The present work aims to primarily provide a general representation of the solution of the simplified elastostatics version of Mindlin’s Form II first-strain gradient elastic theory, which converges to the solution of the corresponding classica...
The free vibration of isotropic gradient elastic thick non-rectangular microplates is analyzed in this paper. To capture the microstructure-dependent effects of microplates, a negative second-order gradient elastic theory with symmetry is utilized. T...
The applicability of piezoelectric energy harvesting is increasingly investigated in the field of renewable energy. In improving harvester efficiency, manipulating elastic waves through a geometric configuration as well as upgrading harvester element...
In this study, a new anisotropic elastic shell model with a nonlocal strain gradient is developed to investigate the vibrations of simply supported single-walled carbon nanotubes (SWCNTs). The Sanders–Koiter shell theory is used to obtain strai...
This paper presents an alternative approach to formulating a rational bar-elastic substrate model with inclusion of small-scale and surface-energy effects. The thermodynamics-based strain gradient model is utilized to account for the small-scale effe...
Nanoplates have been extensively utilized in the recent years for applications in nanoengineering as sensors and actuators. Due to their operative nanoscale, the mechanical behavior of such structures might also be influenced by inter-atomic material...
We consider material bodies exhibiting a response function for free energy, which depends on both the strain and its gradient. Toupin–Mindlin’s gradient elasticity is characterized by Cauchy stress tensors, which are given by space-like Euler–Lagrang...
An introductory discussion on a (weakly non-local) gradient generalization of some one-dimensional elastic and viscoelastic models, and their fractional extension is provided. Emphasis is placed on the possible implications of micro- and nano- engine...
We formulate a series of strong ellipticity inequalities for equilibrium equations of the gradient elasticity up to the Nth order. Within this model of a continuum, there exists a deformation energy introduced as an objective function of deformation...
In the first part of our review paper, we consider the problem of approximating the Green’s function of the Lagrange chain by continuous analogs. It is shown that the use of continuous equations based on the two-point Padé approximants g...
Nowadays, the modified nonlocal strain gradient theory provides a mathematically well-posed and technically reliable methodology to assess scale effects in inflected nano-structures. Such an approach is extended in this paper to investigate the exten...
In this manuscript the dynamic response of porous functionally-graded (FG) Bernoulli–Euler nano-beams subjected to hygro-thermal environments is investigated by the local/nonlocal stress gradient theory of elasticity. In particular, the influence of...
Linear regression is the use of linear functions to model the relationship between a dependent variable and one or more independent variables. Linear regression models have been widely used in various fields such as finance, industry, and medicine. T...
In continuum physics the dissipation principle, first proposed by Coleman and Noll in 1963, regards second law of thermodynamics as a unilateral differential constraint on the constitutive equations. In 1996, Muschik and Ehrentraut provided a rigorou...
The paper is concerned with the boundary conditions of explicit gradient elasticity of Mindlin’s type in dynamics. It has been argued in an earlier paper that acceleration terms should not be present in the boundary tractions because of objecti...
Nonlinear transverse free vibrations of porous functionally-graded (FG) Bernoulli–Euler nanobeams in hygrothermal environments through the local/nonlocal stress gradient theory of elasticity were studied. By using the Galerkin method, the gover...
This paper investigated the reflection of plane waves at the interface of dipolar gradient elastic solids under the control of an external magnetic field. This study focused on the increasing influence of the microstructural effect as the incident wa...
An analytical method is presented in this work for the linear vibrations and buckling of nano-plates in a hygro-thermal environment. Nonlinear von Kármán terms are included in the plate kinematics in order to consider the instability ph...
To address the fact that changes in network topology can have an impact on the performance of routing, this paper proposes an Elastic Routing Algorithm based on Multi-Agent Deep Deterministic Policy Gradient (ERA-MADDPG), which is implemented within...
In this paper, the refined plate theory (RPT), Hamilton’s principle, and isogeometric analysis (IGA) are applied to investigate the static bending, free vibration and buckling behaviors of functionally graded graphene-platelet-reinforced piezoe...
Metamaterials are composed of arrays of subwavelength-sized artificial structures; these architectures give rise to novel characteristics that can be exploited to manipulate electromagnetic waves and acoustic waves. They have been also used to manipu...
This paper is devoted to the modelling of nonlocality in continuum physics through constitutive functions that depend on suitable gradients. For definiteness, the attention is addressed to elastic solids, heat conductors, and magnetic solids. Models...
Natural materials are generally damage adaptive through their multilevel architectures, with the characteristics of compositional and mechanical gradients. This study demonstrated that the desired elastic gradient can be in-situ stress-induced in a t...
This paper examines the static and dynamic responses of strain gradient planar trusses. Classical elasticity (CE) theory lacks a material microstructural length parameter in its governing equations, making it insufficient to capture size-dependent ef...
The displacement and stress-based error estimates in a posteriori error recovery of compressible and nearly-incompressible elastic finite element solutions is investigated in the present study. The errors in the finite element solutions, i.e., in dis...
The porous structure can reduce the elastic modulus of a dental implant and better approximate the elastic characteristics of the material to the alveolar bone. Therefore, it has the potential to alleviate bone stress shielding around the implant. Ho...
Refractory complex concentrated alloys (RCCAs) have drawn increasing attention recently owing to their balanced mechanical properties, including excellent creep resistance, ductility, and oxidation resistance. The mechanical and thermal properties of...
This paper proposes a novel nanobar–substrate medium model for static and free vibration analyses of single-walled carbon nanotube (SWCNT) systems embedded in the elastic substrate medium. The modified strain-gradient elasticity theory is utili...
Ni-based superalloys, essential for high-temperature applications, derive strength from coherent second-order precipitates that impede dislocation motion through coherency misfit and elastic mismatch. This study employs multi-component phase-field cr...
We present a joint 2D inversion approach for magnetotelluric (MT) and gravity data with elastic-net regularization and cross-gradient constraints. We describe the main features of the approach and verify the inversion results against a synthetic mode...
Composite materials are frequently used in the construction of rail, tunnels, and pipelines as well as in the construction of aircraft, ships, and chemical pipelines. When such structural elements are formed from new-generation composites, such as CN...
Petal gas bearings are widely used in industrial turbine installations. However, there are practically no mathematical models that take into account the nonlinear dependence of the elastic element deformations of the gas-dynamic bearing on the pressu...
A finite strain gradient model for the 3D analysis of materials containing spherical voids is presented. A two-scale approach is proposed: a least-squares methodology for RVE analysis with quadratic displacements and a full high-order continuum with...
Large-span steel trusses are widely used in public buildings such as large-span factory buildings, exhibition halls, gymnasiums, and bridges because of their fast construction speed and easy industrial manufacturing. Due to construction errors and en...
This work studies the dynamic response of Bernoulli–Euler multilayered polymer functionally graded carbon nanotubes-reinforced composite nano-beams subjected to hygro-thermal environments. The governing equations were derived by employing Hamilton’s...
This article investigates the size dependent on piezoelectrically layered perforated nanobeams embedded in an elastic foundation considering the material Poisson’s ratio and the flexoelectricity effects. The composite beam is composed of a regu...
In this study, a dynamic Mindlin–Reissner-type plate is developed based on a simplified version of Mindlin’s form-II first-strain gradient elasticity theory. The governing equations of motion and the corresponding boundary conditions are derived usin...
Analysis of the electromechanical-size-dependent bending of piezoelectric composite structural components with flexoelectricity has been considered by many researchers because of the developments of nanotechnology and the applicability of piezoelectr...
Admittedly, the design requirements of compactness, low frequency, and broadband seem to constitute an impossible trinity, hindering the further development of elastic metamaterials (EMMs) in wave shielding engineering. To break through these constra...
The presented research aims to find a data-driven formula for the compressive stress–strain behaviour of closed-cell aluminium foams with respect to the apparent density of the material. This is a continuation and new development of an earlier...
It was recently proved that the knowledge of the transverse displacement of a nanoplate in an open subset of its mid-plane, measured for any interval of time, allows for the unique determination of the spatial components
This review details a large panel of experimental studies (Inelastic Neutron Scattering, Quasi-Elastic Neutron Scattering, Nuclear Magnetic Resonance relaxometry, Pulsed-Gradient Spin-Echo attenuation, Nuclear Magnetic Resonance Imaging, macroscopic...
Accurate estimation of the elastic modulus (E) of rock is critical for the design of geotechnical projects such as mining, slopes, and tunnels. However, the determination of rock mechanical parameters usually involves high budget and time requirement...
In this paper, a functionally graded piezoelectric plate on an elastic foundation composed of two different piezoelectric materials bonded together in the form of plate is studied, and its static bending and fundamental frequencies are analyzed. Firs...
Near-infrared (NIR) spectroscopy is widely used as a nondestructive evaluation (NDE) tool for predicting wood properties. When deploying NIR models, one faces challenges in ensuring representative training data, which large datasets can mitigate but...
A non-local solution is obtained here in the theory of cracks, which depends on the scale parameter in the non-local theory of elasticity. The gradient solution is constructed as a regular solution of the inhomogeneous Helmholtz equation, where the f...
This paper presents a novel non-classical Timoshenko–Ehrenfest beam model based on a reformulated strain gradient elasticity theory. The strain gradient effect, couple stress effect, and velocity gradient effect for vibration are included in th...
We are focusing on the algorithms for solving the large-scale convex optimization problem in linear elasticity contact problems discretized by Finite Element method (FEM). The unknowns of the problem are the displacements of the FEM nodes, the corres...
For many engineering applications, it is sufficient to use the concept of simple materials. However, higher gradients of the kinematic variables are taken into account to model materials with internal length scales as well as to describe localization...
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