A review of size-dependent continuum mechanics models for micro- and nano-structures

Roudbari, Mir Abbas; Jorshari, Tahereh Doroudgar; Li, Chaofeng; Ansari, R.; Kouzani, Abbas Z.; Amabili, Marco

doi:10.1016/j.tws.2021.108562

Cited by 101 publications

(24 citation statements)

References 483 publications

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“…The powder is assumed to be a “compressible continuum”; hence, continuum mechanics theory is applied. 91,92 The classic von Mises yield criterion is expressed as follows:…”

Section: Power Molding Theoriesmentioning

confidence: 99%

Polymer-based graphene composite molding: a review

Gao

Wang³

et al. 2023

RSC Adv.

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“…The powder is assumed to be a “compressible continuum”; hence, continuum mechanics theory is applied. 91,92 The classic von Mises yield criterion is expressed as follows:…”

Section: Power Molding Theoriesmentioning

confidence: 99%

Polymer-based graphene composite molding: a review

Gao

Wang³

et al. 2023

RSC Adv.

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“…According to nonlocal model previously proposed by Eringen [8,11,[40][41][42], we have the nonlocal constitutive equations for elasticity and heat conduction as follows:…”

Section: The Establishment and Setting Of Model Problemsmentioning

confidence: 99%

The analysis and computation on nonlocal thermoelastic problems of blend composites via enriched second-order multi-scale computational method

Dong

Nie

et al. 2022

Mathematics and Mechanics of Solids

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This paper proposes an innovative enriched second-order multi-scale (SOMS) computational method to simulate and analyze the nonlocal thermoelastic problems of blend composites with stress and heat flux gradient behaviors. The multiple periodical heterogeneities and periodic configurations of investigated blend composites in different substructures result in a huge computational cost for direct numerical simulations. The significant characteristics of this study are as follows. (1) The nonlocal properties of blend composites in constitutive equations are converted into the source terms of thermoelastic balance equations. The novel macro-micro coupled SOMS computational model for these transformed nonlocal multi-scale problems is derived on the basis of multi-scale asymptotic analysis. The nonlocal thermoelastic behaviors of blend composites can be merely uncovered in the enriched SOMS solutions. (2) The error analysis in the pointwise sense is presented to elucidate the importance and necessity of establishing the enriched SOMS solutions. Furthermore, an explicit error estimate for the SOMS approximate solutions is obtained in the integral sense for these nonlocal multi-scale problems. (3) A multi-scale numerical algorithm is presented to effectively simulate nonlocal thermoelastic problems of blend composites based on finite element method (FEM). Finally, the capability of the proposed enriched SOMS computational method is demonstrated by typical two-dimensional (2D) and three-dimensional (3D) blend composites, presenting not only the excellent numerical accuracy but also the less computational cost. This work proposes a unified multi-scale computational framework for enabling nonlocal thermoelastic behavior analysis of blend composites.

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“…There are several interesting papers in the literature pertinent to the review of micro/nano-structures [63][64][65][66][67]. It is significant to mention that the investigation of the important outcomes pertinent to the influences of the nonlocal-stress gradient size-dependent methods on various micro/nano-structures is the main motivation of this study as well as the major difference between the current review and published papers.…”

Section: Researchersmentioning

confidence: 99%

A Review on the Mechanical Behavior of Size-Dependent Beams and Plates using the Nonlocal Strain-Gradient Model

Jorshari

Roudbari

2021

J. Basic Appl. Sci.

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Nowadays, the mechanical characteristics of micro-/nano-structures in the various types of engineering disciplines are considered as remarkable criteria which may restrict the performance of small-scale structures in the reality for a certain application. This paper deals with a comprehensive review pertinent to using the nonlocal strain-gradient continuum mechanics model of size-dependent micro-/nano-beams/-plates. According to the non-classical features of materials, using size-dependent continuum mechanics theories is mandatory to investigate accurately the mechanical characteristics of the micro-/nano-structures. Recently, the number of researches related to the analysis of micro-/nano-structures with various geometry including beams as well as plates is considerable. In this regard, the mechanical behavior of these structures induced by different loadings such as vibration, wave propagation, and buckling behavior associated with the nonlocal strain-gradient continuum mechanics model is presented in this review work. Proposing the most valuable literature pertinent to the nonlocal strain-gradient continuum mechanics theory of micro-/nano-beams/plates is the main objective of this detailed survey.

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A review of size-dependent continuum mechanics models for micro- and nano-structures

Cited by 101 publications

References 483 publications

Polymer-based graphene composite molding: a review

Polymer-based graphene composite molding: a review

The analysis and computation on nonlocal thermoelastic problems of blend composites via enriched second-order multi-scale computational method

A Review on the Mechanical Behavior of Size-Dependent Beams and Plates using the Nonlocal Strain-Gradient Model

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