Nonlocal Stress Research Articles

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.

Nonlinear static behaviors of nonlocal nanobeams incorporating longitudinal linear temperature gradient

The elastic parameters and the coefficient of thermal expansion (CTE) of nanomaterials change with temperature. If the elastic modulus, the CTE, and the longitudinal linear temperature gradient are coupled, the longitudinal symmetry of the mechanical properties of nanobeams is broken. However, researchers have not yet to examine how this symmetry breaking affects the mechanical properties of nanobeams. This paper provides a new analysis of the modified thermoelastic beam model established by the nonlocal stress gradient theory. The present analysis incorporates the coupling of the longitudinal linear temperature gradient, elastic modulus, thermal expansion, and scale effect. Afterward, we apply the Galerkin method to explore the buckling, post-buckling, and transverse bending of a (10,10) single-walled carbon nanotube (SWCNT). The results show that the linear temperature gradient induces the breaking of the nanobeam's longitudinal symmetry and then results in the coupling of the symmetrical and antisymmetrical weight functions of the deformations. While the linear temperature gradient marginally affects the symmetry of nanobeams, it significantly raises the buckling temperature and introduces the complexity of the post-buckling and transverse force bending. In addition, the integration of the linear longitudinal temperature gradient, elastic modulus, and nonlocal effect more significantly affects nanobeams' mechanical properties than individual factors.

Exact solution for free vibration analysis of non-uniform thickness functionally graded porous nanosheet with surface effect based on variable nonlocal and length-scale parameters

In this article, the analytical solution for free oscillation of non-uniform thickness functionally graded porous (FGP) rectangular nanosheets resting on a Pasternak foundation with various boundary conditions (BCs) based on the nonlocal strain gradient theory and surface effect are discovered. The nonlocal stress and strain effects are captured on the nonlocal strain gradient hypothesis, while the surface energy effects are based on the surface elasticity hypothesis. The FGP nanosheet has a nonlinear thickness change in both x and y directions and is placed on the Pasternak elastic foundation. The unique point of this study is to investigate the change of nonlocal and length-scale coefficients along the thickness as mechanical properties of the material. Applying classical shear deformation theory (ignore the effect of shear deformation) combined with Hamilton’s principle, the motion balance equation of non-uniform thickness nanosheets is established. The accuracy of the proposed method is verified through reliable publications. A set of results of natural vibration frequencies of variable thickness FGP nanosheets under the influence of factors are discovered and discussed. The results of this study can be used in design calculations of MEM and NEMs systems in mechanics.

Non-local stress approach in conjunction with reinforcement isotropic solid model (NLS-RIS): an efficient orthotropic mixed mode I/II fracture criterion

Non-local stress approach in conjunction with reinforcement isotropic solid model (NLS-RIS): an efficient orthotropic mixed mode I/II fracture criterion

Nonlocal Couple Stress Vibration of Pasted Thermo Elastic Multilayered Cylinder with Hall Current and Multi Dual Phase Lags

Nonlocal Couple Stress Vibration of Pasted Thermo Elastic Multilayered Cylinder with Hall Current and Multi Dual Phase Lags

Effects of translaminar edge crack and fiber angle on fracture toughness and crack propagation behaviors of laminated carbon fiber composites

Abstract In this study, the translaminar fracture toughness of carbon fiber laminated composites with different layer sequences was investigated experimentally and numerically for different crack directions. In the numerical study, first of all, the critical stress intensity factor was determined by using the M-integral method. Three-dimensional model and M-integral analysis were achieved in the ANSYS finite element package program. The non-local stress fracture criterion was used to in order to find failure curves of the materials. Then, in order to find the crack propagation directions numerically, the solid model was transferred to the LS-DYNA program and progressive failure analysis was performed. Fracture toughness decreased by 9.92 % with the change of crack angle from 15° to 90°. As the fiber angle changed from 0° to 45°, it decreased by 9.17 %. The biggest error between the experimental and numerical study results was found at α = 45°, with a rate of 12.3 %.

Two-phase flow-induced vibration of tilted curved bi-directional functionally graded nanopipe in supersonic airflow

Flow-induced vibration is known as a prevalent phenomenon in various industries. As a result of the flow, dynamic fluid forces are generated, which lead to the excitation of the system. Multiphase flow, found commonly in both natural and industrial settings, including industrial plants, is a significant source of noise and vibration. In the two-phase flow, as a particular case of multiphase flow, flow configuration plays a major role in the system’s traits. Despite recent advancements in flow-induced vibration, it is still considered an unresolved topic. This research develops a new multi-physics simulation for the stability study of a two-directional functionally graded tilted curved cylindrical nanopipe conveying a liquid-gas two-phase flow. Nonlocal stress–strain gradient theory (NSGT) with two size-dependent parameters (nonlocal and length scale) is presented to simulate the current nanostructure. Newton’s second law has been employed to govern the resultant forces that act on a control volume at a differential fluid element of fluid. Hiring the finite element (FE) approach alongside the generalized differential quadrature role (GDQR), both the eigenvector and eigenvalue problems are presented for analyzing the characteristics of the nanosystem under various situations. An exhaustive parametric analysis is also provided to make clear the role of varied parameters such as velocity of fluid flow, aerodynamic pressure, air yaw angle, and gas volume fraction coefficient on the system’s fundamental frequency.

Photothermoelastic interaction in a two-dimensional semiconductor with nonlocal stress theory

The present contribution enlightens a viable simulation which describes the photothermoelastic interactions for a two-dimensional thermoelastic transversely isotropic thick semiconducting plate due to the presence of a varying heat source. The upper surface of the semiconductor is traction-free, subjected to prescribed surface temperature and prescribed carrier density flux while the lower surface of the plate rests on a rigid foundation and is thermally insulated. In this new model, the conventional Fourier law has been modified assimilating the memory-dependent derivative within a slipping interval in association with the nonlocal stress theory. On utilizing Laplace and Fourier transformation mechanism, the governing equations for displacement, carrier density and temperature have been obtained in the Laplace–Fourier transform domain. In order to have the solutions in the space-time domain, the inversion of the double transform have been carried out numerically based on the method of Fourier series expansion. From the graphical representations corresponding to the numerical results, the significance of effective parameters such as nonlocality parameter, delay-time parameter is discussed. Noteworthy differences in the results have been demonstrated for different kernel functions. Also, the superiority of a nonlinear kernel function and its effectiveness is also reported in the study.

Elasto‐thermodiffusive interaction under void due to nonlocal stress theory

AbstractThe current investigation address a novel generalized elasto‐thermodiffusion model for a thermoelastic porous half‐space incorporating the nonlocal stress theory proposed by Eringen. Modeling of the problem is performed by adopting Moore‐Gibson‐Thompson (MGT) thermoelasticity theory defined in an integral form of a common derivative on a slipping interval, well known as the memory‐dependent derivative. The bounding plane of the medium is subjected to time‐dependent thermal and chemical shocks and there is no change in the volume fraction field. Laplace transform and the Fourier transform techniques have been adopted to represent the analytical solutions in the transformed domain. The distributions of the physical fields such as the temperature, stress, chemical potential, mass concentration and the volume fraction field were found in the real space‐time domain adopting suitable numerical scheme based on the Fourier series expansion. According to the discussion of the computational results and the respective graphical representations, the prominent role of different parameters such as the effect of nonlocality, effect of void and thermodiffusion is analyzed. Moreover, the superiority of a nonlinear kernel function compared to a linear form is also reported.

Nonlinear Vibration of Function Graded Magneto-electro-elastic Microplates using Nonlocal Stress Theory

This work presents an analysis of nonlinear vibration in Function Graded Magneto-Electro-Elastic (FG-MEE) plates subjected to mechanical, electrical, and magnetic loads using the nonlocal stress theory approach. In this study two types of MEE plates, namely BaTiO3 and CoFe2O4 were considered. The basic equations are derived using classical plate theory with nonlocal stress theory and are solved using the Galerkin method and Runge-Kutta method. We investigated the effects of nonlocal parameters, materials, and geometrical characteristics on the natural frequencies and nonlinear vibration of the FG-MEE microplates.
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Nonlocal strain gradient‐based nonlinear dynamics of sinusoidal impulsive actuated porous/piezoelectric multilayer energy nanoharvesters

AbstractThe applications of nanoelectromechanical systems integrating simultaneously the mechanical and electrical functionalities at nanoscale have been gotten wider in the last decade. The main objective of this exploration is to analyze the small scale‐dependent nonlinear dynamical feedback of multilayer energy nanoharvesters containing a graded porous passive core coated by piezoelectric facesheets under a sinusoidal impulsive external actuation. For this purpose, the technique of meshless collocation is constructed at the same time the nonlocal stress and strain gradient tensors without any necessary background meshes and integration procedure. It is found that by taking the nonlocal stress tensor into account, the average of extremum points of maximum lateral deflection increases from to , and from to for simply supported and clamped multilayer nanoharvesters, respectively. On the contrary, through considering the strain gradient tensor, the average of extremum values of the maximum lateral deflection reduces from to for the simply supported nanoharvester, and from to for the clamped one.Highlights Development a third‐order shear flexible nonlocal strain gradient (NSG)‐based plate‐type nanoharvester model Incorporating the role of nonlocal stress and strain gradient tensors in nonlinear dynamics of nanoharvesters Time‐histories of achieved voltage of sinusoidal impulsive loaded plate‐type nanoharvesters Influence of porosity on the NSG‐based nonlinear dynamic performance.

Nonlocal stress gradient integral model with discontinuous and symmetrical conditions for size-dependent fracture of centrally-cracked nanobeams

We study the fracture of nanobeams containing central cracks using nonlocal stress gradient integral model (NSGIM) with discontinuous and symmetrical conditions. Compared with the traditional NSGIM, the present model includes some definite integral terms in the constitutive boundary constraints and the newly introduced constitutive continuity conditions. Subsequently, the Mode I and Mode II fracture problems are studied under given uniform loading (or concentrated force) conditions in opposite and same directions. In the numerical simulations, the effects of nonlocal and gradient length scale parameters on normalized energy release rates and works by external loads are investigated in detail.

Torsional Dynamics of Axially Graded Viscoelastic Carbon Nanotubes

Torsional vibration analysis of the axially functionally graded carbon nanotubes has been carried out. Nonlocal stress gradient elasticity theory has been used in continuum mechanics model of the carbon nanotube. Variation of the material properties of the axially graded nanostructure has been assumed in exponential form. Differently from the majority of literature works, viscous damping and nonlocal parameters have been assumed in grading form. Energy functional for the carbon nanotube has been achieved with minimum potential energy principle and weak form solution has been obtained with the Ritz Method. Effects of material grading, nonlocality and viscoelasticity to the torsional dynamics of axially graded carbon nanotube have been investigated. Results of the present work could be useful in modeling and production of axially functionally graded nanostructures.

Vibration analysis of higher-order nonlocal strain gradient plate via meshfree moving Kriging interpolation method

In this paper, a higher-order nonlocal strain gradient plate model combining nonlocal elasticity theory with strain gradient theory in the form of adding signs is constructed. The governing equation for the higher-order nonlocal strain gradient plate model is derived by Hamilton’s principle. Two higher-order parameters with nonlocal stress and strain gradient are introduced here to explain the size effect and dispersive behaviour. The meshfree moving Kriging interpolation method is utilized to address the frequency of higher-order nonlocal strain gradient plate under complicated boundary conditions. Nonlocal elasticity theory, strain gradient theory in the form of add signs and minus signs on the effect of frequency are compared by degenerating the higher-order nonlocal strain gradient plate model. The other goal of this paper is to compare the present model with higher-order nonlocal strain gradient theory in the form of minus signs on the effect of frequency. It is shown that these two items can describe the size effect well. The present method can also produce lower natural frequencies corresponding to ultrahigh-order mode shapes and applied in a discrete medium.

A non-local damage model-based FFT framework for elastic-plastic failure analysis of UD fiber-reinforced polymer composites

A novel computational framework combining fast Fourier transform (FFT) with the non-local damage model is proposed to simulate the nonlinear mechanical behaviors of unidirectional composites. Integral-type non-local damage model and gradient-regularized non-local damage model are integrated to analyze brittle materials and ductile materials, respectively. Under transverse tensile load, the failure of matrix in the composites is characterized by non-local maximum principal stress damage model or the elastic-plastic damage model obeying the parabolic yield criterion, respectively. It is verified that predicted stiffness, strength, and ultimate crack morphologies obtained by the proposed model are in good agreement with traditional finite element method (FEM) and phase field method (PFM) in the literature. The effects of microstructure features on the mechanical behaviors and the suitability of multiple crack propagation are further studied effectively and accurately.

Integral nonlocal stress gradient elasticity of functionally graded porous Timoshenko nanobeam with symmetrical or anti‐symmetrical condition

AbstractUtilization of symmetrical or anti‐symmetrical condition could improve the calculation efficiency. In this paper, a mathematical formulation is proposed to deal with the symmetrical or anti‐symmetrical condition in an integral nonlocal stress gradient model (INSGM), which is transformed equivalently into differential form with constitutive boundary condition as well as constitutive symmetrical or anti‐symmetrical condition. Unlike general constitutive boundary conditions, an integral item is introduced to constitutive symmetrical and anti‐symmetrical conditions, and they are opposite to each other. Based on INSGM with symmetrical or anti‐symmetrical conditions, static bending of simply‐supported (SS) and clamped‐clamped (CC) functionally graded porous Timoshenko nanobeams is investigated for symmetrical loads, including uniformly distributed load (UDL) and middle point force, as well as anti‐symmetrical loads, including anti‐symmetrical UDL and middle point moment. The exact solutions are deduced and expressed in explicit form for different boundary and loading conditions. Calculation shows that, under UDL, bending deflections of half Timoshenko nanobeams based on current model agree well with those for whole Timoshenko nanobeams based on general INSGM for both SS and CC boundary conditions. Numerical study is performed to show the effectiveness of current model.

A bond-level energy-based peridynamics for mixed-mode fracture in rocks

This paper deals with the numerical simulation of initiation and propagation of mixed mode fracture in rocks. A bond-level energy-based peridynamic model is developed by introducing a dilatation function to capture both volumetric and deviatoric deformations. We proceed to define the nonlocal stresses to obtain the isotropic and deviatoric forces commensurate with the deformations. We then come up with a new failure model to link computational peridynamics with some phenomenological failure criteria, which is highly relevant for both brittle and quasi-brittle rocks. Finally, several numerical examples of mixed-mode fractures are presented to show the performance of our model.

Theoretical thermal damping vibration analysis of functionally graded viscoelastic Timoshenko microbeam with integral nonlocal strain gradient model

In this work, nonlocal strain gradient integral model is applied to investigate the free damping vibration analysis of functionally graded (FG) viscoelastic Timoshenko microbeam with immovable boundary conditions in thermal environment. The microbeam is assumed to be viscoelastic and modeled by Kelvin–Voigt model. The differential governing equations and corresponding boundary conditions are derived with the Hamilton’s principle. Combining nonlocal strain gradient integral model and Kelvin–Voigt viscoelastic model, the integral constitutive equations of nonlocal stress with thermal effect are derived and then converted into differential form plus constitutive constraints. The size-dependent axial force due to thermal expansion is explicitly derived through the immovable boundary conditions. The bending deflection and moment, cross-sectional rotation as well as shear force are explicitly derived with Laplace transformation for linear thermo-elastic vibration. Taking into account the boundary conditions as well as constitutive constraints, one gets a nonlinear equation with complex coefficients, from which one can determine the complex characteristic frequency. A two-step numerical method is proposed to solve the elastic vibration frequency and damping ratio. The influence of length scale parameters, viscos coefficient, FG index, thermal effect, vibration order and ratio between beam length and thickness on the vibration frequencies and damping ratio is investigated numerically for FG viscoelastic Timoshenko microbeams under different immovable boundary conditions.

Nonlocal couple stress-based meshless collocation model for nonlinear dynamic performance of microbeam-type piezoelectric energy harvesters

The prime aim of the current exploration is that to analyze the size-dependent nonlinear dynamics of microsize laminated bridge-type piezoelectric energy harvesters containing a passive core made of an agglomerated nanocomposite and piezoelectric surface layers under a time-dependent mechanical load. For this purpose, the both nonlocal and couple stress tensors are incorporated to the classical quasi-3D shear flexible beam theory to model microsize beam-type laminated energy harvesters. After that, a numerical solution methodology based on the meshless collocation method is employed to discretize the obtained size-dependent nonlinear equations via using a coalesce basis function including polynomial and multiquadric parts on the basis of the Chebyshev node distribution scheme to remove any possible singularity. The nonlinear time histories relevant to the induced lateral deflection and extracted voltage are plotted in the presence and absence of the nonlocal and couple stress tensors as well as various values of the agglomeration constants relevant to the nanocomposite passive core of microsize energy harvesters. One can find that by increasing the cluster volume fraction, the effect of the nonlocal stress tensor on the extracted voltage from the microsize energy harvester increases from +16.50% to +17.53% in the case of simply supported end conditions, and from +21.84% to +22.99% in the case of clamped end conditions. In addition, the effect of the couple stress tensor enhances from −22.21% to −23.09% in the case of simply supported end conditions, and from −27.15% to −27.94% in the case of clamped end conditions.

Simulation and experimental study on cold sprayed W[sbnd]Cu composite with high retainability of W using core-shell powder

A WCu composite coating with high W retention was fabricated by cold spraying using a novel W@Cu core-shell powder. The impact and deposition mechanism of W@Cu core-shell powder during cold spraying were investigated using finite element modeling in comparison to typical WCu satellite powder. The results revealed that the W@Cu core-shell powder shows non-local strain and dispersive residual stress in the final coating, resulting in a low rebound energy and interfacial bonding energy. As a result of employing the core-shell powder, a cold-sprayed WCu composite coating with a high W content can be prepared, and the coating has a non-pancake-like layer morphology. After optimizing the core-shell powder with a Ni transition layer, the final coating demonstrated super-high W retention (98.3 %) and decreased bulk porosity (1 %).