
PublicationThis paper considers a singlewalled composite nanoshell (SWCNS) exposed in a torsional critical stability situation. As the magnetic field affects remarkably nanostructures in the small size, a threedimensional 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 smallscale approach and the firstorder...

HYGROMAGNETIC VIBRATION OF THE SINGLEWALLED CARBON NANOTUBE WITH NONLINEAR TEMPERATURE DISTRIBUTION BASED ON A MODIFIED BEAM THEORY AND NONLOCAL STRAIN GRADIENT MODEL
PublicationIn this study, vibration analysis of singlewalled carbon nanotube (SWCNT) has been carried out by using a refined beam theory, namely one variable shear deformation beam theory. This approach has one variable lesser than a contractual shear deformation theory such as firstorder shear deformation theory (FSDT) and acts like classical beam approach but with considering shear deformations. The SWCNT has been placed in an axial or...

Damped forced vibration analysis of singlewalled carbon nanotubes resting on viscoelastic foundation in thermal environment using nonlocal strain gradient theory
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Implementation of Haar wavelet, higher order Haar wavelet, and differential quadrature methods on buckling response of strain gradient nonlocal beam embedded in an elastic medium
PublicationThe present investigation is focused on the buckling behavior of strain gradient nonlocal beam embedded in Winkler elastic foundation. The firstorder strain gradient model has been combined with the Euler–Bernoulli beam theory to formulate the proposed model using Hamilton’s principle. Three numerically efficient methods, namely Haar wavelet method (HWM), higher order Haar wavelet method (HOHWM), and differential quadrature method...

Buckling analysis of piezomagnetoelectric nanoplates in hygrothermal environment based on a novel one variable plate theory combining with higherorder nonlocal strain gradient theory
Publication 
Victor Eremeev dr hab.
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On the Equations of the Surface Elasticity Model Based on the Theory of Polymeric Brushes
PublicationMotivating by theory of polymers, in particular, by the models of polymeric brushes we present here the homogenized (continual) twodimensional (2D) model of surface elasticity. A polymeric brush consists of an system of almost aligned rigid polymeric chains. The interaction between chain links are described through Stockmayer potential, which take into account also dipoledipole interactions. The presented 2D model can be treated...

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...

On existence and uniqueness of weak solutions for linear pantographic beam lattices models
PublicationIn this paper, we discuss wellposedness of the boundaryvalue problems arising in some “gradientincomplete” straingradient elasticity models, which appear in the study of homogenized models for a large class ofmetamaterials whosemicrostructures can be regarded as beam lattices constrained with internal pivots. We use the attribute “gradientincomplete” straingradient elasticity for a model in which the considered strain energy...

On instabilities and postbuckling of piezomagnetic and flexomagnetic nanostructures
PublicationWe focus on the mechanical strength of piezomagnetic beamlike nanosize sensors during postbuckling. An effective flexomagnetic property is also taken into account. The modelled sensor is selected to be a EulerBernoulli type beam. Longrange interactions between atoms result in a mathematical model based on the nonlocal strain gradient elasticity approach (NSGT). Due to possible large deformations within a postbuckling phenomenon,...

On the peculiarities of antiplane surface waves propagation for media with microstructured coating
PublicationWe discuss new type of surface waves which exist in elastic media with surface energy. Here we present the model of a coating made of polymeric brush. From the physical point of view the considered model of surface elasticity describes a highly anisotropic surface coating. Here the surface energy model could be treated as 2D reduced strain gradient continuum as surface strain energy depends on few second spatial derivatives of...

On the plastic buckling of curved carbon nanotubes
PublicationThis research, for the first time, predicts theoretically static stability response of a curved carbon nanotube (CCNT) under an elastoplastic behavior with several boundary conditions. The CCNT is exposed to axial compressive loads. The equilibrium equations are extracted regarding the Euler–Bernoulli displacement field by means of the principle of minimizing total potential energy. The elastoplastic stressstrain is concerned...

Effect of Axial Porosities on Flexomagnetic Response of InPlane 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 sizedependent property. Therefore,...

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...

On AntiPlane Surface Waves Considering Highly Anisotropic Surface Elasticity Constitutive Relations
PublicationWithin the framework of highly anisotropic surface elasticity model we discuss the propagation of new type of surface waves that are antiplane surface waves. By the highly anisotropic surface elasticity model we mean the model with a surface strain energy density which depends on incomplete set of second derivatives of displacements. From the physical point of view this model corresponds to a coating made of a family of parallel...

Torsional elasticity and energetics of F1ATPase
PublicationFoF1ATPase is a rotary motor protein synthesizing ATP from ADP driven by a crossmembrane proton gradient. The proton flow through the membraneembedded Fo generates the rotary torque that drives the rotation of the asymmetric shaft of F1. Mechanical energy of the rotating shaft is used by the F1 catalytic subunit to synthesize ATP. It was suggested that elastic power transmission with transient storage of energy in some compliant...

On Nonlinear Bending Study of a PiezoFlexomagnetic Nanobeam Based on an AnalyticalNumerical Solution
PublicationAmong various magnetoelastic 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 higherorder 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...

Postcritical buckling of truncated conical carbon nanotubes considering surface effects embedding in a nonlinear Winkler substrate using the RayleighRitz method
PublicationThis research predicts theoretically postcritical axial buckling behavior of truncated conical carbon nanotubes (CCNTs) with several boundary conditions by assuming a nonlinear Winkler matrix. The postbuckling of CCNTs has been studied based on the EulerBernoulli beam model, Hamilton’s principle, Lagrangian strains, and nonlocal strain gradient theory. Both stiffnesshardening and stiffnesssoftening properties of the nanostructure...

Strongly anisotropic surface elasticity and antiplane surface waves
PublicationWithin the new model of surface elasticity, the propagation of antiplane surface waves is discussed. For the proposed model, the surface strain energy depends on surface stretching and on changing of curvature along a preferred direction. From the continuum mechanics point of view, the model describes finite deformations of an elastic solid with an elastic membrane attached on its boundary reinforced by a family of aligned elastic...

Stressdriven nonlocal elasticity for nonlinear vibration characteristics of carbon/boronnitride heteronanotube subject to magnetothermal environment
PublicationStressdriven nonlocal theory of elasticity, in its differential form, is applied to investigate the nonlinear vibrational characteristics of a heteronanotube in magnetothermal environment with the help of finite element method. In order to more precisely deal with the dynamic behavior of sizedependent nanotubes, a twonode beam element with six degreesof freedom including the nodal values of the deflection, slope and curvature...

Surface and interfacial antiplane waves in micropolar solids with surface energy
PublicationIn this work, the propagation behaviour of a surface wave in a micropolar elastic halfspace with surface strain and kinetic energies localized at the surface and the propagation behaviour of an interfacial antiplane wave between two micropolar elastic halfspaces 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....

Buckling analysis of a nonconcentric doublewalled carbon nanotube
PublicationOn the basis of a theoretical study, this research incorporates an eccentricity into a system of compressed doublewalled 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...

Applications of Tensor Analysis in Continuum Mechanics
PublicationA tensor field is a tensorvalued function of position in space. The use of tensor fields allows us to present physical laws in a clear, compact form. A byproduct is a set of simple and clear rules for the representation of vector differential operators such as gradient, divergence, and Laplacian in curvilinear coordinate systems. The tensorial nature of a quantity permits us to formulate transformation rules for its components...

Mechanical analysis of eccentric defected bilayer graphene sheets considering the van der Waals force
PublicationIn this article, we have tried to simulate nonlinear bending analysis of a doublelayered graphene sheet which contains a geometrical imperfection based on an eccentric hole. The firstorder shear deformation theory is considered to obtain the governing equations. Also, the nonlinear von Kármán strain field has been assumed in order to obtain large deformations. Whereas the doublelayered graphene sheet has been considered, the...

On the geometrically nonlinear vibration of a piezoflexomagnetic 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 piezoflexomagnetic elastic wall is considered. By the inclusion of EulerBernoulli beam and using Hamilton’s principle, the equations governing the system...

A coldadapted esterase from psychrotrophic Pseudoalteromonas sp. strain 643A
PublicationDzięki zastosowaniu lipaz możliwa jest biotechnologiczna produkcja m.in. biodegradowalnych biopolimerów, biopaliw (tzw. biodiesel), wielu terapeutyków, herbicydów, pestycydów, kosmetyków, substancji smakowych, serów i in. Szczególnie interesującą grupę stanowią enzymy lipolityczne, pochodzące z organizmów psychrofilnych i psychrotrofowych, ze względu na zdolność do wydajnego katalizowania reakcji w temperaturach rzędu 1020 ºC....

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Journals 
Drilling couples and refined constitutive equations in the resultant geometrically nonlinear theory of elastic shells
PublicationIt is well known that distribution of displacements through the shell thickness is nonlinear, in general. We introduce a modified polar decomposition of shell deformation gradient and a vector of deviation from the linear displacement distribution. When strains are assumed to be small, this allows one to propose an explicit definition of the drilling couples which is proportional to tangential components of the deviation vector....

Proper gradient otopies
PublicationWe prove that the inclusion of the space of proper gradient local maps into the space of proper local maps induces a bijection between the sets of the respective otopy classes of these maps.

Proper gradient otopies
PublicationWe prove that the inclusion of the space of proper gradient local maps into the space of proper local maps induces a bijection between the sets of the respective otopy classes of these maps.

The Hopf theorem for gradient local vector fields on manifolds
PublicationWe prove the Hopf theorem for gradient local vector fields on manifolds, i.e., we show that there is a natural bijection between the set of gradient otopy classes of gradient local vector fields and the integers if the manifold is connected Riemannian without boundary.

Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree
PublicationConsider the Euclidean space Rn with the orthogonal action of a compact Lie group G. We prove that a locally Lipschitz Ginvariant mapping f from Rn to R can be uniformly approximated by Ginvariant smooth mappings g in such a way that the gradient of g is a graph approximation of Clarke’s generalized gradient of f . This result enables a proper development of equivariant gradient degree theory for a class of setvalued gradient...

Linear Micropolar Elasticity Analysis of Stresses in Bones Under Static Loads
PublicationWe discuss the finite element modeling of porous materials such as bones using the linear micropolar elasticity. In order to solve static boundaryvalue problems, we developed new finite elements, which capture the micropolar behavior of the material. Developed elements were implemented in the commercial software ABAQUS. The modeling of a femur bone with and without implant under various stages of healing is discussed in details

On Effective Bending Stiffness of a Laminate Nanoplate Considering Steigmann–Ogden Surface Elasticity
PublicationAs at the nanoscale the surfacetovolume 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 surfacerelated...

The Hopf type theorem for equivariant gradient local maps
PublicationWe construct a degreetype otopy invariant for equivariant gradient local maps in the case of a real finitedimensional orthogonal representation of a compact Lie group. We prove that the invariant establishes a bijection between the set of equivariant gradient otopy classes and the direct sum of countably many copies of Z.

On relations between gradient and classical equivariant homotopy groups of spheres
PublicationWe investigate relations between stable equivariant homotopy groups of spheres in classical and gradient categories. To this end, the auxiliary category of orthogonal equivariant maps, a natural enlargement of the category of gradient maps, is used. Our result allows for describing stable equivariant homotopy groups of spheres in the category of orthogonal maps in terms of classical stable equivariant groups of spheres with shifted...

Path components of the space of gradient vector fields on the two dimensional disc
PublicationWe present a short proof that if two gradient maps on the twodimensional disc have the same degree, then they are gradient homotopic.

Analysis of Accuracy of Modified Gradient Method in Indoor Radiolocalisation System
PublicationIn this paper a new method, called modified gradient method, has been proposed for position calculation on the basis of distance measurement in indoor environment. It is shown that well known method of position calculation such as Foy is inefficient in indoor environment. In this article is also described the indoor radiolocalisation system which was used for collecting distance measurements which were employed for further comparative...

Classification of homotopy classes of equivariant gradient maps
PublicationNiech V będzie ortogonalną reprezentacją zwartej grupy Liego Gi niech S(V),D(V) oznaczają sferę jednostkową i kulę jednostkową V.Jeżeli F jest Gniezmienniczą funkcją rzeczywistą klasy C^1 na Vto mówimy, że grad F (gradient F) jest dopuszczalny, jeżeli(grad F)(x) jest różny od zera dla x należących do S(V). Pracapoświęcona jest homotopijnej klasyfikacji dopuszczalnychGniezmienniczych odwzorowań gradientowych.

Free Vibration of Flexomagnetic Nanostructured Tubes Based on Stressdriven 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, EulerBernoulli 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,...

Refinement of the Hardening Soil model within the small strain range
PublicationThe popularity of the elastoplastic Hardening Soil (HS) model is based on simple parameter identification from standard testing and empirical formulas. The HS model is implemented in many commercial FE codes designed to analyse geotechnical problems. In its basic version, the stress–strain behaviour within the elastic range is subject to the hypoelastic power law, which assures the barotropy of the elastic stiffness. However,...