Strain gradient theory of chiral Cosserat thermoelasticity without energy dissipation

Ieşan, D.; Quintanilla, R.

doi:10.1016/j.jmaa.2016.01.058

Cited by 11 publications

(4 citation statements)

References 48 publications

(43 reference statements)

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“…Recently, Iesan and Quintanilla [22] developed the strain gradient theory of thermoviscoelasticity. There are various applications of strain gradient theories in literature including Ahmadi and Firoozbakhsh [23], Aifantis ([24], [25]), Forest et al [26], Forest and Aifantis [27], Iesan and Quintanilla ( [28] and [29]). Aouadi et al [30] developed a consistent nonlinear theory of strain gradient theory for thermoelastic diffusion materials and derived the basic equation of nonlinear strain gradient theory of thermoelasticity with mass diffusion effect.…”

Section: Introductionmentioning

confidence: 99%

Plane waves in an isotropic thermoelastic diffusive material using strain gradient theory

Singh,

Singla

2023

J., eng., them. sci.

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The governing equations of motion for an isotropic strain-gradient thermoelastic material with diffusion are formulated in context of Lord and Shulman generalization of thermoelasticity and are further specialised for a two dimensional plane. Plane harmonic solution of the governing equations in two-dimension suggests the existence of five plane waves which include four coupled longitudinal waves and a shear vertical wave. A numerical example is considered to illustrate graphically the effect of frequency, measure constant of diffusion, measure constant of thermo-diffusion, thermal relaxation time, diffusive relaxation time and the coefficients of hyperstress tensor on the phase speed and attenuation coefficients of the plane waves.

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Section: Introductionmentioning

confidence: 99%

Plane waves in an isotropic thermoelastic diffusive material using strain gradient theory

Singh,

Singla

2023

J., eng., them. sci.

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“…Many studies dedicated to Cosserat bodies are published, of which we mention the following Refs. [21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

On weak solutions of boundary values problem in the theory of Cosserat porous bodies

2022

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In our study, we adapt certain basic results from the abstract theory of differential equations of the elliptic type with the purpose to deduce some basic results in the case of a concrete type of media. Namely, after the boundary values problem is formulated in the context of elasticity of Cosserat bodies with voids, some results on existence of a generalized solution and the uniqueness of this solution are proven.

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“…Eltaher et al [3] illustrated nonlinear static behavior of size-dependent and material-dependent nonlocal CNTs by using non-local differential form of Eringen and energy equivalent method. Iesan and Quintanilla [57] used the Green-Naghdi theory of thermomechanics of continua to derive a linear strain gradient theory of Cosserat thermoelastic bodies. Qin et al [58] designed and synthesized a Sn-core/CNT-shell nanocable anchored interconnected carbon networks structure via a simple CVD process.…”

Section: Introductionmentioning

confidence: 99%

Postbuckling of Curved Carbon Nanotubes Using Energy Equivalent Model

Eltaher

Mohamed

et al. 2019

JNanoR

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This paper presents a novel numerical procedure to predict nonlinear buckling and postbuckling stability of imperfect clamped–clamped single walled carbon nanotube (SWCNT) surrounded by nonlinear elastic foundation. Nanoscale effect of CNTs is included by using energy-equivalent model (EEM) which transferring the chemical energy between carbon atoms to mechanical strain energy. Young’s modulus and Poisson’s ratio for zigzag (n, 0), and armchair (n, n) carbon nanotubes (CNTs) are presented as functions of orientation and force constants by using energy-equivalent model (EEM). Nonlinear Euler-Bernoulli assumptions are proposed considering mid-plane stretching to exhibit a large deformation and a small strain. To simulate the interaction of CNTs with the surrounding elastic medium, nonlinear elastic foundation with cubic nonlinearity and shearing layer are employed. The governing nonlinear integro-partial-differential equations are derived in terms of only the lateral displacement. The modified differential quadrature method (DQM) is exploited to obtain numerical results of the nonlinear governing equations. The static problem is solved for critical buckling loads and the postbuckling deformation as a function of applied axial load, curved amplitude, CNT length, and orientations. Numerical results show that the effects of chirality angle and curved amplitude on static response of armchair and zigzag CNTs are significant. This model is helpful especially in mechanical design of NEMS manufactured from CNTs.

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Strain gradient theory of chiral Cosserat thermoelasticity without energy dissipation

Cited by 11 publications

References 48 publications

Plane waves in an isotropic thermoelastic diffusive material using strain gradient theory

Plane waves in an isotropic thermoelastic diffusive material using strain gradient theory

On weak solutions of boundary values problem in the theory of Cosserat porous bodies

Postbuckling of Curved Carbon Nanotubes Using Energy Equivalent Model

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