Nonlocal Theory Research Articles

Investigation of guided wave propagation in nanoscale layered periodic piezoelectric plates based on Eringen's nonlocal and strain gradient theory

This paper investigates the dynamic propagation behavior of guided waves in nanoscale media composed of alternating layers of piezoelectric phases. The study employs Eringen's nonlocal and strain gradient theories to derive equations for symmetric wave propagation and the scattering relations of guided waves perpendicular to these structures. Dispersion curves are calculated and plotted to compare these theories, considering the influence of nanoscale size-effect, volume ratio of constituent layers, and material length scale. Using the strain gradient theory, the paper explores the impact of length scale parameters on the propagation behavior of horizontally polarized guided waves in an alternating layer structure of nanoscale piezoelectric material, specifically nanoscale piezoelectric laminates. The analysis involves calculating localization factors and dispersion curves to analyze the effects of size-effect and length scale parameters on wave propagation and band structures. Additionally, the study plots and analyzes changes in mechanical displacement and electrical potential, followed by an investigation and discussion of nanoscale size effects and the effects of the material's length scale parameter on dispersion curves and conversion modes within specific regions. The results highlight that the length scale effect parameter significantly impacts the mode conversion zones and band gap structures, more so than the NLPE continuum theory suggests. As the strain gradient parameter increases, these zones shift towards higher wavenumbers and to the right . Furthermore, introducing the length scale factor results in a substantial decrease in both the formation of conversion zones and the density of dispersion curves.

Updated Lagrangian nonlocal general particle dynamics for large deformation problems

The traditional general particle dynamics (GPD) has been successfully applied in modeling fracture propagation, frictional contact and stick–slip problems in rocks. In this study, the updated Lagrangian nonlocal general particle dynamics (UL-NGPD) method is proposed to solve large deformation problems. In the UL-NGPD, the continuity equation and momentum equation are reformulated in the integro-differential formulation by introducing nonlocal theories in the updated Lagrangian framework. The artificial viscosity and artificial force state are utilized to enhance the numerical stability and accuracy in modeling large deformation. The nonlocal velocity gradient in the deformed configuration is used to update the Cauchy stress rate from the Drucker-Prager elasto-plastic constitutive model with strain-softening behaviour for solids. The UL-NGPD paradigm is numerically implemented through an explicit Predictor-Corrector scheme for high-performance computing. The stability and accuracy of the UL-NGPD are verified by numerical tests on compression test, slope stability analysis and aluminum bar collapse experiment. Thereafter, simulations of granular soil collapse and retrogressive landslide in sensitive clays are presented to demonstrate its efficacy and robustness in modeling challenging geotechnical problems involving large deformation. The numerical results show that the proposed UL-NGPD is powerful and suitable for analyzing large deformation problems in geotechnical engineering.

Constraints on non-local gravity from binary pulsars gravitational emission

Non-local theories of gravity are considered extended theories of gravity, meaning that when the non-local terms are canceled out, the limit of General Relativity (GR) is obtained. Several reasons have led us to consider this theory with increasing interest, but primarily non-locality emerges in a natural way as a ‘side’ effect of the introduction of quantum corrections to GR, the purpose of which was to cure the singularity problem, both at astrophysical and cosmological level. In this paper we studied a peculiar case of the so called Deser-Woodard theory consisting in the addition of a non-local term of the form R□−1R to the Hilbert-Einstein lagrangian, where R is the Ricci scalar, and derived, for the first time, constraints on the dimensionaless non-local parameter A by exploiting the predicted gravitational wave emission in three binary pulsars, namely PSR J1012+5307, PSR J0348+0432 and PSR J1738+0333. We discovered that the instantaneous flux strongly depends on A and that the best constraints (0.12<A<0.16) come from PSR J1012+5307, for which the GR prediction is outside the observational ranges. However, since for PSR J1012+5307 scintillation is suspected, as emerged in a recent census by LOFAR corruptions in pulsar timing could be hidden. We finally comment on the usability and reliability of this type of test for extended theories of gravity.

Dynamic stability and frequency responses of the tilted curved nanopipes in a supersonic airflow via 2D hybrid nonlocal strain gradient theory

In the presented work, vibrational behavior related to a curved nanopipe which is under supersonic airflow and conveying fluid flow, is examined. To model the size-dependent nanopipe, the Quasi-2D hybrid type of nonlocal strain gradient theory (QHNSGT) is presented. Formulations are obtained by means of Hamilton’s principle for bi-directional functionally graded (Bi-FG) nanopipe. Also, formulations are solved by means of the generalized differential quadrature method (GDQM). By taking into account that the fluid flow is infinite, incompressible, uniform flow, Newtonian, laminar, as well, as viscous, and with the help of the Navier-Stokes equation, the fluid-structure interaction is obtained. A quasi-2D hybrid type of higher-order shear deformation theory is employed to introduce the displacement fields. The verification section shows that the results of this paper are very near to the results of the published article in the literature. One of the important findings of the current research is critical values of the Mach number could have increased with the aid of increasing the rigidity of edges and decreasing fluid flow velocity. Another marvelous output is that opening angle and airflow stability have an indirect relation, and increasing the opening angle provides an expansion in the unstable area.

Investigation of CO2 adsorption on nitrogen-doped activated carbon based on porous structure and surface acid-base sites

The purpose of this paper is to reveal the effects of porous structure and surface acid-base sites on CO2 adsorption for those nitrogen-doped activated carbons, which were prepared in a tube furnace with anaerobic conditions (TF) and muffle furnace with oxygen-poor conditions (MF), respectively. Subsequently, the porous structure and surface group distribution of the prepared activated carbons TF and MF were characterized in detail through those methods such as scanning electron microscope (SEM), Brunauer-Emmett-Teller (BET), Barret-Joyner-Halenda method (BJH), Horvath-Kawazoe method (HK), Dubinin-Radushkevich method (DR), mercury intrusion porosimetry (MIP), non-local density functional theory method (NLDFT), (in-situ) Fourier transform infrared spectroscopy (FTIR), Raman spectra (RS), X-ray photoelectron spectroscopy (XPS), and temperature programmed desorption (TPD). Then the thermodynamic and kinetic characteristics of CO2 adsorption such as adsorption capacity, selectivity, and activation energy were systematically investigated based on the static volumetric method and dynamic adsorption method. The results showed that the anaerobic or oxygen-poor preparation atmosphere affected the micropore volume and surface functional group distribution of activated carbons. Thus the activated carbon TF exhibited a higher adsorption capacity of CO2 (7.9 mmol g−1, 100 kPa and 273 K) and longer dynamic breakthrough time due to the higher microporosity (Vmic/Vt = 90 %), while the activated carbon MF exhibited the higher selectivity (14.7, CO2/N2 molar ratio of 1:1) and adsorption rate due to the higher nitrogen and oxygen contents (11.23 %, 13.53 %) in the main forms such as pyrrole nitrogen (N-5), carbony, and carboxyl. Overall, CO2 adsorption on the activated carbons was verified to be a dominant physical adsorption and exothermic process, which was suitable to be described by a quasi-first-order dynamic model. Meanwhile, compared with TF, the activated carbon MF exhibited the higher activation energy of CO2 adsorption (12.98 kJ mol−1 for TF and 17.23 kJ mol−1 for MF), accompanied by the larger rate constants (k1) and diffusion coefficients (D). The higher activation energy for MF meant that the adsorption temperature had a stronger effect on the rate constant during CO2 adsorption.

Bending analysis of FGSP nanoplate resting on elastic foundation by using nonlocal quasi-3D theory

In this paper, the bending response of a functionally graded saturated porous (FGSP) nanoplate resting on the Pasternak elastic foundation is analyzed within the framework of quasi-3D higher-order shear deformation theory (quasi-3D HSDT) for the first time. The material properties are presumed to change gradually along the thickness direction following three patterns of porosity distribution: uniform, non-uniform symmetric, and asymmetric. The theory of poroelasticity developed by Biot is utilized in modeling the stress-strain relationships for the saturated condition. Moreover, the nanoscale effects of the structures are considered by Eringen's nonlocal elasticity theory. The governing equations are derived by using the principle of minimum potential energy according to quasi-3D HSDT, which ensures transverse shear stress-free on the upper and lower surfaces of the nanoplate. Based on the obtained closed-form solution, the impacts of the porosity distribution patterns, porosity coefficient, Skempton coefficient, geometrical parameters, elastic foundation, and nonlocal parameters on the bending behavior have been explored. According to the findings, when the pores are saturated by the fluid, the plate stiffness increases. Additionally, increasing the values of the nonlocal parameter for FGSP nanoplates leads to an increase in deflection and stresses. Finally, the present study quantitatively reveals the size-dependent effects of a saturated porous medium.

A nonlocal elasticity theory to model the static behaviour of edge-cracked nanobeams

In the present paper, the mechanical behaviour of edge-cracked nanobeams under Mixed-Mode loading is analytically investigated by means of the Stress-Driven nonlocal model. Firstly, the proposed formulation is outlined, and then applied to the case of a cantilever edge-cracked nanobeam. A parametric study is performed by varying both the crack depth and the crack position along the beam axis. Finally, the above formulation is applied to simulate some experimental tests available in the literature.

Numerical investigation on the thermal-nanofluidic flow induced transverse and longitudinal vibrations of single and multi-walled branched nanotubes resting on nonlinear elastic foundations in a magnetic environment

Carbon nanotubes (CNTs) have attracted great attention due to their tremendous mechanical, thermal, structural and electrical properties leading to many promising applications. The unique and interesting properties of CNTs, such as their mechanical and electrical features, have fascinated industries and researchers to implement CNTs for production of different electromechanical devices. However, it is established that the phenomenon of buckling often occurs when CNTs are subjected to compressive loads and their frequencies under vibration are in order of Tera-Hz and Giga-Hz. Moreover, the profound dynamic behaviours of nanotube under the influences of slip when conveying fluid and magnetic field require a serious and meticulous study. Therefore, this study focuses on the vibration analysis of nanofluid-conveying embedded multi-walled branched nanotubes resting on Winkler-Pasternak foundation in a thermal-magnetic environment. Using Euler-Bernoulli theory, Hamilton's principle and nonlocal elasticity theory, fully coupled equations of motion governing the transverse and longitudinal vibrations of the nanotube are developed. Also, the equation of the deformation of the nanotubes as well as the pressure variation in the tubes are developed. Additionally, Navier-Stoke's equation and energy equation for the fluid and nanotube are coupled with the vibration models. The dynamics of the multi-walled carbon nanotubes when coupled with Navier-Stokes and energy equations require meticulous study as it is different from the usual assumption of plug flow. Therefore, in this present work, the developed coupled systems of nonlinear partial differential equations are solved using multi-dimensional numerical PDEs solvers coupled with PDE-tools in MATLAB. With the aids of the solutions, parametric studies were performed. The results indicate that increasing the downstream angle decreases the stability of the system. Also, the results obtained from the dynamic behaviour of the system indicate that the magnetic effect has an attenuating or damping effect of about 20 %. Furthermore, the plug flow assumption deviates from actual working processes by over 11 %. The analytical solutions verified and validated with existing analytical, numerical and experimental results. It is envisaged that the present study will give better insight into nanotubes design and serve as an index for subsequent works in the research area.

Application of nonlocal strain gradient theory for the analysis of bandgap formation in metamaterial nanobeams

The aim of this paper is to investigate bandgap formation in an Euler-Bernoulli nanobeam using the nonlocal strain gradient theory. Such a model enables the capture of both softening and stiffening size-dependent behavior of the nanobeams using two length-scale parameters, namely, a nonlocal parameter and a strain gradient parameter. Hamilton's principle is used to develop the normalized equation of motion yielding a sixth order differential equation. The nanobeam is assumed to be infinitely long and the dispersion of an elastic wave in a single representative periodic unit cell of the structure is used to estimate the bandgap edge frequencies. To this end, two unit cell approaches are employed to obtain the dispersion relations, namely, the homogenization and transfer matrix approaches. Both methods yield similar dispersion curves and showed good agreement with classical cases from the literature. A parametric study was carried out to investigate the effect of several parameters on the bandgap formation in the metamaterial nanobeams. These parameters include, the nonlocal parameter, the strain gradient parameter, the length of the unit cell and the resonator mass to unit cell mass ratio. The study conducted using a purely strain gradient model showed a comparable response to that of the classical macro problem with the usual hardening when increasing the value of the strain gradient length scale. Nonlocal and nonlocal strain gradient models introduced coupling between parameters of the study with the occasional introduction of non-monotonic dispersion curves. Such non-monotonic behavior is believed to be characteristic of large values of the nonlocal length-scale.

Nonlinear forced vibration of a nanobeam resting on Winkler-Pasternak elastic foundation and subjected to a mechanical impact

The nonlinear governing equations of nanobeam taking into consideration its curvature, resting on an elastic Winkler-Pasternak foundation and based on non-local Euler-Bernoulli beam theory is analyzed. The equation of motion and the boundary conditions are modeled within the framework of a simple supported nanobeam which accounts the presence of a mechanical impact and nonlinear von-Karman strain. The resulting nonlinear differential equations are reduced to only one differential equation which is studied by means of the Optimal Auxiliary Functions Method (OAFM). An explicit analytical solution is proposed for a complex problem. The main quality of our technique consists in the existence of some auxiliary functions derived from the expressions of the solution for the initial linear equation and the form of nonlinear term calculated from the above solution of the linear equation. The convergence-control parameters present in the auxiliary functions are evaluated by a rigorous mathematical procedure. The obtained solutions are in very good agreement with the numerical solution.

Vibrational analysis of size-dependent thermo-piezo-photo-electric semiconductor medium under memory-dependent Moore–Gibson–Thompson photo-thermoelasticity theory

This study presents a comprehensive approach to vibrational analysis in a size-dependent, orthotropic thermo-piezo-photo-electric semiconductor half-space under Moore–Gibson–Thompson (MGT) photo-thermoelasticity theory with memory-dependent derivatives. Following Eringen’s nonlocal elasticity theory, the governing equations for the considered material are derived. The normal mode technique is applied to investigate the photothermal excitation process. Focusing on the interface adjacent to the vacuum, the study considers plasma, thermal, and mechanical stress boundary conditions to determine fundamental physical quantities. Through a detailed exploration, this research examines the impact of various thermo-piezo-photo-electric models, time, nonlocal parameters, and spatial coordinates on different physical quantities. The effects are meticulously analyzed and visually represented through graphical illustrations. While the literature survey reveals numerous studies on vibrational analysis in thermo-piezo-photo-electric semiconductor mediums under different thermoelasticity theories, to the best of the authors’ knowledge, no research emphasizing vibrational analysis in a size-dependent thermo-piezo-photo-electric semiconductor medium has been conducted. Moreover, the effect of memory-dependent MGT photo-thermoelasticity theory on a size-dependent thermo-piezo-photo-electric semiconductor half-space has not been illuminated until now, significantly defining the novelty of the conducted research.

Small scale analysis of porosity-dependent functionally graded triply periodic minimal surface nanoplates using nonlocal strain gradient theory

In recent years, the triply periodic minimal surface (TPMS) has emerged as a remarkable solution for constructing structures, drawing inspiration from natural architectures. TPMS offers several outstanding features, including porous architectures with high interconnectivity, smooth surfaces and the ability to achieve mathematically controllable geometry features. However, it is evident that the current research has not fully harnessed the extensive potential and benefits of TPMS structures. In this paper, a groundbreaking approach for analyzing functionally graded triply periodic minimal surface (FG-TPMS) nanoplate, which is utilized a novel nonlocal strain gradient isogeometric analysis, is provided. Three patterns of the FG-TPMS nanoplate, namely Primitive (P), Gyroid (G) and I-gragh and Wrapped Package-graph (IWP), are utilized in this study. The primary focus is to investigate size dependent problems with two types of density distributions. The proposed model successfully incorporates both nonlocal effects and strain gradient effects into nanoplate structures. The paper demonstrates how the mechanisms responsible for both reducing and enhancing stiffness in the nanoplate can be understood by fine-tuning the nonlocal and strain gradient parameters. The findings of this study offer promising prospects for future design and optimization as they provide a robust approach to address the complex mechanical behavior observed in the FG-TPMS nanoplate. The proposed model not only captures the behavior accurately but also opens up new avenues for exploring the capabilities of FG-TPMS structures.

Comparison of local, gradient-enhanced and integral form of continuum damage approaches to strain localization in fiber reinforced composites

Structures often have inserts and notches that cause stress concentration and consequent reduction in the load bearing capacity. The literature on numerical implementation of continuum damage mechanics (CDM) has generally focused on using local theories of damage. However, their use to analyze deformations of notched laminates that are prone to strain localization can cause numerical convergence issues that can be alleviated by employing a non-local theory. There are a few studies using a non-local damage theory for fiber-reinforced polymeric composites (FRPCs) and even fewer for strain localization in FRPCs. The non-local theories employ an equivalent (or effective or von Mises) strain often used in metal plasticity while most theories for studying failure of FRPCs use individual strain/stress components. Here, we compare predictions from local and nonlocal CDM approaches that are effective in studying strain localization in FRPCs. For the local approach, we employ a rate-dependent evolution relation. For the non-local approach, we either compute damage at a point as the weighted sum of damage at its neighbors that introduces a length scale into the problem, or employ a gradient-enhanced approach that also introduces a length scale. It is shown that numerical predictions from both the rate-dependent and the non-local theory alleviate to different degrees sensitivity of results to the finite element mesh used and the strain localization issues. Of these, a local rate-type approach is more convenient and cost effective.

Nonlocal effective medium theory for phononic temporal metamaterials

We have developed a nonlocal effective medium theory (EMT) for phononic temporal metamaterials using the multiscale technique. Our EMT yields closed-form expressions for effective constitutive parameters and reveals these materials as reciprocal media with symmetric band dispersion. Even without spatial symmetry breaking, nonzero Willis coupling coefficients emerge with time modulation and broken time-reversal symmetry, when the nonlocal effect is taken into account. Compared to the local EMT, our nonlocal version is more accurate for calculating the bulk band at high wavenumbers and essential for understanding nonlocal effects at temporal boundaries. This nonlocal EMT can be a valuable tool for studying and designing phononic temporal metamaterials beyond the long-wavelength limit.

Discovery and In Situ Crystallization Studies of Cerium-Based Metal-Organic Frameworks with V-Shaped Linker Molecules.

We report the discovery and characterization of two porous Ce(III)-based metal-organic frameworks (MOFs) with the V-shaped linker molecules 4,4'-sulfonyldibenzoate (SDB2-) and 4,4'-(hexafluoroisopropylidene)bis(benzoate) (hfipbb2-). The compounds of framework composition [Ce2(H2O)(SDB)3] (1) and [Ce2(hfipbb)3] (2) were obtained by using a synthetic approach in acetonitrile that we recently established. Structure determination of 1 was accomplished from 3D electron diffraction (3D ED) data, while 2 could be refined against powder X-ray diffraction (PXRD) data using the crystal structure of an isostructural La-MOF as the starting model. Their framework structures consist of chain-like inorganic building units (IBUs) or hybrid-BUs that are interconnected by the V-shaped linker molecules to form framework structures with channel-type pores. The composition of both compounds was confirmed by PXRD, elemental analysis, as well as NMR and IR spectroscopy. Interestingly, despite the use of (NH4)2[CeIV(NO3)6] in the synthesis, cerium ions in both MOFs occur exclusively in the + III oxidation state as determined by X-ray absorption near edge structure (XANES) and X-ray photoelectron spectroscopy (XPS). Thermal analyses reveal remarkably high thermal stabilities of ≥400 °C for the MOFs. Initial N2 sorption measurements revealed the peculiar sorption behavior of 2 which prompted a deeper investigation by Ar and CO2 sorption experiments. The combination with nonlocal density functional theory (NL-DFT) calculations adds to the understanding of the nature of the different pore diameters in 2. An extensive quasi-simultaneous in situ XANES/XRD investigation was carried out to unveil the formation of Ce-MOFs during the solvothermal syntheses in acetonitrile. The crystallization of the two Ce(III)-MOFs presented herein as well as two previously reported Ce(IV)-MOFs, all obtained by a similar synthetic approach, were studied. While the XRD patterns show time-dependent MOF crystallization, the XANES data reveal the presence of Ce(III) intermediates and their subsequent conversion to the MOFs. The addition of acetic acid in combination with the V-shaped linker molecule was identified as the crucial factor for the formation of the crystalline Ce(III/IV)-MOFs.

On shear-dependent vibration of nano frames

In this study, the effect of shear deformation on the atomic size-dependent free vibration of nanoframes is investigated. The equations of motion of axial and bending vibrations are obtained via the variational algebra according to nonlocal elasticity theory. Axial and bending behaviors are expressed by using simple rod theory and first-order shear deformation beam theory, respectively. By combining the nonlocal finite element solutions for the equations of motion, an eigenvalue formulation for the free vibration of nanoframe is developed. In the presentation of numerical results, firstly, some comparison studies are carried out to show the accuracy of the present analysis. Then, the variations of nondimensional frequencies of three different nanoframe structures are investigated with respect to various parameters, and the results are discussed in detail. The focus of this study is to better understand the dynamic behavior of nanostructures that are within the scope of nano-electro-mechanical systems (NEMS) technology and can be modelled with discrete members.

On aeroelastic flutter assessment of thick nanoshell convening two-phase fluid flow using mathematical simulation and deep-neural networks

It is well known that flow-induced vibration occurs often in many different sectors. Dynamic fluid forces are produced by the flow, and these forces cause the system to become excited. One of the most prominent flows in nature and industrial domains, such as industrial facilities, is the multiphase flow which may contribute to creating noise and vibration. As one specific example of a multiphase flow, a two-phase flow relies heavily on flow arrangement for its characteristics. Furthermore, despite the most recent developments and advancements, flow-induced vibration is still considered an open topic. So, in this work, for the first time, frequency analysis of a thick nanoshell convening two-phase fluid flow subjected to aerodynamic pressure is presented. Via nonlocal strain gradient theory (NSGT), Hamilton's principle, trigonometric shear deformation theory, the reappraisal of the fluid-structure interaction relation, and non-conservative aerodynamic pressure formulation, the governing equations, and various boundary conditions of the system are presented. After that, using the generalized differential quadrature method (GDQM) the obtained governing equations are solved, numerically. For more verification of the results, the results are compared with the outcomes of the artificial neural network (ANN) model. For this purpose, the obtained results using mathematical modeling are presented to generate the training dataset and test dataset of the neural network in batches. Finally, some suggestions for improving the stability of the thick nanoshell convening two-phase fluid flow subjected to aerodynamic pressure are presented for future handbooks.

Thermal vibration and buckling analysis of magneto-electro-elastic functionally graded porous higher-order nanobeams using nonlocal strain gradient theory

Thermal vibration and buckling analysis of magneto-electro-elastic functionally graded porous higher-order nanobeams using nonlocal strain gradient theory

Shapes of the cosmological low-speed collider

Abstract Massive particles produced during inflation leave specific signatures in soft limits of correlation functions of primordial fluctuations. When the Goldstone boson of broken time translations acquires a reduced speed of sound, implying that de Sitter boosts are strongly broken, we introduce a novel discovery channel to detect new physics during inflation, called the cosmological low-speed collider signal. This signal is characterised by a distinctive resonance lying in mildly-soft kinematic configurations of cosmological correlators, indicating the presence of a heavy particle, whose position enables to reconstruct its mass. We show that this resonance can be understood in terms of a non-local single-field effective field theory, in which the heavy field becomes effectively non-dynamical. This theory accurately describes the full dynamics of the Goldstone boson and captures all multi-field physical effects distinct from the non-perturbative particle production leading to the conventional cosmological collider signal. As such, this theory provides a systematic and tractable way to study the imprint of massive fields on cosmological correlators. We conduct a thorough study of the low-speed collider phenomenology in the scalar bispectrum, showing that large non-Gaussianities with new shapes can be generated, in particular beyond weak mixing. We also provide a low-speed collider template for future cosmological surveys.

Natural vibrations of circular nanoarches of piecewise constant thickness

The free vibrations of elastic circular arches made of a nano-material are considered. A method of determination of eigenfrequencies of nanoarches weakened with stable cracks is developed making use of the concept of the massless spring and Eringen's nonlocal theory of elasticity. The aim of the paper is to evaluate the sensitivity of eigenfrequencies on the geometrical and physical parameters of the nanoarch.