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The global dynamics of a nonlocal predator–prey model with mutation are investigated in this paper. First, by building a new comparison principle and constructing monotone iterative sequences, we give the existence of the solution for the corresponding initial boundary value problem. Then the uniqueness and uniformly boundedness of the solution are established by using the fundamental solution and quasi-fundamental solution of the heat equation, Grönwall's inequality and auxiliary functions. Finally, under the truncation function method, we discuss the asymptotic behavior of the solution. It is worth mentioning that the asymptotic behavior here is different from the conclusion of the classical model and we use more refined analysis and estimation in the research process. [ABSTRACT FROM AUTHOR]

In this article, we apply NURBS-based isogeometric method to solve a nonlocal degenerate parabolic problem. The isogeometric method has advantages over classical finite element method in terms of exact geometry representation and higher order smooth basis functions. We consider the NURBS-based semi-discretization of the problem. The second-order Crank–Nicolson method is applied for the complete discretization of the problem. Error estimates of the semi-discrete and fully-discrete problems are derived. Few numerical examples are provided to verify the theoretical findings. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to investigate exponential attractors for a nonlocal delayed reaction-diffusion equation on an unbounded domain. We first obtain the existence of a globally attractive absorbing set for the dynamical system generated by the equation under the assumption that the nonlinear term is bounded. Then, we construct exponential attractors of the equation directly in its natural phase space, i.e., a Banach space with explicit fractal dimension by combining squeezing properties of the system as well as a covering lemma of finite dimensional subspaces of a Banach space. Our result generalizes the methods established in Hilbert spaces and weighted spaces, and the fractal dimension of the obtained exponential attractor does not depend on the entropy number but only depends on some inner characteristic of the studied equation. [ABSTRACT FROM AUTHOR]

This paper deals with propagation of Rayleigh-type waves in nonlocal inhomogeneous transversely isotropic half-space. From the characteristic equation of wave for the nonlocal inhomogeneous transversely isotropic medium, the existence of the number of surface waves depends on the inhomogeneity of the medium through the number of solutions satisfying the damping condition of the characteristic equation discussed. It has also been concluded that there exist cut-off frequency and escape frequency for the wave propagating in size-dependent materials based on the nonlocal theory. Dispersion equation for the propagation of Rayleigh-type surface waves at the free surface has been derived. Based on the obtained dispersion equation, the effects of the inhomogeneity of material and nonlocality parameter on the Rayleigh wave propagation are considered through some numerical examples. [ABSTRACT FROM AUTHOR]

The paper deals with a new model based on Eringen's nonlocal thermoelasticity. The propagation of Rayleigh waves in a nonlocal thermoelastic layer which is lying over a nonlocal thermoelastic half-space is considered in the context of energy dissipation theory. The normal mode analysis is employed to the considered equations to obtain vector matrix differential equation which is then solved by state space approach.The frequency equation of Rayleigh surface wave is derived. The effect of the nonlocal parameter on phase velocity, attenuation coefficient, specific loss and penetration depth of Rayleigh surface waves is presented graphically. [ABSTRACT FROM AUTHOR]

Propagation of Rayleigh-type waves is investigated in a half-space composed of nonlocal micropolar thermoelastic material containing void pores. Dispersion relation is derived for a mechanically stress-free and thermally insulated boundary surface of the half-space. The particle motion during the propagation of the waves is found to follow elliptical path. Numerical computations for a specific material are performed to analyze the characteristics of propagating Rayleigh-type waves in detail. Comparison between the phase speed and corresponding attenuation coefficient in some particular cases is also carried out. The effect of various parameters on the characteristics of waves in question is also studied. [ABSTRACT FROM AUTHOR]

The Boussinesq equation and its related types are able to provide a significant explanation for a variety of different physical processes that are relevant to plasma physics, ocean engineering, and fluid flow. Within the framework of shallow water waves, the aim of this research is to find solutions for solitary waves using newly developed nonlocal models of Boussinesq’s equations. The extraction of bright and dark solitary wave solutions along with bright–dark hybrid solitary wave solutions is accomplished through the implementation of two integration algorithms. The general projective Riccati equations method and the enhanced Kudryashov technique are the ones that have been implemented as techniques. The enhanced Kudryashov method combines the benefits of both the original Kudryashov method and the newly developed Kudryashov method, which may generate bright, dark, and singular solitons. The Projective Riccati structure is determined by two functions that provide distinct types of hybrid solitons. The solutions get increasingly diverse as these functions are combined. The techniques that were applied are straightforward and efficient enough to provide an approximation of the solutions discovered in the research. Furthermore, these techniques can be utilized to solve various kinds of nonlinear partial differential equations in mathematical physics and engineering. In addition, plots of the selected solutions in three dimensions, two dimensions, and contour form are provided. [ABSTRACT FROM AUTHOR]

The objective of this study is to analyze the thermo-mechanical interactions occurring in a nonlocal transversely isotropic functionally graded (nonhomogeneous) micropolar thermoelastic half-space when subjected to an inclined load, based on the Lord and Shulman (LS) theory. The material properties are assumed to be graded exponentially along the z -direction. Utilizing the normal mode technique, the exact expressions for physical fields such as normal displacement, normal stress, shear stress, temperature field, and couple stress are derived. Numerical computation of the derived results is performed for a material resembling a magnesium crystal, and graphical representations are presented to illustrate the impacts of nonhomogeneity parameter, material's anisotropy, time, nonlocal parameter, microinertia, and the inclination angle of the applied load on the variations of different physical fields. Some specific cases of interest have been deduced from the present investigation. [ABSTRACT FROM AUTHOR]

The main objective of this work is to create a new thermoelastic model for hyperbolic thermoelasticity in the context of double porosity structure based on nonlocal elasticity theory and the dual-phase-lag model. Nonlocal elasticity theory is used to construct new constitutive relations and equations. In a homogeneous, isotropic thermoelastic material, thermomechanical interactions are studied using normal mode analysis. A time-dependent thermal shock is applied on the boundary surface. This study also produces a few unique situations, which are compared with previous results of other researchers. The normal and tangential stresses, temperature, displacement components, change in void volume fractions, and equilibrated stress vectors concerning distances and time intervals are all calculated numerically. The physical quantities mentioned above are also visually displayed for various thermoelastic models to compare and illustrate the theoretical results. A comparative analysis and graphical presentation of the effects of nonlocal parameters and porosity on various physical characteristics have been performed. The figures show that most of the physical variables decrease with the increase in distance and show oscillatory behavior with the increase in time. The behavior of the void volume fraction field of the first kind is opposite to the behavior of the void volume fraction field of the second kind with the increase in distance. It is also noticed that the behavior of equilibrated stress of the first kind is opposite to the behavior of the second kind. [ABSTRACT FROM AUTHOR]

In this work, we consider a more general version of the nonlocal thermistor problem, which describes the temperature diffusion produced when an electric current passes through a material. We investigate the doubly nonlinear problem where the nonlocal term is present on the right-hand side of the equation that describes the temperature evolution. Specifically, we employ topological degree theory to establish the existence of a solution to the considered problem. Furthermore, we separately address the uniqueness of the obtained solution. Additionally, we establish a priori estimates to demonstrate the convergence of a developed finite volume scheme used for the discretization of the continuous parabolic problem. Finally, to numerically simulate the proposed finite volume scheme, we use the Picard-type iteration process for the fully implicit scheme and approximate the nonlocal term represented by the integral with Simpson's rule to validate the efficiency and robustness of the proposed scheme. [ABSTRACT FROM AUTHOR]

With expanding demand of electronic gadgets at miniature/nano-scales, mathematical modelling of the related problems calls for the study of various properties of nanostructures. Also, memory dependence phenomenon plays significant role to make models more rational. Considering this frame, thermoelasticity with diffusion based on memory-dependent derivatives and nonlocal elastic effect is studied under unified model of four theories of thermoelasticity. Infinite body containing a spherical cavity whose inner surface is acted upon by chemical and thermal shock in stress-free state is considered. Initially the medium is assumed to be quiescent. In heat conduction equation, laser pulse heat source which is decaying exponentially with time is present. Laplace transformation technique is adopted to obtain the solution by direct approach. The consideration of spherical cavity in infinite medium and combined model of thermoelastic theories with coupling of elastic, thermal, diffusion processes augments the novelty of present work. The study analyzes the effect of memory-dependent and nonlocal parameters on the various field quantities involved in the model which are calculated numerically using MATLAB software & presented graphically. Memory dependence of heat conduction and diffusion with nonlocal elasticity is observed to have significant impact on the variations of considered field quantities. [ABSTRACT FROM AUTHOR]

This study developed a novel nonlocal numerical model based on the peridynamic differential operator to analyze the thermoelectric coupling field. The thermoelectric coupling equations and boundary conditions are transformed from the classical partial differential form to the nonlocal integral form. By introducing the peridynamic function, a one-dimensional nonlocal model is established. This model can accurately capture the spatial distributions of the temperature field and material parameters when considering temperature-dependent thermoelectric material parameters. The numerical solutions from this nonlocal peridynamic model were found to agree well with those from the homotopy analysis method. Using this model, the influence of temperature boundary conditions and structure length on output performance is studied. The intrinsic relationship between the material parameters and the output properties within the structure is revealed. This presented nonlocal model provides an accurate mathematical tool to solve the thermoelectric coupling field for thermoelectric structures performance analysis. [ABSTRACT FROM AUTHOR]

In this paper we investigate the 2d-model for a thin plate Ω ε : = ω × ε I of R 3 having two components: a circular stiff layer F ε and its complement the soft matrix M ε with 1 ε 2 as a ratio between their respective elasticity coefficients. We prove that the limit model is associated to a nonlocal system involving Kirchoff-Love displacements in the layer and we exhibit a corrector for the displacements in the initial cylindrical structure of R 3 . [ABSTRACT FROM AUTHOR]

The main objective of this article is to study how a finite crack interacts with horizontally polarized shear (SH) waves in a nonlocal isotropic medium when a magnetic field is present. The study aims to understand the effects of various parameters, including the magnetic field, non-locality, frequency of SH waves, on the behavior of the crack. Here, we are concerned with Griffith's theory of a brittle fracture crack mechanism. The article starts by formulating the governing equations for the propagation of SH waves in the given medium. These equations are converted into dual integral equations using Fourier transformation. Subsequently, an Abel transformation is applied to obtain a Fredholm integral equation of the second kind. Daubechies wavelet family has been used to find an approximate solution for the integral equation. The article aims to determine specific physical quantities including stress intensity factor (SIF), shear stress, and crack energy related to the behavior of the crack. These parameters are essential in understanding how the crack responds to the external conditions. The application of Daubechies wavelets in this context is a relatively new and innovative approach. The study performed a comprehensive analysis of the effects of various factors on the crack behavior. The findings are presented in graphical form to help illustrate the conclusions. To assess the accuracy of the proposed method, the obtained results are compared with known results from the literature for local media. This is an important step in demonstrating the reliability and effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

AbstractA nonlocal layerwise 3D bending solution for multilayered functionally graded shallow nanoshells is presented. Eringen’s nonlocal elasticity theory is used for approaching the small length scale effect. Curvilinear orthogonal coordinate system is employed for writing the constitutive and equilibrium equations. The middle-plane of displacements are assumed as a Navier solution which are only valid for simply supported spherical, cylindrical panels and rectangular plates. The thickness domain is discretized by the well-known Chebyshev–Gauss–Lobatto, and its derivatives are calculated numerically by the Differential Quadrature method (DQM). Lagrange interpolation polynomials are utilized as the basis functions for DQM. The traction conditions at the top and the bottom of the shell panel and continuity conditions of the interlaminar adjacent layers for transverse stresses are considered, so this method presents layerwise capabilities. The results are compared with higher order theories proposed in the literature, and due to the 3D nature of the presented formulation, benchmark solutions are provided. [ABSTRACT FROM AUTHOR]

The present study is concerned with the reflection and transmission of plane waves at an imperfect interface between two nonlocal transversely isotropic liquid-saturated porous half-spaces. The model is considered for two different cases with one is for excluding fluid nonlocal effect, and the other is for including fluid nonlocal effect. The expression for the reflection and transmission coefficients (RTC) which are the ratios of the amplitude of reflected and transmitted waves to the amplitude of incident waves are obtained for an imperfect interface, perfect interface and loose interface. The numerical examples are provided to show the effect of the imperfect interface, nonlocal parameter and incident angle on the reflection and transmission coefficients. [ABSTRACT FROM AUTHOR]

We consider an abstract concept of perimeter measure space as a very general framework in which one can properly consider two of the most well-studied variational models in image processing: the Rudin–Osher–Fatemi model for image denoising (ROF) and the Mumford–Shah model for image segmentation (MS). We show the linkage between the ROF model and the two phases piecewise constant case of MS in perimeter measure spaces. We show applications of our results to nonlocal image segmentation, via discrete weighted graphs, and to multiclass classification on high dimensional spaces. [ABSTRACT FROM AUTHOR]

Peridynamics is a new approach to continuum mechanics. There has been rapid progress in peridynamics research, especially in recent years. In this review study, recent advances in peridynamics research were summarised. A large number of studies were considered and classified into different categories ranging from additive manufacturing, artificial intelligence and machine learning, composite materials, fatigue, functionally graded materials, impact, reduced order modelling, structural health monitoring, topology optimisation, and many more. Finally, some future directions were highlighted.

Peridynamics is a new approach to continuum mechanics. There has been rapid progress in peridynamics research, especially in recent years. In this review study, recent advances in peridynamics research were summarised. A large number of studies were considered and classified into different categories ranging from additive manufacturing, artificial intelligence and machine learning, composite materials, fatigue, functionally graded materials, impact, reduced order modelling, structural health monitoring, topology optimisation, and many more. Finally, some future directions were highlighted. [ABSTRACT FROM AUTHOR]

In the context of the three-phase hysteresis model (3PHL), a system of equations is established for a generalized thermoelastic medium under the influence of a magnetic field and an internal heat source. The problem is discussed using Eringen's nonlocal elastic model. The exact expression of the physical quantity is obtained by normal mode analysis and illustrated graphically by comparison and discussion. All calculation results obtained are graphically presented and explained. This paper investigates a specific type of material called a generalized magneto-thermoelastic medium. This material is subjected to the presence of a non-locality parameter and an internal heat source using the three-phase-lag model. [ABSTRACT FROM AUTHOR]

A unique three-dimensional model of generalized thermoelasticity, incorporating a single relaxation time and relying on stress gradient nonlocal elasticity, is presented in this study. The fundamental coupled equations governing the model are applied to a semi-infinite spatial medium with a rigidly fixed bounding surface, which is exposed to a time-dependent thermal shock. The general solution for the field variables is obtained in a closed form through the utilization of normal mode analysis and the eigenvalue approach technique. Numerical results, specific to a substance resembling copper, are provided for the field variables. Parametric studies are conducted to assess the impact of elastic nonlocality on various physical quantities. The graphical representation reveals a noteworthy influence of the nonlocal parameter on the field variables. The study further discusses and compares predictions from the new model with the Lord and Shulman theory of generalized thermoelasticity. Ultimately, the article concludes with a summary of key remarks. [ABSTRACT FROM AUTHOR]

In the paper, we present a time two-grid difference (TGD) method for the approximation of two-dimensional (2D) nonlocal nonlinear wave equation (NNWE). First, the solution is obtained by solving a nonlinear system on the coarse grid (CG), then by using the numerical solutions obtained on the CG we construct a linearized system on the fine grid (FG). Meanwhile the auxiliary values calculated by Lagrange linear interpolation formula. Further, we prove the existence and uniqueness of solution on the CG and FG. Also the stability and convergence is proved strictly through the energy analysis scheme. Finally, two numerical examples are shown, which verify the proposed TGD method is more efficient than the general finite difference (GFD) method. [ABSTRACT FROM AUTHOR]

Purpose: This paper uses analytical methods to analyze the buckling behavior of sandwich nanobeams composed of three layers of material, with the central layer including a hollow hole. This study is the first instance of using such analytical techniques for investigating the buckling response of these specific FGM (functionally graded material) nanobeams. Methods: The calculation formulas have been derived using a novel third-order shear deformation theory. The equilibrium equation of the nanobeam is formulated based on the notion of virtual work. Analytical solutions have been used to get the precise answer for the ultimate load of the beam. Empirical evidence has substantiated the dependability of this particular approach. Results: This feature complicates the response of the beam and gives rise to several fascinating phenomena, including the idea of the virtual critical load which allows for the evaluation of the loss of the critical load. This research also looks at how the buckling behavior of the beam is affected by some geometric elements, material characteristics, hollow features of the intermediate layer, and viscous resistance-related parameters. Conclusion: Based on the findings of this investigation, several inferences can be inferred. The third-order theory employed in this investigation exhibits commendable reliability in the computation of the buckling issue pertaining to sandwich beams experiencing substantial deformations. The presence of a viscoelastic foundation has a significant impact on the critical buckling load of the beam, resulting in the inclusion of both real and fictitious components. The critical buckling load is influenced by various factors, including the core thickness, foundation parameters, material composition ratio, and the number of hollows, nonlocal characteristics, and core layer material. These factors not only impact the actual magnitude of the critical buckling load, but also affect the rate at which it is lost. The findings of this study hold considerable importance for engineers in their calculations and designs of similar structures within the field of engineering. Moreover, this serves as the foundation for other forthcoming study avenues that can serve as valuable sources of reference. [ABSTRACT FROM AUTHOR]

In this study, a two-dimensional "double-horizon peridynamics" formulation was presented for membranes. According to double-horizon peridynamics, each material point has two horizons: inner and outer horizons. This new formulation can reduce the computational time by using larger horizons and smaller inner horizons. To demonstrate the capability of the proposed formulation, various different analytical and numerical solutions were presented for a rectangular plate under different boundary conditions for static and dynamic problems. A comparison of peridynamic and classical solutions was given for different inner and outer horizon size values. [ABSTRACT FROM AUTHOR]

In this paper, we study a time‐fractional initial‐boundary value problem of Kirchhoff type involving memory term for non‐homogeneous materials. As a consequence of energy argument, we derive L∞0,T;H01(Ω)$$ {L}^{\infty}\left(0,T;{H}_0^1\left(\Omega \right)\right) $$ bound as well as L2(0,T;H2(Ω))$$ {L}^2\left(0,T;{H}^2\left(\Omega \right)\right) $$ bound on the solution of the considered problem by defining two new discrete Laplacian operators. Using these a priori bounds, existence and uniqueness of the weak solution to the considered problem are established. Further, we study semi discrete formulation of the problem by discretizing the space domain using a conforming finite element method (FEM) and keeping the time variable continuous. The semi discrete error analysis is carried out by modifying the standard Ritz‐Volterra projection operator in such a way that it reduces the complexities arising from the Kirchhoff type nonlinearity. Finally, we develop a new linearized L1 Galerkin FEM to obtain numerical solution of the problem under consideration. This method has a convergence rate of O(h+k2−α)$$ O\left(h+{k}^{2-\alpha}\right) $$, where α(0<α<1)$$ \alpha \kern0.1em \left(0<\alpha <1\right) $$ is the fractional derivative exponent and h$$ h $$ and k$$ k $$ are the discretization parameters in the space and time directions, respectively. This convergence rate is further improved to second order in the time direction by proposing a novel linearized L2‐1 σ$$ {}_{\sigma } $$ Galerkin FEM. We conduct a numerical experiment to validate our theoretical claims. [ABSTRACT FROM AUTHOR]

This article intends to investigate the free vibration damping characteristics of functionally graded viscoelastic nanobeams embedded in viscoelastic foundations using the infinite Kelvin–Voigt model of the Winkler–Pasternak type. This model is based on the nonlocal strain-driven gradient elasticity theory of Eringen. A power law model is then adopted to describe the continuous variation in the material properties of functionally graded material nanobeams. The study was carried by means of the first-order shear deformation theory with the shear correction factor using the finite element method. For the purpose of validating the developed model, it was decided to compare the results obtained with those reported about elastic nanobeams in the literature. Moreover, the influence of the power law exponent, structural damping coefficient, foundation coefficient, nonlocal parameter, and boundary conditions on the free frequency response of viscoelastic nanobeams was also investigated. [ABSTRACT FROM AUTHOR]

The anomaly cancellation in superstring theory is known to hold at leading order in the curvature for the gauge groups S O (3 2) and E 8 × E 8 . The coefficients of the next-to-leading order terms may be evaluated, and a mechanism for cancellation is described, which would remain valid at higher genus when there exists a global splitting of the coordinates of supermoduli space. Since the spin- 1 2 fields transform under the adjoint representation in these models, compactification of the heterotic string over G 2 / S U (3) or a fundamental 12-dimensional theory, from which superstrings are produced through an elliptic fibration, over G 2 × S U (2) × U (1) S U (3) × U (1) ′ × U (1) ′ ′ , provides another phenomenologically viable theory at lower energies compatible with the standard description of the elementary particle interactions. The 96 spin- 1 2 fields now would transform under the fundamental representation of G 2 × S U (2) × U (1) and the spin-one gauge fields would belong to the adjoint representation. The sum of the anomaly polynomials for the particle content of the G 2 × S U (2) × U (1) model vanishes at n 1 2 ≃ 1 0 3. 3 4 2 7 1 9 2 4. The contributions to the gravitational anomaly from the particles and antiparticles cancel by the CPT theorem and the duality transformations of polynomials of degree 6 in the curvature and the field strength. The existence of the interaction of a spin-2 charge, which is conserved only over a finite time interval, can be traced to nonlocal terms in the reduction of the string field theory to the gravitational sector. The source of the global gravitational anomaly cancellation in the modular form equations derived from an elliptic fibration of a 12-dimensional theory would restrict the compactifications and provide a method for preserving the absence of anomalies in four dimensions. [ABSTRACT FROM AUTHOR]

We consider a two dimensional electroconvection model which consists of a nonlinear and nonlocal system coupling the evolutions of a charge distribution and a fluid. We show that the solutions decay in time in L 2 (R 2) at the same sharp rate as the linear uncoupled system. This is achieved by proving that the difference between the nonlinear and linear evolution decays at a faster rate than the linear evolution. In order to prove the sharp L 2 decay we establish bounds for decay in H 2 (R 2) and a logarithmic growth in time of a quadratic moment of the charge density. [ABSTRACT FROM AUTHOR]

This particular work is an effort to investigate the propagation of wave in hygrothermoelastic medium in the light of Eringen’s nonlocal theory of elasticity. The coupled wave equations in terms of displacement, temperature and moisture concentration are solved in an analytical way. The phase velocities of longitudinal displacement wave, transverse displacement wave, diffusion wave and thermal wave, under the influence of nonlocal variable, moisture concentration, and diffusion coefficient, in the medium are obtained analytically and presented graphically to show the effect of these parameters on the wave velocities.

Speckle filtering is a key preprocessing approach for the applications of polarimetric synthetic aperture radar (PolSAR) data. Most current PolSAR filtering algorithms can hardly get good balance in suppressing speckle and retaining image details. In this article, an algorithm for fully PolSAR image filtering is proposed by embedding the idea of the advanced block matching theory into the classical Lee filter, which ensures that image details can be well preserved after the significant reduction of speckle. First, taking each image block as the reference, a block matching step is taken to group those similar blocks in the nonlocal area; the Lee filter is employed to simultaneously process the center pixel of each block in the group, followed by an aggregation step which estimates the same pixel been grouped in different groups; then, the block matching step is taken again to regroup similar blocks by using the information of both the original image and the image filtered in last stage; again, the Lee filter is collaborated with the aggregation step in filtering the image. Despeckling experiments demonstrate that the proposed PolSAR filter can not only significantly suppress the image noise but also well preserve edges and textures.

In this paper, we studied the stability of traveling wave solutions of a two-species Lotka-Volterra competition model in the form of a coupled system of reaction diffusion equations with nonlocal intraspecific and interspecific competitions in space at times. First, the uniform upper bounds for the solutions of the model was proved. By using the anti-weighted method and the energy estimates, the asymptotic stability of traveling waves with large wave speeds of the system was established.

The current study explores two-dimensional disturbances in a nonlocal photothermoelastic semiconducting medium with two temperatures by implementing the Green Naghdi-II theory. The thermal conductivity of the medium is assumed to be varying with temperature changes. The formulation is subjected to an inclined mechanical load. A lot of research has been carried out in recent years on photothermoelastic medium, but not much attention has been given to study the dynamical interactions in a nonlocal photothermoelastic medium with two temperatures and variable thermal conductivity under the effect of inclined mechanical load. The analytical solutions of physical field variables such as temperatures, stresses, carrier density and displacement are obtained by using the normal mode analysis method. For a specific material, numerical computations are performed to illustrate the results. The results that were obtained through numerical analysis for the physical quantities are displayed graphically. The comparisons are made among the results obtained by taking into account the different values of time, inclination angle, two temperature parameter, nonlocal parameter, variable thermal conductivity and photothermal elastic constants. Some special cases of interest have been inferred from the present study for validation. [ABSTRACT FROM AUTHOR]

In the present study, we explored a new mathematical formulation involving modified couple stress thermoelastic diffusion (MCTD) with nonlocal, voids and phase lags. The governing equations are expressed in dimensionless form for the further investigating. The desired equations are expressed in terms of elementary functions by assuming time harmonic variation of the field variables (displacement, temperature field, chemical potential and volume fraction field). The fundamental solutions are constructed for the obtained system of equations for steady oscillation and some basic features of the solutions are established. Also, plane wave vibrations has been examined for two dimensional cases. The characteristic equation yields the attributes of waves like phase velocity, attenuation coefficients, specific loss and penetration depth which are computed numerically and presented in form of distinct graphs. Some unique cases are also deduced. The results provide the motivation for the researcher to investigate thermally conducted modified couple stress elastic material under nonlocal, porosity and phase lags impacts as a new class of applicable materials. [ABSTRACT FROM AUTHOR]

Purpose: This work initially started a research on the natural vibrations of bamboo-reinforced composite beams placed in a fluid environment based on the classical beam theory as well as the new high-order shear deformation theory. Methods: This study makes use of the analytical solution. Results: The results of the calculations have demonstrated that the ply angle, material drag, foundation drag, and nonlocal parameter l, in addition to the surrounding environment, all have an effect on both the real and imaginary components of the natural frequency of the bamboo-reinforced composite nanobeams. The analytical approach presented in this article is the mathematical foundation for validating other bamboo beam calculation methods. Concurrently, the article demonstrates that the viscous resistance of the structure cannot be disregarded when evaluating the mechanical response of bamboo beams in engineering practice. Conclusion: This study offers a precise solution to the specific vibration issue of bamboo-reinforced composite nanobeams placed in the water environment, taking into account the size effect, based on novel third-order shear deformation theory and classical beam theory coupled with analytical methods. The reason why this study is different from others is that it is the first to take into account not only the resistance parameter of the material but also the resistance parameter of the foundation, in relation to the particular vibration response of this nanobeam. Due to the presence of both the viscous drag coefficient of the foundation and the viscous resistance of the structure, the natural frequency of the beam consists of both real and imaginary components. [ABSTRACT FROM AUTHOR]

We study a weak solution of a homogeneous nonlocal parabolic equation of the p-Laplacian type. We identify a minimal regularity assumption on the associated parabolic nonlocal tail for which the weak solution enjoys Hölder's regularity. [ABSTRACT FROM AUTHOR]

This study couples peridynamic (PD) theory with strain gradient elasticity (SGE) theory to investigate the combined effect of PD and SGE length scale parameters on size effect. The SGE theory introduces a length scale parameter in the stress–strain relations to account for size effect. The solution to the classical form of SGE equation of motion requires two additional non-classical boundary conditions arising from the presence of fourth-order spatial derivatives. The wave dispersions level off as the wave number increases as observed in real materials. The PD theory allows for nonlocal interactions of a material point within its horizon which serves as the PD length scale parameter. The equation of motion emerges in the form of an integral equation and the internal forces are expressed through nonlocal interactions (bonds) between the material points within a continuous body. It is a reformulation of classical continuum mechanics which is free of spatial derivatives. The numerical results concern a previously considered carbon nanotube (CNT). Under quasi-static axial loading, the results indicate an increased strengthening effect along the length of the tube. Under dynamic loading, its longitudinal vibration response is captured through explicit time integration. The numerical predictions capture the reference solutions corresponding to the classical SGE equation. [ABSTRACT FROM AUTHOR]

Motivated by the expanding demand of semiconductors at miniature/nanoscales used in micro-electromechanical systems and nano-electromechanical systems, etc., authors solved the problem of coupled plasma, thermal, elastic, and diffusion waves due to photothermal transport processes within an infinite semiconductor medium containing a spherical cavity. To highlight the hereditary properties, thermal and diffusion processes are considered to be memory dependent. The investigation is carried out in the context of a generalized photothermo-elastic-diffusion model considering the spatial nonlocal effects of concentration, thermal, and strain fields, which augments the novelty of the present work. Initially, the medium is held quiescent. The boundary of the cavity is subjected to an exponentially decaying pulse, and carrier density is expressed in terms of recombination velocity. Laplace transformation, along with the numerical inversion technique using the physical data of silicon, is applied to solve the governing equations and constitutive relations of the problem. The distribution of dimensionless quantities such as temperature, radial stress, and carrier density is represented graphically. [ABSTRACT FROM AUTHOR]

Summary: This paper presents the construction of a mean‐field homogenization (MFH) surrogate for nonlinear stochastic multiscale analyses of two‐phase composites that allows the material response to be studied up to its failure. The homogenized stochastic behavior of the studied unidirectional composite material is first characterized through full‐field simulations on stochastic volume elements (SVEs) of the material microstructure, permitting to capture the effect of the microstructural geometric uncertainties on the material response. Then, in order to conduct the stochastic nonlinear multiscale simulations, the microscale problem is substituted by a pressure‐dependent MFH reduced order micromechanical model, that is, a MF‐ROM, whose properties are identified by an inverse process from the full‐field SVE realizations. Homogenized stress‐strain curves can be used for the identification process of the nonlinear range, however, a loss of size objectivity is encountered once the strain softening onset is reached. This work addresses this problematic introducing a calibration of the energy release rate obtained with a nonlocal MFH micromechanical model, allowing to scale the variability found on each SVE failure characteristics to the macroscale. The obtained random effective properties are then used as input of a data‐driven stochastic model to generate the complete random fields used to feed the stochastic MF‐ROM. To show the consistency of the methodology, two MF‐ROM constructed from SVEs of two different sizes are successively considered. The performance of the MF‐ROM is then verified against an experimental transverse‐compression test and against full‐field simulations through nonlocal Stochastic Finite Element Method (SFEM) simulations. The implementation of the energy release rate calibration allows to conduct stochastic studies on the failure characteristics of material samples without the need for costly experimental campaigns, paving the way for more complete and affordable virtual testing. [ABSTRACT FROM AUTHOR]

The development of thermomechanical coupled simulations for rolling contacts is challenging when the adjacent material is temperature-dependent or when there are cracks or other discontinuities on the contact surface. This paper proposes a novel thermomechanical coupled modeling method for rolling contacts using a nonlocal peridynamic (PD) approach. Fully coupled, ordinary state-based PD thermomechanical equations for the plane strain and plane stress cases are derived based on the strain-energy density, including thermal coupling terms, and detailed information on each parameter is provided. Subsequently, an algorithm for rolling thermal contacts in PD is proposed based on the penalty method. This study further provides a detailed modeling process and an algorithm for the proposed method based on a multi-rate time-integration scheme for numerical implementation. A typical two-dimensional (2D) wheel–rail rolling contact model is established to evaluate the performance of the proposed contact modeling method in wheel–rail thermal contact and to analyze the influence of temperature-dependent material and rail-surface cracks on the thermomechanical response. It is found that the contact stress and rail-surface temperature rise in the case of small creepages and temperature-independent materials are in good agreement with the analytical solution. In the case of large creepages, the mechanical and temperature results of using temperature-dependent materials and temperature-independent materials are quite different, and the frictional heat generated can cause martensitic transformation of adjacent materials. Rail-surface cracks cause a sharp increase in the contact stress and temperature rise near the cracks, and the high temperature also promotes crack growth. • A nonlocal thermomechanical coupled modeling method for rolling contacts using peridynamic is proposed. • Fully coupled, ordinary state-based PD thermomechanical equations are derived. • An algorithm for rolling thermal contacts in PD is proposed based on the penalty method. • A typical 2D wheel–rail rolling contact model is established for a case study. [ABSTRACT FROM AUTHOR]

We introduce a nonlocal model of peridynamic type for fracture evolution in the quasistatic regime. Nonlocal quasistatic fracture evolution is developed and supporting numerical examples are presented. The approach is implicit and is based on local stationary and fixed point methods. Here a smooth cohesive force-strain model is used. Initially the force increases with strain then softens and decreases to zero. It is proved that the fracture evolution decreases stored elastic energy with each displacement step as the cracks advance; provided the displacement increments are chosen sufficiently small. These results apply to any system of multiple cracks. This is also seen in the numerical examples. The numerical examples include evolution of a straight crack, a crack propagating inside an L-shaped domain, and two offset inward propagating cracks. [ABSTRACT FROM AUTHOR]

The aim of this article is to study a problem of thermomechanical deformation in a homogeneous, isotropic, micropolar thermoelastic half-space based on the Moore–Gibson–Thompson heat equation under the influence of nonlocal and hyperbolic two-temperature (HTT) parameters. The problem is formulated for the considered model by reducing the governing equations into 2D and then converting to dimensionless form. Laplace transform and Fourier transform techniques are employed to obtain the system of differential equations. In the transformed domain, the physical quantities like displacement components, stresses, thermodynamic temperature, and conductive temperature are calculated under the specific types of normal force and thermal source at the boundary surface. A numerical inversion technique is used to recuperate the equations in the physical domain to exhibit the influence of nonlocal and HTT in the form of graphs. Particular cases of interest are also discussed in the present problem. The present study finds applications in a wide range of problems in engineering and sciences, control theory, vibration mechanics, and continuum mechanics. [ABSTRACT FROM AUTHOR]

In this study, a new double horizon peridynamics formulation was introduced by utilising two horizons instead of one as in traditional peridynamics. The new approach allows utilisation of large horizon sizes by controlling the size of the inner horizon size. To demonstrate the capability of the current approach, four different numerical cases were examined by considering static and dynamic conditions, different boundary and initial conditions, and different outer and inner horizon size values. For both static and dynamic cases, it was observed that as the inner horizon decreases, peridynamic solutions converge to classical continuum mechanics solutions even by using a larger horizon size value. Therefore, the proposed approach can serve as an alternative approach to improve computational efficiency of peridynamic simulations by obtaining accurate results with larger horizon sizes. [ABSTRACT FROM AUTHOR]

In this paper, we study a nonlocal approximation of the time-dependent (local) Eikonal equation with Dirichlet-type boundary conditions, where the kernel in the nonlocal problem is properly scaled. Based on the theory of viscosity solutions, we prove existence and uniqueness of the viscosity solutions of both the local and nonlocal problems, as well as regularity properties of these solutions in time and space. We then derive error bounds between the solution to the nonlocal problem and that of the local one, both in continuous time and forward Euler time discretization. We then turn to studying continuum limits of nonlocal problems defined on random weighted graphs with $n$ vertices. In particular, we establish that if the kernel scale parameter decreases at an appropriate rate as $n$ grows then, almost surely, the solution of the problem on graphs converges uniformly to the viscosity solution of the local problem as the time step vanishes and the number vertices $n$ grows large. [ABSTRACT FROM AUTHOR]

The present paper examines the plane wave's reflection in a semiconducting magneto-thermoelastic rotating nonlocal half-space medium, which is stress-free, thermally insulated, and with a diffusion transport process at the boundaries. The novel mathematical model of extended three-phase-lag (TPL) heat transfer law with memory-dependent derivative (MDD) and two temperatures (2T) is used to model this problem. The investigated 2D model shows that a longitudinal wave, when striking the surface z = 0, produces four reflected waves. The characteristics of the plane wave such as phase velocity, amplitude ratios, penetration depth, attenuation-coefficients-specific loss, and energy ratios of various reflected waves are obtained. The symmetric and asymmetric tensor representations of all physical quantities are used. The effects of various theories of thermoelasticity, two temperatures, and rotation on wave characteristics are illustrated graphically using MATLAB software. [ABSTRACT FROM AUTHOR]