The general strain gradient theory of Mindlin is re-visited on the basis of a new set of higher-order metrics, which includes dilatation gradient, deviatoric stretch gradient, symmetric rotation gradient and curvature. A strain gradient bending theor...
Gradient-nanostructured material is an emerging category of material with spatial gradients in microstructural features. The incompatibility between gradient nanostructures (GNS) in the surface layer and coarse-grained (CG) core and their roles in ex...
In this paper, we examine the inherent mathematical and physical inconsistencies of strain-gradient theories. It is shown that strain gradients are not proper measures of deformation, because their corresponding energetically conjugate stresses are n...
In this study, we created a new model to determine strain fatigue characteristics obtained from a bending test. The developed model consists of comparing the stress and strain gradient surface ratio for bending and tensile elements. For model verific...
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 results of measuring gradient strain fields by embedded or mounted point fiber-optic sensors based on Bragg gratings and distributed fiber-optic sensors based on Rayleigh scattering are discussed. Along with the experiment, the results of numeric...
Predicting the performances of a manufactured part is extremely important, especially for industries in which there is almost no room for uncertainties, such as aeronautical or automotive. Simulations performed by means of numerical methods such as F...
Many investigators have become interested in nanostructures due to their outstanding mechanical, chemical, and electrical properties. Two-dimensional nanoplates with higher mechanical properties compared with traditional structural applications are a...
In the contact of rough surfaces, most contact patches are at the scale of micrometers, and thus, their contact deformation can be dominated by the size-dependent plasticity. In this paper, we propose a new strategy to analyze the role of strain grad...
The mathematical nature of the flow rule for the strain gradient plasticity theory proposed by Nix and Gao (W.D. Nix and H. Gao, J Mech Phys Solids 46(3), 411(1998)) is discussed based on the paradigm developed by Gurtin and Anand (M.E. Gurtin and L....
An improved model based on the Chaboche constitutive model is proposed for cyclic plastic behavior of metal and low cycle fatigue of notched specimens under cyclic loading, considering the effect of strain gradient on nonlinear kinematic hardening an...
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 paper addresses the second law of thermodynamics through the Clausius–Duhem inequality in its general form, with entropy flux and entropy production given by suitable constitutive functions. For definiteness the paper investigates possible...
A nonlinear static analysis of a circular/annular nanoplate on the Winkler–Pasternak elastic foundation based on the nonlocal strain gradient theory is presented in the paper. The governing equations of the graphene plate are derived using firs...
This study presents a mathematical size-dependent model capable of investigating the dynamic behavior of a sandwich perforated nanobeam incorporating the flexoelectricity effect. The nonlocal strain gradient elasticity theory is developed for both co...
A dynamic impact test was performed on as-rolled AZ31 alloys with gradient microstructure under various strains. The microstructural evolution and mechanical properties were systematically investigated. As the strain rate gradually increased, an incr...
In this contribution, the variational problem for the Kirchhoff plate based on the modified strain gradient theory (MSGT) is derived, and the Euler-Lagrange equations governing the equation of motion are obtained. The Galerkin-type weak form, upon wh...
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...
The present paper aims at providing a comprehensive investigation of the abilities and limitations of strain gradient crystal plasticity (SGCP) theories in capturing different kinds of localization modes in single crystals. To this end, the small def...
The present research focuses on the use of a meshless method for the solution of nanoplates by considering strain gradient thin plate theory. Unlike the most common finite element method, meshless methods do not rely on a domain decomposition. In the...
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...
The annealing behavior of surface-locally cold-deformed 0.2 mass% carbon steel with a large strain gradient was investigated, with special attention paid to the change in grain size. The surface local deformation was introduced by a ball-dropping (BD...
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...
This article presents the nonlinear investigation of the thermal and mechanical buckling of orthotropic annular/circular single-layer/bilayer nanoplate with the Pasternak and Winkler elastic foundations based on the nonlocal strain gradient theory. T...
This study investigates the fabrication, nanomechanical behavior, and tribological performance of nanostructured superlattice coatings (NSCs) composed of alternating TiAlSiNb-N/TiCr-CN bilayers. Deposited via High-Power Ion-Plasma Magnetron Sputterin...
Gradient nanostructured (GNS) surface layer with a controllable martensite fraction has been synthesized on 316L austenitic stainless steel by means of surface mechanical rolling treatment (SMRT) with temperature being controlled. The mean grain size...
This study examines the bending of cross-ply laminated composite nanoplates coupled to a piezoelectric fiber-reinforced composite layer via the nonlocal strain gradient theory. The aim is to accurately capture size-dependent impacts and electromechan...
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 provides an overview of various size-dependent theories based on modified/consistent couple stress and strain gradient theories (CSTs and SGTs), highlighting the development of two-dimensional (2D) refined and advanced shear deformation th...
Two methods for the determination of geometrically necessary dislocation (GND) densities are implemented in a lower-order strain-gradient crystal plasticity finite element model. The equations are implemented in user material (UMAT) subroutines. Meth...
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 aim of the paper is the development of a third-order theory for laminated composite plates that is able to accurately investigate their bending behavior in terms of displacements and stresses. The starting point is given by the corresponding Redd...
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...
In this context, the nonlinear bending investigation of a sector nanoplate on the elastic foundation is carried out with the aid of the nonlocal strain gradient theory. The governing relations of the graphene plate are derived based on the higher-ord...
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...
With the rapid development of society, the number of hydropower projects has increased. During the construction of these projects, due to excavation-induced unloading, the high sidewalls of the hydropower station are often subject to splitting failur...
Stress corrosion cracking (SCC) is an important destruction form of materials such as stainless steel, nickel-based alloy and their welded components in nuclear reactor pressure vessels and pipes. The existing popular quantitative prediction models o...
This research investigates the stabilization and control of an uncertain Euler–Bernoulli nano-beam with fixed ends. The governing partial differential equations of motion for the nano-beam are derived using Hamilton’s principle and the no...
A strain gradient was produced in an AZ31B magnesium alloy through a plastic deformation of pure torsion at a torsional speed of π/2 per second. Compared with the base material and with the alloy processed by conventional severe plastic deformatio...
Background: Atherosclerotic plaque detection is a clinical and technological problem that has been approached by different studies. Nowadays, intravascular ultrasound (IVUS) is the standard used to capture images of the coronary walls and to detect p...
This paper discusses how the strain gradient influences the fatigue life of carbon steel in the low-cycle and high-cycle fatigue regimes. To obtain fatigue data under different strain distributions, cyclic alternating bending tests using specimens wi...
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...
The trimodal grain-structured (TGS) carbon nanotube-reinforced aluminum matrix composites (CNT/Al) exhibit better strength–ductility synergy compared to bimodal grain-structured (BGS) composites. The addition of fine grain (FG) to the TGS compo...
Rock-like brittle materials under dynamic load will show more complex dynamic mechanical properties than those under static load. The relationship between pulse waveform characteristics and strain rate effect and inertia effect is rarely discussed in...
In this work, commercial AISI 304 stainless steel rods were subjected to cyclic forward/reverse torsion (CFRT) treatments at low-speed and high-speed torsion at room temperature. Microstructures in the core and surface layers of the CFRT-treated samp...
This study investigates the nanomechanical and tribological behavior of multilayered nitride/carbonitride nanostructured superlattice type coatings (NTCs) composed of alternating TiAlSiNb-N and TiCr-CN sublayers, deposited via high-power ion-plasma m...
The fractional change in the reaction progress variable gradient depends on the flow normal straining within the flame and also upon the corresponding normal gradients of the reaction rate and its molecular diffusion transport. The statistical behavi...
To improve the structural stiffness, strength and reduce the weight of nanoplate structure, functionally graded (FG) graphene-reinforced nanocomposite (GRNC) laminated plates are exploited in this paper. The bending and buckling behaviors of FG-GRNC...
One ambitious objective of Integrated Computational Materials Engineering (ICME) is to shorten the materials development cycle by using computational materials simulation techniques at different length scales. In this regard, the most important aspec...
Extensive experiments have shown that gradient nano-grained metals have outstanding synergy of strength and ductility. However, the deformation mechanisms of gradient metals are still not fully understood due to their complicated gradient microstruct...
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