Nonlocal Theory Research Articles

Nonlinear Analysis of the Multi-Layered Nanoplates

This text investigates the bending/buckling behavior of multi-layer asymmetric/symmetric annular and circular graphene plates through the application of the nonlocal strain gradient model. Additionally, the static analysis of multi-sector nanoplates is addressed. By considering the van der Waals interactions among the layers, the higher-order shear deformation theory (HSDT), and the nonlocal strain gradient theory, the equilibrium equations are formulated in terms of generalized displacements and rotations. The mathematical nonlinear equations are solved utilizing either the semi-analytical polynomial method (SAPM) and the differential quadrature method (DQM). Also, the available references are used to validate the results. Investigations are conducted to examine the effect of small-scale factors, the van der Waals interaction value among the layers, boundary conditions, and geometric factors.

A novel modified nonlocal strain gradient theory for comprehensive analysis of functionally graded nanoplates

A novel modified nonlocal strain gradient theory for comprehensive analysis of functionally graded nanoplates

Buckling analysis of single‐walled carbon nanotubes using the initial value method and approximate transfer matrix based on nonlocal elasticity theory

AbstractIn this study, a novel method is presented to analyze the buckling behavior of single‐walled carbon nanotubes (SWCNTs) using the initial value method (IVM) in conjunction with the approximate transfer matrix, within the framework of nonlocal elasticity theory. The study aims to accurately approximate critical buckling load parameters under various boundary conditions, without encountering high computational requirements. IVM enables the computation of displacements and stress resultants along the entire beam from given initial conditions. The approximate transfer matrix is employed to analyze system states at different points through successive integration of solutions, generating the principal matrix needed for IVM and ensuring systematic and precise results that optimize the accuracy of the analysis. A convergence study confirms the effectiveness and precision of the proposed method, revealing a decrease in the critical buckling load parameters as the nonlocal parameter increases, applicable across all boundary conditions studied (simply supported, clamped–clamped, clamped–simply supported, and clamped‐free). These results underscore the need to incorporate nonlocal effects for more accurate nanostructure mechanics predictions. The integration of IVM and the approximate transfer matrix provides a computationally efficient alternative to traditional numerical and semi‐analytical methods, aiding researchers and engineers working with SWCNTs and other nanomaterials.

An analysis of the textural properties of activated carbons obtained from biomass via the LBET, NLDFT and QSDFT methods

This article presents the unique research results of the comprehensive analysis of the porous structure of activated carbons obtained from biomass waste materials from the wood industry during activation in an air atmosphere. The porous structure was analysed on the basis of nitrogen and argon adsorption isotherms via complementary multi-method analysis, i.e. the new numerical clustering-based adsorption analysis, the non-local density functional theory and the quenched solid density functional theory methods. The analytical results for the prepared activated carbons were compared with analogous results obtained for commercial activated carbon. On the basis of the conducted studies it has been determined that the new numerical clustering-based adsorption analysis method gives credible and valuable information on the textural properties of activated carbons which are in strict correlation and mutually complement with the results of the analysis with the use of the quenched solid density functional theory method. The research results obtained in this paper, it has also been shown that from waste materials of the wood industry, in a relatively cheap and cleaner production process, it is possible not only to obtain carbonaceous materials almost comparable to commercial activated carbon, but also to manage the waste in accordance with the principles of a closed-loop economy and sustainable development. The paper pays also attention to the often overlooked economic and ecological aspects, which should nevertheless be taken into account when comparing different adsorbents, rather than their textural properties alone.

Dynamic of composite nanobeams resting on an elastic substrate with variable stiffness

This study introduces a novel approach by combining finite simulation and an enhanced shear deformation theory to analyze the dynamic behavior of multi-layer composite nanobeams supported by an elastic foundation. The calculation formulae are derived from nonlocal theory in order to account for the impact of size effect. An intriguing aspect of this research is the presence of intricate curved profiles in the two material layers of the beam. The elastic foundation exhibits varying stiffness throughout the beam's length, accounting for many imperfections in the beam and including the drag parameter of the material. These elements contribute to the steady evolution of the issue model towards more realistic structures. Nevertheless, the computation gets intricate and impedes the precise approach. However, our work has successfully resolved this difficult and significant difficulty using the two-node element. This research demonstrates the temporal evolution of the dynamic reactions of the point with the greatest displacement and velocity, as dictated by the law of change. Simultaneously, it also presents visual representations of every point on the beam as it undergoes temporal variations. These conclusions possess both scientific and practical value, establishing a foundation for real-world implementations.

Vibration response of nanobeams subjected to random reactions

Nanobeams composed of materials exhibiting flexoelectric properties have been successfully used in advanced technological equipment, including electronic circuits and very sensitive sensors, owing to their remarkable unique effects. Therefore, it is essential to determine their mechanical behavior as a practical need. This study employs an analytical methodology to provide a precise solution to the vibration issue of nanobeams under random stationary loads. Under such circumstances, the nanobeam is influenced by both the temperature and moisture conditions simultaneously. Additionally, the beam is supported by a viscoelastic foundation that considers both the viscous resistance parameter and the elastic parameter. Analytical formulations are derived by integrating classical beam theory with nonlocal strain gradient theory in order to elucidate the impact of size effects on nanobeams. This research also demonstrates the reliability verification, which clearly validates the accuracy of the calculation formula used in this work. This study examines the impact of material parameters, viscoelastic foundation, temperature, and moisture on the displacement spectrum at the middle and entire length of the beam. The study also explores how the flexoelectric effect decreases the displacement in the nanobeam. Subsequently, we provide scientifically derived findings that have significant relevance for building practical nanobeam specifications.

Thermoelastic bending wave propagation of FG hybrid nanocomposite microbeam reinforced by GPLs and CNTs under fractional order nonlocal elasticity theory

Thermoelastic bending wave propagation of FG hybrid nanocomposite microbeam reinforced by GPLs and CNTs under fractional order nonlocal elasticity theory

A finite element based approach for nonlocal stress analysis for multi-phase materials and composites

AbstractThis study proposes a numerical method for calculating the stress fields in nano-scale multi-phase/composite materials, where the classical continuum theory is inadequate due to the small-scale effects, including intermolecular spaces. The method focuses on weakly nonlocal and inhomogeneous materials and involves post-processing the local stresses obtained using a conventional finite element approach, applying the classical continuum theory to calculate the nonlocal stresses. The capabilities of this method are demonstrated through some numerical examples, namely, a two-dimensional case with a circular inclusion and some commonly used scenarios to model nanocomposites. Representative volume elements of various nanocomposites, including epoxy-based materials reinforced with fumed silica, silica (Nanopox F700), and rubber (Albipox 1000) are subjected to uniaxial tensile deformation combined with periodic boundary conditions. The local and nonlocal stress fields are computed through numerical simulations and after post-processing are compared with each other. The results acquired through the nonlocal theory exhibit a softening effect, resulting in reduced stress concentration and less of a discontinuous behaviour. This research contributes to the literature by proposing an efficient and standardised numerical method for analysing the small-scale stress distribution in small-scale multi-phase materials, providing a method for more accurate design in the nano-scale regime. This proposed method is also easy to implement in standard finite element software that employs classical continuum theory.

Nonlocal buckling analysis of double-walled carbon nanotubes using initial value method and matricant approach

In this study, the buckling behavior of double-walled carbon nanotubes (DWCNTs) is investigated using the initial value method (IVM) combined with the approximate transfer matrix (ATM) approach within the framework of nonlocal elasticity theory. The aim is to provide a method that best estimates the critical buckling loads with improved accuracy and computational efficiency. To validate the method, the critical buckling loads obtained without considering nonlocal effects were compared with results from the literature, showing a high degree of agreement. Various boundary conditions, including simply supported (S-S), clamped-simply supported (C-S), clamped-free (C-F), and clamped-clamped (C-C), have been considered for investigation. The effects of nonlocal parameters, aspect ratios, and boundary conditions on the critical buckling loads are analyzed. The findings emphasize the importance of accounting for these parameters in mechanical analyses to ensure accurate predictions. The proposed framework provides an efficient alternative to existing numerical methods and offers valuable benchmarks for future research on the mechanical behavior of nanostructures.

Novel hydrogen-bonded organic frameworks-based coating for fat oil and grease deposition control in the sewer system

Hydrogen-bonded organic frameworks (HOFs) represent an emerging class of porous materials characterized by crystalline frame structures, self-assembled from organic molecules through hydrogen bonding. This study demonstrates that HOFs fragment into small particles while preserving their original structure when dispersed in a polymeric epoxy solution. The intermolecular hydrogen bond structural and electronic properties of the LH4-HOF complex as well as the mechanism of HOF incorporated epoxy were extensively studied using density functional theory. LH4-HOF has a high Langmuir surface area of 2758.3 m2/g and nonlocal density functional theory pore size distributions of 3 A°. This unique solution processability enables the fabrication of coatings with high stability in aqueous systems. Results from a 30-day leaching test under controlled conditions (pH 7, temperature 20 ± 2 °C) indicate that LH4-HOF incorporated epoxy-coated concrete samples exhibited an over 85 % reduction in calcium release compared to uncoated samples, with epoxy-coated samples alone showing a 60 % reduction in calcium leaching. Additionally, the LH4-HOF-incorporated epoxy coating reduced the formation of fats, oils and grease deposits by more than 73 % on the concrete samples. Thus, this novel coating approach offers a sustainable solution with significant potential applications in sewer management.

Introduction to Nonlocal Field Theory Including Gravity

We give minireview of nonlocal field theory (infinite derivative field theory). We start with the discussion of the main peculiarities of nonlocal field theory on the example of \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d = 4$$\\end{document} scalar \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\phi }^{4}}$$\\end{document}-model. The nonlocal \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\phi }^{4}}$$\\end{document}-model is ultraviolet finite, unitary, and macrocausal. One of the problems of nonlocal field theory is that the formfactor is an arbitrary entire function that makes the predictions extremely weak. We propose some additional principle that allows to fix the formfactor. Also we review the main results obtained in nonlocal quantum gravity, namely the nonlocal generalization of Einstein gravity leads to the superrenormalizable theory.

A Gauss kernel non-local stress-driven plate theory

This study presents a novel stress-driven formulation, incorporating Kirchhoff’s plate assumptions and accounting for the non-local size-dependent feature in both plate geometric axes, which is practical, especially near the origin of the axis in the polar coordinates. The presented formulation does not impose any additional constraints on the elastic radial curvatures, which are known as constitutive boundary conditions. Therefore, taking into account the non-local behavior in both radial and circumferential directions does not lead to an overconstrained problem. The study focuses on the analysis of a circular plate with an outer radius (R), thickness (h), and the length scale parameter (L). The governing differential equations are derived in Cartesian coordinates and then transformed to the polar coordinates to analyze circular plates. When R tends to infinity, the governing equation is solved analytically. Using the Galerkin technique, a finite element solution is presented for the analysis of a bounded circular plate with a clamped boundary condition at the outer radius R. The study discusses the size effects and the gradient properties of functionally graded plates in stress-driven non-local theory. It reveals that while increasing the non-local parameter results in a reduction of transverse displacement, the moments remain unaffected.

Nonlinear vibration and parametric excitation of magneto‐thermo elastic embedded nanobeam using homotopy perturbation technique

AbstractThe present study focuses on the modeling and analyzing the nonlinear vibration patterns and parametric excitation of embedded Euler–Bernoulli nanobeams subjected to thermo‐magneto‐mechanical loads. The Euler–Bernoulli nanobeam is developed with external parametric excitation. The governing equation of motion is derived by utilizing nonlocal continuum theory and nonlinear von Karman beam theory. Subsequently, the homotopy perturbation technique is employed to determine the vibration frequencies. Finally, the modulation equation of Euler–Bernoulli nanobeams is derived for simply supported boundary condition. In order to validate our findings, we conduct a comparative analysis against existing literature, thereby underscoring the effectiveness and robustness of our proposed methodology. The influence of stress, magnetic potential, temperature, damping coefficient, Winkler coefficient, and nonlocal parameters are tested numerically on nonlinear frequency‐amplitude and parametric excitation–amplitude responses. The numerical examples indicate the significant impact of physical variables on the nonlinear frequency and parametric excitation. The primary objective of this study is to investigate the effects of external physical variables on the dynamic behavior of nanobeams, particularly in nonlinear regimes. This study provides insights into the design and control of nanostructures under complex load conditions, contributing to developing advanced materials and nanosystems.

Doubly special relativity as a nonlocal quantum field theory

In this work, we explore the quantum theories of the free massive scalar, the massive fermionic, and the electromagnetic fields in a doubly special relativity scenario. This construction is based on a geometrical interpretation of the kinematics of this kind of theory. In order to describe the modified actions, we find that a higher (indeed infinite) derivative field theory is needed, from which the deformed kinematics can be read. From our construction, we are able to restrict the possible models of doubly special relativity to those that preserve linear Lorentz invariance. We quantize the theories and also obtain a deformed version of the Maxwell equations. We analyze the electromagnetic vector potential for both an electric pointlike source and magnetic dipole. We observe that the electric and magnetic fields do not diverge at the origin for some models described with an anti–de Sitter momentum space, but they do for a de Sitter space in both problems. Published by the American Physical Society 2024

Buckling analysis of nanoscale beams based on nonlocal Timoshenko beam theory

Abstract Eigen-buckling problems of nanoscale beams continue to be of great research interest, and the nonlocal theory is widely used. However, the existing research generally adopted some simplified assumptions of nonlocal effects. This article studies the buckling behaviors of the nonlocal Timoshenko beam, where the nonlocal effects are considered both on the governing equations and boundary conditions. The variational principle is adopted to obtain the nonlocal governing equations and boundary conditions. The buckling solutions for nanoscale beams are obtained analytically. Numerical comparisons validate the correctness of the present results. Parameter study shows that the buckling characteristic of nonlocal beams is different from that of classical beams, and the nonlocal effect is dependent on boundary conditions and geometry size of nanoscale beams.

The application of novel shear deformation theory and nonlocal elasticity theory to study the mechanical response of composite nanoplates

The use of composite structures, which have many layers of materials, has become more prevalent in the field of engineering. One of the advantages of this approach is its ability to use the inherent strengths of the constituent materials, resulting in a substantial increase in their load-bearing capability. Hence, this research represents the pioneering investigation into the static bending and free vibration characteristics of composite nanoplates including several layers of materials, whereby the material layers are interconnected via intricate profiles characterized by square wave and sine waveforms. The purpose of this endeavor is to fully capitalize on the benefits of attending courses in order to enhance practical working efficiency. This study also incorporates the use of two innovative third-order shear deformation theories. Simultaneously, considering the negligible size impact facilitated by the nonlocal theory, the mathematical formulations and equilibrium equations are derived using the Hamilton principle. The issue has been addressed using a four-node element with six degrees of freedom per node. One novel aspect of this study is its consideration of the impact of initial shape imperfections in various manifestations. Additionally, the elastic foundation incorporates characteristics that exhibit spatial variation. This statement provides a somewhat more accurate depiction of the behavior shown by actual structures. The numerical findings have been meticulously computed and thoroughly examined. Notably, it is possible to determine the optimal number of wavelengths in the profile to enhance the load-bearing capability of the structure. The findings derived from this study have significant value in informing the design of operational frameworks in practical settings.

Numerical Modeling of Fatigue Fracture Based on the Nonlocal Theory of Cyclic Damage

Numerical Modeling of Fatigue Fracture Based on the Nonlocal Theory of Cyclic Damage

Nonlocal chiral contributions to generalized parton distributions of the proton at nonzero skewness

We compute the one-loop contributions to spin-averaged generalized parton distributions (GPDs) in the proton from pseudoscalar mesons with intermediate octet and decuplet baryon states at nonzero skewness. Our framework is based on nonlocal covariant chiral effective theory, with ultraviolet divergences regularized by introducing a relativistic regulator derived consistently from the nonlocal Lagrangian. Using the splitting functions calculated from the nonlocal Lagrangian, we find the nonzero skewness GPDs from meson loops by convoluting with the phenomenological pion GPD and the generalized distribution amplitude, and verify that these satisfy the correct polynomiality properties. We also compute the lowest two moments of GPDs to quantify the meson loop effects on the Dirac, Pauli, and gravitational form factors of the proton. Published by the American Physical Society 2024

Increasing the Interlayer Fracture Toughness of Polymer Fabric Composites Using Local 3D-Reinforcement (Felting)

Introduction. One of the reasons for undesirable delamination of polymer composites with fabric reinforcement is low transverse shear properties. It is known that the reinforcement of polymer fabric composites in the Z direction reduces the sensitivity to delamination and increases the viscosity of interlayer fracture. Various methods of three-dimensional reinforcement of polymer fabric composites are proposed in the literature. However, they complicate the manufacturing process of the structure. The problem is solved by the method of three-dimensional reinforcement proposed in this article — felting. This is a local reinforcement of the composite in the Z direction with minimal production changes. The degree of Z-reinforcement is determined by the felting density, i.e., the number of needle punches per 1 cm2 of the fabric package. The work is aimed at evaluating the effect of felting on the interlayer crack resistance of a composite material.Materials and Methods. The interlayer fracture toughness GIIc was determined on a cross-woven fiberglass with felting of 10 cm-2. The material was impregnated with Etal-370 resin and Etal-45 hardener. Experiments according to ASTM D7905M–14 and GOST 33685–2015 standards were carried out on an Instron 5900R test machine. The stress state at the crack tip was analyzed with regard to the nonlocal strength theory in the ANSYS Workbench program (option “static strength analysis”). The finite element method (FEM) was used.Results. The “load — displacement” curves were considered for the samples. Values GIIc were calculated. The results of ENF tests for felting density of 0 cm–2 and 10 cm–2 were summarized. Control samples and felting samples were compared. In the latter case, GIIс turned out to be ~33% higher. The stress state at the crack tip was calculated under DCB and ENF loading. The dependences of maximum normal and shear stresses, as well as displacements, were visualized in the form of graphs and color charts. To get the calculated “load — displacement” dependences using FEM, the reverse method of obtaining transverse shear constants was used. DCB loading showed that felting provided increasing the rupture strength in the Z direction to ~18%, by 39 to 46 MPa, and in the planes XZ— to ~16%, by 77 to 89 MPa.Discussion and Conclusion. Felting as a method of local three-dimensional reinforcement enhances the interlayer crack resistance of polymer fabric composites. It provides reducing the area of stratifications after local impacts during the operation of structures. Flexible felting technology makes it possible to create zones with an arbitrary impact density, increasing fracture toughness only in the required places of structures. The FEM analysis of the stress state at the crack tip within the framework of the nonlocal strength theory has shown that in strength calculations, the stratification crack can be considered as a stress concentrator.

A semi-analytical methodology for predicting the vibroacoustic response of functionally graded nanoplates under thermal loads

In this investigation, the analysis of the nonlinear vibroacoustic and sound transmission loss behaviors of nanoplates made of functionally graded materials considering the nonlocal strain gradient theory is presented. It is presumed that the properties of the functionally graded nanoplate are in the form of the simple power law scheme and continuous along the thickness, under nonlinear temperature rise and incident oblique acoustic wave as well as the first-order shear deformation theory. For this purpose, applying Hamilton’s principle, the nonlinear partial differential equations of motion are derived by the displacement field function approach and by considering the von Kármán nonlinear strain-displacement relations. To solve the equations, using the Galerkin method, the nonlinear partial differential equations of motion lead to the Duffing equation. Then, applying the homotopy analysis method, the equation of the transverse movement of the nanoplate is solved semi-analytically to obtain the nonlinear frequencies. Lastly, the nonlinear vibration and acoustic response of functionally graded nanoplate are investigated by considering the variation of the significant factors such as material gradient indices, nonlocal parameters, length scale parameters, aspect ratio, dimensionless amplitude, nonlinear temperature changes, and sound characteristics of the functionally graded nanoplate.