Stress-driven integral elastic theory for torsion of nano-beams

Barretta, Raffaele; Diaco, Marina; Feo, Luciano; Sciarra, Francesco Marotti de; Penna, Rosa

doi:10.1016/j.mechrescom.2017.11.004

Cited by 83 publications

(26 citation statements)

References 32 publications

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“…with the dot into the integral denoting the inner product between vectors. c Î Â writes as [28] ( ) ( ) ( )…”

Section: Modified Nonlocal Strain Gradient Law For Torsionmentioning

confidence: 99%

“…The stress-driven nonlocal integral model, conceived for nano-beams in [37] and recently extended to axisymmetric nano-plates in [38], yields instead a mathematically well-posed and effective nonlocal approach in structural applications of nanotechnology. Pure and two-phase stress-driven nonlocal elasticities have been applied in a series of papers to study elastostatic responses [28,29,[39][40][41][42][43], free vibrations [44][45][46][47][48] and stability of nano-beams [49].…”

Section: Introductionmentioning

confidence: 99%

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Nonlocal strain gradient torsion of elastic beams: variational formulation and constitutive boundary conditions

et al. 2019

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Nonlocal strain gradient continuum mechanics is a methodology widely employed in literature to assess size effects in nanostructures. Notwithstanding this, improper higher-order boundary conditions (HOBC) are prescribed to close the corresponding elastostatic problems.In the present study, it is proven that HOBC have to be replaced with univocally determined boundary conditions of constitutive type, established by a consistent variational formulation.The treatment, developed in the framework of torsion of elastic beams, provides an effective approach to evaluate scale phenomena in smaller and smaller devices of engineering interest.Both elastostatic torsional responses and torsional free vibrations of nano-beams are investigated by applying a simple analytical method. It is also underlined that the nonlocal strain gradient model, if equipped with the inappropriate HOBC, can lead to torsional structural responses which unacceptably do not exhibit nonlocality. The presented variational strategy is instead able to characterize significantly peculiar softening and stiffening behaviours of structures involved in modern Nano-Electro-Mechanical-Systems (NEMS). KeywordsTorsion; nano-beams; nonlocal strain gradient model; strain gradient elasticity; integral elasticity; size effects; analytical modelling; NEMS. d J J dx J J dx J

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“…with the dot into the integral denoting the inner product between vectors. c Î Â writes as [28] ( ) ( ) ( )…”

Section: Modified Nonlocal Strain Gradient Law For Torsionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlocal strain gradient torsion of elastic beams: variational formulation and constitutive boundary conditions

et al. 2019

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“…But the effect of crystallinity was not mentioned in the research. On the other hand, modelling work based on continuum phase modelling was developed [36][37][38][39][40][41] and applied to related nanocomposite system [42]. However, as restricted by modelling methodology, the detailed information about polymer/CNT interface was not clear.…”

Section: Introductionmentioning

confidence: 99%

A computer simulation of stress transfer in carbon nanotube/polymer nanocomposites

Zhao

Song

2019

Composites Part B: Engineering

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The reinforcing efficiency or stress transfer of carbon nanotubes (CNT) on polymers in polymer/CNT composites mainly is controlled by the polymer-CNT interface. Enhancement of polymer-CNT interactions and interfacial crystallisation is as an important way for improvement of the reinforcement experimentally. However, it is not clear about the crystallisation and orientation of polymer chains on the CNT surface, and how the interfacial crystallisation layer affects the failure of the composite. In this work, poly(vinyl alcohol)/CNT nanocomposites was selected as an example and based on the molecular dynamics simulation, the crystallisation process, failure behaviour and stress transfer in poly(vinyl alcohol)/CNT nanocomposites were analysed. The crystallisation temperature of the polymer chains on the CNT surface is slightly higher than the bulk crystallisation temperature. CNT induced crystallisation can be divided into three stages: chain folding, orientating and growing on the CNT surface. A slower crack growth was observed in the interfacial crystallised polymer/CNT systems, compare to relative amorphous systems. The effect of the interfacial crystalline layer on stress transfer is similar as enhanced polymer-CNT interaction systems. The change of the polymer-CNT surficial energy to strain has been used to analyse the interfacial failure and the stress transfer.

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“…Generally, elaborate mathematical techniques make the integral nonlocal theories more difficult . Romano and Barretta, introduced the stress‐driven nonlocal integral model to study torsion of nanobeams, vibration of nanobeam and nanorods . In addition, the stress‐driven model was used in analysis of Euler‐Bernoulli nanobeams without taking the effect of chirality into account.…”

Section: Introductionmentioning

confidence: 99%

Doublet mechanical analysis of bending of Euler‐Bernoulli and Timoshenko nanobeams

2018

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By taking the effect of the scale parameter explicitly into account, bending behavior of Euler‐Bernoulli and Timoshenko nanobeams is studied using doublet mechanics. In addition, the effect of chirality on the softening or hardening behavior of an Euler‐Bernoulli nanobeam in bending is studied by taking the effect of the chiral angle explicitly into account. For the bending of the Timoshenko nanobeam the effect of the scale parameter and chirality on the axial and shear stresses is studied and the results are compared with the gradient and Eringen‐like models. It is shown that as the chiral angle increases, a simply supported Timoshenko nanobeam under a uniform loading changes from a softening to a hardening nanobeam indicating that chirality has a pronounced effect on the bending response of the nanobeams.

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Stress-driven integral elastic theory for torsion of nano-beams

Cited by 83 publications

References 32 publications

Nonlocal strain gradient torsion of elastic beams: variational formulation and constitutive boundary conditions

Nonlocal strain gradient torsion of elastic beams: variational formulation and constitutive boundary conditions

A computer simulation of stress transfer in carbon nanotube/polymer nanocomposites

Doublet mechanical analysis of bending of Euler‐Bernoulli and Timoshenko nanobeams

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