Couple stress based strain gradient theory for elasticity

Yang, Fan; Chong, Arthur C.M.; Lam, David Chuen Chun; Tong, Penger

doi:10.1016/s0020-7683(02)00152-x

Cited by 2,793 publications

(1,217 citation statements)

References 12 publications

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“…In this regards, the non-classical theories such as non-local elasticity (Eringen and Edelen 1972), couple stress theory (Kong, 2013;Ejike, 1969), strain gradient theory (Lam et al, 2003), modified couple stress theory (Yang et al, 2002) etc. have been developed to consider the size effect in theoretical continuum models.…”

Section: Using Various Approachesmentioning

confidence: 99%

Modeling the size dependent pull-in instability of beam-type NEMS using strain gradient theory

Koochi

Sedighi

Abadyan

2014

Lat. Am. j. solids struct.

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It is well recognized that size dependency of materials characteristics, i.e. size-effect, often plays a significant role in the performance of nano-structures. Herein, strain gradient continuum theory is employed to investigate the size dependent pull-in instability of beam-type nano-electromechanical systems (NEMS). Two most common types of NEMS i.e. nano-bridge and nano-cantilever are considered. Effects of electrostatic field and dispersion forces i.e. Casimir and van der Waals (vdW) attractions have been considered in the nonlinear governing equations of the systems. Two different solution methods including numerical and Rayleigh-Ritz have been employed to solve the constitutive differential equations of the system. Effect of dispersion forces, the size dependency and the importance of coupling between them on the instability performance are discussed.

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Section: Using Various Approachesmentioning

confidence: 99%

Modeling the size dependent pull-in instability of beam-type NEMS using strain gradient theory

Koochi

Sedighi

Abadyan

2014

Lat. Am. j. solids struct.

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“…Regardless of the details of specific formulation, it is common that non-local model introduces characteristic length (or time) which is inherent to the inner material structure. This new material parameter can be measured directly from experiment, determined from experiments via inverse analysis, or derived theoretically from micromechanics [11][12][13][14][15][16]. Nowadays there are many concepts dealing with non-local formulations, like general non-local theories [17,18], strain-gradient theories [2,19], micropolar theories [20,21] or theories of material surfaces [22].…”

Section: Introductionmentioning

confidence: 99%

Fractional calculus for continuum mechanics – anisotropic non-locality

Sumelka¹

2016

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. In this paper, a generalisation of previous author's formulation of fractional continuum mechanics for the case of anisotropic non-locality is presented. The discussion includes a review of competitive formulations available in literature. The overall concept is based on the fractional deformation gradient which is non-local due to fractional derivative definition. The main advantage of the proposed formulation is its structure, analogous to the general framework of classical continuum mechanics. In this sense, it allows to define similar physical and geometrical meaning of introduced objects. The theoretical discussion is illustrated by numerical examples assuming anisotropy limited to single direction. NotationSection 2and finallywhere] denotes the interval of non-local interaction, and Γ is the Euler gamma functionNext, based on non-standard definition of motion by Eq. (4) the authors define the deformation gradient F α aswhere e a and E A are base vectors in coordinate systems {x a } and {X A }, respectively.

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“…in which the components of the strain tensor, the dilatation gradient tensor, the deviatoric stretch gradient tensor, and the symmetric rotation gradient tensor are respectively represented by e ij , c i , g 1 ð Þ ijk , v s ij and can be defined as [27] e ij ¼ 1…”

Section: Modified Strain Gradient Theorymentioning

confidence: 99%

“…Utilizing the couple stress elasticity theory, some studies have been carried out different investigations in which size-dependent continuum beam models have been developed. [19][20][21][22][23][24][25][26] Later, Yang et al [27] introduced a newly established theory namely as modified couple stress theory in which the constitutive equations contain only one additional material length scale parameter. The simplified couple stress theory contains an additional equilibrium relation which causes to create symmetric couple stress tensor.…”

Section: Introductionmentioning

confidence: 99%

Size-Dependent Resonant Frequency and Flexural Sensitivity of Atomic Force Microscope Microcantilevers Based on the Modified Strain Gradient Theory

Ansari

Pourashraf

Gholami

et al. 2015

International Journal of Optomechatronics

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In the present study, the resonant frequency and flexural sensitivity of atomic force microscope (AFM) microcantilevers are predicted incorporating size effects. To this end, the modified strain gradient elasticity theory is applied to the classical Euler-Bernoulli beam theory to develop a non-classical beam model which has the capability to capture sizedependent behavior of microcantilevers. On the basis of Hamilton's principle, the sizedependent analytical expressions corresponding to the frequency response and sensitivity of AFM cantilevers are derived. It is observed that by increasing the contact stiffness, the resonant frequencies of AFM cantilevers firstly increase and then tend to remain constant at an especial value. Moreover, the resonant frequencies of AFM cantilevers obtained via the developed non-classical model is higher than those of the classical beam theory, especially for the values of beam thickness close to the internal material length scale parameter.

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Couple stress based strain gradient theory for elasticity

Cited by 2,793 publications

References 12 publications

Modeling the size dependent pull-in instability of beam-type NEMS using strain gradient theory

Modeling the size dependent pull-in instability of beam-type NEMS using strain gradient theory

Fractional calculus for continuum mechanics – anisotropic non-locality

Size-Dependent Resonant Frequency and Flexural Sensitivity of Atomic Force Microscope Microcantilevers Based on the Modified Strain Gradient Theory

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