• Structural Engineering and Mechanics
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• v.61 no.2
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• pp.275-282
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• 2017

The Fleck-Hutchinson theory on strain gradient plasticity (SGP), proposed in Adv. Appl Mech 33 (1997) 295, has recently been reformulated by adopting the strategy of decomposing the second order strain presented by Lam et al. in J Mech Pays Solids 51 (2003) 1477. The newly built SGP satisfies the non negativity of plastic dissipation, which is still an outstanding issue in other SGP theories. Furthermore, it explicitly shows how elastic strain gradients and corresponding elastic characteristic length scales come into play in general elastic-plastic loading histories. In this study, the relation between elastic length scales and plastic length scales is investigated by taking wire torsion as an example. It is concluded that the size effects arising when two sets of length scales are of the same order are essentially elastic instead of plastic.

• Structural Engineering and Mechanics
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• v.65 no.6
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• pp.645-656
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• 2018

Importance of procuring adequate knowledge about the mechanical behavior of double-layered graphene sheets (DLGSs) incensed the authors to investigate wave propagation responses of mentioned element while rested on a visco-Pasternak medium under hygro-thermal loading. A nonlocal strain gradient theory (NSGT) is exploited to present a more reliable size-dependent mechanical analysis by capturing both softening and hardening effects of small scale. Furthermore, in the framework of a classical plate theory the kinematic relations are developed. Incorporating kinematic relations with the definition of Hamilton's principle, the Euler-Lagrange equations of each of the layers are derived separately. Afterwards, combining Euler-Lagrange equations with those of the NSGT the nonlocal governing equations are written in terms of displacement fields. Interaction of the each of the graphene sheets with another one is regarded by the means of vdW model. Then, a widespread analytical solution is employed to solve the derived equations and obtain wave frequency values. Subsequently, influence of each participant variable containing nonlocal parameter, length scale parameter, foundation parameters, temperature gradient and moisture concentration is studied by plotting various figures.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.185-192
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• 2000

A novel indentation theory is proposed by examining the data from the incremental plasticity theory based finite element analyses. First the optimal data acquisition location is selected, where the strain gradient is the least and the effect of friction is negligible. This data acquisition point increases the strain range by a factor of five. Numerical regressions of obtained data exhibit that strain hardening exponent and yield strain are the two main parameters which govern the subindenter deformation characteristics. The new indentation theory successfully provides the stress-strain curve with an average error less than 3%.

• Korean Journal of Materials Research
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• v.33 no.2
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• pp.54-62
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• 2023

The most comprehensive and particularly reliable method for non-destructively measuring the residual stress of the surface layer of metals is the sin²ψ method. When X-rays were used the relationship of ε_φψ-sin²ψ measured on the surface layer of the processing metal did not show linearity when the sin²ψ method was used. In this case, since the effective penetration depth changes according to the changing direction of the incident X-ray, σ_φ becomes a sin²ψ function. Since σ_φ cannot be used as a constant, the relationship in ε_φψ-sin²ψ cannot be linear. Therefore, in this paper, the orthogonal function method according to Warren's diffraction theory and the basic profile of normal distribution were synthesized, and the X-ray diffraction profile was calculated and reviewed when there was a linear strain (stress) gradient on the surface. When there is a strain gradient, the X-ray diffraction profile becomes asymmetric, and as a result, the peak position, the position of half-maximum, and the centroid position show different values. The difference between the peak position and the centroid position appeared more clearly as the strain (stress) gradient became larger, and the basic profile width was smaller. The weighted average strain enables stress analysis when there is a strain (stress) gradient, based on the strain value corresponding to the centroid position of the diffracted X-rays. At the 1/5 I_max max height of X-ray diffraction, the position where the diffracted X-ray is divided into two by drawing a straight line parallel to the background, corresponds approximately to the centroid position.

• Steel and Composite Structures
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• v.25 no.3
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• pp.361-374
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• 2017

In this study, the influences of triaxial magnetic field on the wave propagation behavior of anisotropic nanoplates are studied. In order to include small scale effects, nonlocal strain gradient theory has been implemented. To study the nanoplate as a continuum model, the three-dimensional elasticity theory is adopted in Cartesian coordinate. In our study, all the elastic constants are considered and assumed to be the functions of (x, y, z), so all kind of anisotropic structures such as hexagonal and trigonal materials can be modeled, too. Moreover, all types of functionally graded structures can be investigated. eigenvalue method is employed and analytical solutions for the wave propagation are obtained. To justify our methodology, our results for the wave propagation of isotropic nanoplates are compared with the results available in the literature and great agreement is achieved. Five different types of anisotropic structures are investigated in present paper and then the influences of wave number, material properties, nonlocal and gradient parameter and uniaxial, biaxial and triaxial magnetic field on the wave propagation analysis of anisotropic nanoplates are presented. From the best knowledge of authors, it is the first time that three-dimensional elasticity theory and nonlocal strain gradient theory are used together with no approximation to derive the governing equations. Moreover, up to now, the effects of triaxial magnetic field have not been studied with considering size effects in nanoplates. According to the lack of any common approximations in the displacement field or in elastic constant, present theory has the potential to be used as a bench mark for future works.

• Advances in nano research
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• v.12 no.6
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• pp.617-627
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• 2022

In the current study, the nonlinear impact of the Von-Kármán theory on the vibrational response of nonhomogeneous structures of functionally graded (FG) nano-scale tubes is investigated according to the nonlocal theory of strain gradient theory as well as high-order Reddy beam theory. The inhomogeneous distributions of temperature-dependent material consist of ceramic and metal phases in the radial direction of the tube structure, in which the thermal stresses are applied due to the temperature change in the thickness of the pipe structure. The general motion equations are derived based on the Hamilton principle, and eventually, the acquired equations are solved and modeled by the Meshless approach as well as a computer simulation via intelligent mathematical methodology. The attained results are helpful to dissect the stability of the MEMS and NEMS.

• Advances in nano research
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• v.9 no.1
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• pp.33-45
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• 2020

Geometrically nonlinear buckling of functionally graded magneto-electro-elastic (FG-MEE) nanoshells with the use of classical shell theory and nonlocal strain gradient theory (NSGT) has been analyzed in present research. Mathematical formulation based on NSGT gives two scale coefficients for simultaneous description of structural stiffness reduction and increment. Functional gradation of material properties is described based on power-law formulation. The nanoshell is under a multi-physical field related to applied voltage, magnetic potential, and mechanical load. Exerting a strong electric voltage, magnetic potential or mechanical load may lead to buckling of nanoshell. Taking into account geometric nonlinearity effects after buckling, the behavior of nanoshell in post-buckling regime can be analyzed. Nonlinear governing equations are reduced to ordinary equations utilizing Galerkin's approach and post-buckling curves are obtained based on an analytical procedure. It will be shown that post-buckling curves are dependent on nonlocal/strain gradient parameters, electric voltage magnitude and sign, magnetic potential magnitude and sign and material gradation exponent.

• Structural Engineering and Mechanics
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• v.62 no.5
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• pp.551-565
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• 2017

Based on the strain gradient theory (SGT), vibration analysis of an embedded micro cylindrical shell reinforced with agglomerated carbon nanotubes (CNTs) is investigated. The elastic medium is simulated by the orthotropic Pasternak foundation. The structure is subjected to magnetic field in the axial direction. For obtaining the equivalent material properties of structure and considering agglomeration effects, the Mori-Tanaka model is applied. The motion equations are derived on the basis of Mindlin cylindrical shell theory, energy method and Hamilton's principal. Differential quadrature method (DQM) is proposed to evaluate the frequency of system for different boundary conditions. The effects of different parameters such as CNTs volume percent, agglomeration of CNTs, elastic medium, magnetic field, boundary conditions, length to radius ratio and small scale parameter are shown on the frequency of the structure. The results indicate that the effect of CNTs agglomeration plays an important role in the frequency of system so that considering agglomeration leads to lower frequency. Furthermore, the frequency of structure increases with enhancing the small scale parameter.

• Steel and Composite Structures
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• v.33 no.2
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• pp.261-275
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• 2019

The main objective of this paper is to study the axial buckling and post-buckling of geometrically imperfect single-layer graphene sheets (GSs) under in-plane loading in the theoretical framework of the nonlocal strain gradient theory. To begin with, a graphene sheet is modeled by a two-dimensional plate subjected to simply supported ends, and supposed to have a small initial curvature. Then according to the Hamilton's principle, the nonlinear governing equations are derived with the aid of the classical plate theory and the von-karman nonlinearity theory. Subsequently, for providing a more accurate physical assessment with respect to the influence of respective parameters on the mechanical performances, the approximate analytical solutions are acquired via using a two-step perturbation method. Finally, the authors perform a detailed parametric study based on the solutions, including geometric imperfection, nonlocal parameters, strain gradient parameters and wave mode numbers, and then reaching a significant conclusion that both the size-dependent effect and a geometrical imperfection can't be ignored in analyzing GSs.

• Steel and Composite Structures
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• v.43 no.6
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• pp.707-723
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• 2022

This article aims to investigate the size dependent bending behavior of perforated nanobeams incorporating the nonlocal and the microstructure effects based on the nonlocal strain gradient elasticity theory (NSGET). Shear deformation effect due to cutout process is studied by using Timoshenko beams theory. Closed formulas for the equivalent geometrical characteristics of regularly squared cutout shape are derived. The governing equations of motion considering the nonlocal and microstructure effects are derived in comprehensive procedure and nonclassical boundary conditions are presented. Analytical solution for the governing equations of motion is derived. The derived non-classical analytical solutions are verified by comparing the obtained results with the available results in the literature and good agreement is observed. Numerical results are obtained and discussed. Parametric studies are conducted to explore effects of perforation characteristics, the nonclassical material parameters, beam slenderness ratio as well as the boundary and loading conditions on the non-classical transverse bending behavior of cutout nanobeams. Results obtained are supportive for the design, analysis and manufacturing of such nanosized structural system.