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Search results for: NOVEL ELASTICITY THEORY
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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) two-dimensional (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 dipole-dipole interactions. The presented 2D model can be treated...
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Strong ellipticity within the Toupin–Mindlin first strain gradient elasticity theory
PublicationWe 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.
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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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Nonlocal three-dimensional theory of elasticity for buckling behavior of functionally graded porous nanoplates using volume integrals
PublicationIn this paper, the buckling of rectangular functionally graded (FG) porous nanoplates based on threedimensional elasticity is investigated. Since, similar researches have been done in two-dimensional analyses in which only large deflections with constant thickness were studied by using various plate theories; therefore, discussion of large deformations and change in thickness of plates after deflection in this study is examined....
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On the Buckling Response of Axially Pressurized Nanotubes Based on a Novel Nonlocal Beam Theory
PublicationIn the present study, the buckling analysis of single-walled carbon nanotubes (SWCNT) on the basis of a new refined beam theory is analyzed. The SWCNT is modeled as an elastic beam subjected to unidirectional compressive loads. To achieve this aim, the new proposed beam theory has only one unknown variable which leads to one equation similar to Euler beam theory and is also free from any shear correction factors. The equilibrium...
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Differential Quadrature Method for Dynamic Buckling of Graphene Sheet Coupled by a Viscoelastic Medium Using Neperian Frequency Based on Nonlocal Elasticity Theory
PublicationIn the present study, the dynamic buckling of the graphene sheet coupled by a viscoelastic matrix was studied. In light of the simplicity of Eringen's non-local continuum theory to considering the nanoscale influences, this theory was employed. Equations of motion and boundary conditions were obtained using Mindlin plate theory by taking nonlinear strains of von Kármán and Hamilton's principle into account. On the other hand, a...
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Buckling analysis of piezo-magnetoelectric nanoplates in hygrothermal environment based on a novel one variable plate theory combining with higher-order nonlocal strain gradient theory
PublicationIn the present investigation, a new first-order shear deformation theory (OVFSDT) on the basis of the in-plane stability of the piezo-magnetoelectric composite nanoplate (PMEN) has been developed, and its precision has been evaluated. The OVFSDT has many advantages compared to the conventional first-order shear deformation theory (FSDT) such as needless of shear correction factors, containing less number of unknowns than the existing...
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A novel one-variable first-order shear deformation theory for biaxial buckling of a size-dependent plate based on Eringen’s nonlocal differential law
PublicationPurpose – This paper aims to present a new one-variable first-order shear deformation theory (OVFSDT) using nonlocal elasticity concepts for buckling of graphene sheets. Design/methodology/approach – The FSDT had errors in its assumptions owing to the assumption of constant shear stress distribution along the thickness of the plate, even though by using the shear correction factor (SCF), it has been slightly corrected, the errors...
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Ellipticity in couple-stress elasticity
PublicationWe 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...
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Central-force decomposition of spline-based modified embedded atom method potential
PublicationCentral-force decompositions are fundamental to the calculation of stress fields in atomic systems by means of Hardy stress. We derive expressions for a central-force decomposition of the spline-based modified embedded atom method (s-MEAM) potential. The expressions are subsequently simplified to a form that can be readily used in molecular-dynamics simulations, enabling the calculation of the spatial distribution of stress in...
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Saint-Venant torsion based on strain gradient theory
PublicationIn this study, the Saint-Venant torsion problem based on strain gradient theory is developed. A total form of Mindlin's strain gradient theory is used to acquire a general Saint-Venant torsion problem of micro-bars formulation. A new Finite Element formulation based on strain gradient elasticity theory is presented to solve the Saint-Venant torsion problem of micro-bars. Moreover, the problem is solved for both micro and macro...
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Nonlocal elasticity analysis of moderately thick porous functionally graded plates in a hygro-thermal environment
PublicationThis work performs a novel quasi three-dimensional (3D) bending analysis for a moderately thick functionally graded material (FGM) made of nanoceramics and metal powders, in presence of porosities due to some incorrect manufacturing processes. Such porosities can appear within the plate in two forms, namely, even and uneven distributions. The modeled system assumes a polymer matrix where both shear and transverse factors coexist....
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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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HYGRO-MAGNETIC VIBRATION OF THE SINGLE-WALLED CARBON NANOTUBE WITH NONLINEAR TEMPERATURE DISTRIBUTION BASED ON A MODIFIED BEAM THEORY AND NONLOCAL STRAIN GRADIENT MODEL
PublicationIn this study, vibration analysis of single-walled 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 first-order shear deformation theory (FSDT) and acts like classical beam approach but with considering shear deformations. The SWCNT has been placed in an axial or...
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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 size-dependent effect of the nanobeam is captured by the nonlocal strain gradient...
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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 Boundary Conditions Within the Linear Steigmann-Ogden 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...
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Analytical predictions for the buckling of a nanoplate subjected to non-uniform compression based on the four-variable plate theory
PublicationIn the present study, the buckling analysis of the rectangular nanoplate under biaxial non-uniform compression using the modified couple stress continuum theory with various boundary conditions has been considered. The simplified first order shear deformation theory (S-FSDT) has been employed and the governing differential equations have been obtained using the Hamilton’s principle. An analytical approach has been applied to obtain...
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Buckling Analysis of a Micro Composite Plate with Nano Coating Based on the Modified Couple Stress Theory
PublicationThe present study investigates the buckling of a thick sandwich plate under the biaxial non-uniform compression using the modified couple stress theory with various boundary conditions. For this purpose, the top and bottom faces are orthotropic graphene sheets and for the central core the isotropic soft materials are investigated. The simplified first order shear deformation theory (S-FSDT) is employed and the governing differential...
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On mechanics of piezocomposite shell structures
PublicationThis study presents an original and novel investigation into the mechanics of piezo-flexo-magneto-elastic nanocomposite doubly-curved shells (PFMDCSs) and the ability to detect the lower and higher levels of electro-magnetic fields. In this context, by utilizing the first-order shear deformation shell model, stresses and strains are acquired. By imposing Hamilton's principle and the von Kármán approach, the governing equations...
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Effects of Surface Energy and Surface Residual Stresses on Vibro-Thermal Analysis of Chiral, Zigzag, and Armchair Types of SWCNTs Using Refined Beam Theory
PublicationIn this article, vibration characteristics of three different types of Single-Walled Carbon Nanotubes (SWCNTs) such as armchair, chiral, and zigzag carbon nanotubes have been investigated considering the effects of surface energy and surface residual stresses. The nanotubes are embedded in the elastic substrate of the Winkler type and are also exposed to low and high-temperature environments. A new refined beam theory namely, one-variable...
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Implementation of Hermite-Ritz method and Navier’s Technique for Vibration of Functionally Graded Porous Nanobeam Embedded in Winkler-Pasternak Elastic Foundation Using bi-Helmholtz type of nonlocal elasticity
PublicationPresent study is devoted to investigating the vibration characteristics of Functionally Graded (FG) porous nanobeam embedded in an elastic substrate of Winkler-Pasternak type. Classical beam theory (CBT) or Euler-Bernoulli beam theory (EBT) has been incorporated to address the displacement of the FG nanobeam. Bi-Helmholtz type of nonlocal elasticity is being used to capture the small scale effect of the FG nanobeam. Further, the...
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Torsional elasticity and energetics of F1-ATPase
PublicationFoF1-ATPase is a rotary motor protein synthesizing ATP from ADP driven by a cross-membrane proton gradient. The proton flow through the membrane-embedded 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...
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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...
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On a flexomagnetic behavior of composite structures
PublicationThe popularity of the studies is getting further on the flexomagnetic (FM) response of nano-electro-magneto machines. In spite of this, there are a few incompatibilities with the available FM model. This study indicates that the accessible FM model is inappropriate when considering the converse magnetization effect that demonstrates the necessity and importance of deriving a new FM relation. Additionally, the literature has neglected...
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Analiza nieliniowa powłok z materiałów gradientowych w ośrodku mikropolarnym
PublicationW pracy zaprezentowano analizę powłok z materiałów gradientowych dla zakresu dużych przemieszczeń. Macierz konstytutywna została wyprowadzona dla elementu powłokowego o 6 stopniach swobody w węźle w teorii ośrodka mikropolarnego. Zaprezentowano wyniki numeryczne dla swobodnie podpartej kwadratowej płyty FGM i porównano je z wynikami z literatury oraz uzyskanymi w programie Abaqus.
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A Note on Reduced Strain Gradient Elasticity
PublicationWe discuss the particular class of strain-gradient elastic material models which we called the reduced or degenerated strain-gradient 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.
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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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On Anti-Plane 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 anti-plane 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...
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Stress-driven nonlocal elasticity for nonlinear vibration characteristics of carbon/boron-nitride hetero-nanotube subject to magneto-thermal environment
PublicationStress-driven nonlocal theory of elasticity, in its differential form, is applied to investigate the nonlinear vibrational characteristics of a hetero-nanotube in magneto-thermal environment with the help of finite element method. In order to more precisely deal with the dynamic behavior of size-dependent nanotubes, a two-node beam element with six degrees-of freedom including the nodal values of the deflection, slope and curvature...
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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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Non-linear static stability of bi-layer carbon nanosheets resting on an elastic matrix under various types of in-plane shearing loads in thermo-elasticity using nonlocal continuum
PublicationIn this research, the shear and thermal buckling of bi-layer rectangular orthotropic carbon nanosheets embedded on an elastic matrix using the nonlocal elasticity theory and non-linear strains of Von-Karman was studied. The bi-layer carbon sheets were modeled as a double-layered plate, and van der Waals forces between layers were considered. The governing equations and boundary conditions were obtained using the first order shear...
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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 boundary-value 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
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Two- and three-dimensional elastic networks with rigid junctions: modeling within the theory of micropolar shells and solids
PublicationFor 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...
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On the correspondence between two- and three-dimensional Eshelby tensors
PublicationWe 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 throughthe-thickness...
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Ellipticity of gradient poroelasticity
PublicationWe 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...
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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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Thermal Buckling Analysis of Circular Bilayer Graphene sheets Resting on an Elastic Matrix Based on Nonlocal Continuum Mechanics
PublicationIn this article, the thermal buckling behavior of orthotropic circular bilayer graphene sheets embedded in the Winkler–Pasternak elastic medium is scrutinized. Using the nonlocal elasticity theory, the bilayer graphene sheets are modeled as a nonlocal double–layered plate that contains small scale effects and van der Waals (vdW) interaction forces. The vdW interaction forces between the layers are simulated as a set of linear springs...
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ON DYNAMICS OF ELASTIC NETWORKS WITH RIGID JUNCTIONS WITHIN NONLINEAR MICRO-POLAR ELASTICITY
PublicationWithin the nonlinear micropolar elasticity we discuss effective dynamic (kinetic) properties of elastic networks with rigid joints. The model of a hyperelastic micropolar continuum is based on two constitutive relations, i.e., static and kinetic ones. They introduce a strain energy density and a kinetic energy density, respectively. Here we consider a three-dimensional elastic network made of three families of elastic fibers connected...
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Strongly anisotropic surface elasticity and antiplane surface waves
PublicationWithin the new model of surface elasticity, the propagation of anti-plane 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...
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On Nonlinear Dynamic Theory of Thin Plates with Surface Stresses
PublicationWe discuss the modelling of dynamics of thin plates considering surface stresses according to Gurtin–Murdoch surface elasticity. Taking into account the surface mass density we derive the two-dimensional (2D) equations of motion. For the reduction of the three-dimensional (3D) motion equations to the 2D ones we use the trough-the-thickness integration procedure. As a result, the 2D dynamic parameters of the plate depend not only...
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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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Preliminary study of linear viscoelasticity limits of cold recycled mixtures determined in Simple Performance Tester (SPT)
PublicationThe publication presents methodology developed for determination of linear viscoelasticity limits for cold recycled mixtures with cement and bituminous emulsion using Simple Performance Tester (SPT). Methodology was verified on reference materials (PCV and steel dummy specimens, cement concrete and asphalt concrete) to comply with elasticity and viscoelasticity theory. The developed methodology enabled determination of linear viscoelasticity...
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On well-posedness of the first boundary-value problem within linear isotropic Toupin–Mindlin strain gradient elasticity and constraints for elastic moduli
PublicationWithin the linear Toupin–Mindlin strain gradient elasticity we discuss the well-posedness of the first boundary-value problem, that is, a boundary-value problem with Dirichlet-type boundary conditions on the whole boundary. For an isotropic material we formulate the necessary and sufficient conditions which guarantee existence and uniqueness of a weak solution. These conditions include strong ellipticity written in terms of higher-order...
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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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Applications of Tensor Analysis in Continuum Mechanics
PublicationA tensor field is a tensor-valued 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...
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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 double-layered graphene sheet which contains a geometrical imperfection based on an eccentric hole. The first-order 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 double-layered graphene sheet has been considered, the...
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On the deformation and frequency analyses of SARS-CoV-2 at nanoscale
PublicationThe SARS-CoV-2 virus, which has emerged as a Covid-19 pandemic, has had the most significant impact on people's health, economy, and lifestyle around the world today. In the present study, the SARS-CoV-2 virus is mechanically simulated to obtain its deformation and natural frequencies. The virus under analysis is modeled on a viscoelastic spherical structure. The theory of shell structures in mechanics is used to derive the governing...
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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 stress-strain is concerned...
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Modeling of free vibrations and resonant frequencies of simply-supported submerged horizontal plate
PublicationA theoretical approach was applied to study the vibration of simple-supported submerged horizontal plate. The derived analytical solution was used to determine natural frequencies for a horizontal plate vibrating in fluid. The investigations were conducted for a very wide range of material density and elasticity modulus covering all materials used in engineering practice. Analysis shows that plate vibration frequency decreases...