Review on nonlocal continuum mechanics: Physics, material applicability, and mathematics

Shaat, Mohamed; Ghavanloo, Esmaeal; Fazelzadeh, S. Ahmad

doi:10.1016/j.mechmat.2020.103587

Cited by 69 publications

(22 citation statements)

References 260 publications

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“…In that case, the inhomogeneous response is triggered by the boundary conditions for the additional kinematic fields which are applied at the upper and lower surface. We refer the reader to the introduction of [25,27,28,32] concerning the relevance of the scientific question as well as its importance for the determination of material parameters for generalized continua [33]. Indeed, the obtained analytical formulas can be used to determine size-dependent and size-independent material parameters.…”

Section: Introductionmentioning

confidence: 99%

Analytical solution of the uniaxial extension problem for the relaxed micromorphic continuum and other generalized continua (including full derivations)

et al. 2021

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Section: Introductionmentioning

confidence: 99%

Analytical solution of the uniaxial extension problem for the relaxed micromorphic continuum and other generalized continua (including full derivations)

et al. 2021

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“…Several models were proposed to overcome difficulties related to the adoption of classical local models, generally due to the inability of retaining memory of the internal-length scale [20,21]. This was done by introducing non-simple explicit or implicit non-local models [22,23,13,24], which allow one to avoid ill-posed field-equations and mesh dependence in the numerical solutions. Within this framework, various approaches have been presented concerning higher-order models or second gradient models (Mindlin-Toupin type) [25,26,27,28,29,30,31], or also micromorphic continua [23], and in particular, micropolar continua [32], which can be considered non-local models of implicit type [33,34,14,35,36,37,38,39,40,41].…”

Section: Introductionmentioning

confidence: 99%

A multifield continuum model for the description of the response of microporous/microcracked composite materials

Pau

Trovalusci

2021

Mechanics of Materials

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The description of the mechanical behavior of composite materials is an open challenge in engineering. The focus of this work is on micro-cracked/microporous composites, made of stiff grains embedded in a cracked or porous deformable matrix. Grains interact between each other and with cracks or pores localized at the interfaces, which reduce the contact area between grains. Pores' interaction is also taken into account. We apply a two-scale modeling strategy based on a discrete to scale-dependent (non-classical) continuum equivalence procedure. The constitutive relationships of the resulting microcontinuum, identified by requiring equivalence, in terms of virtual work, between discrete and continuum non-local descriptions of the reference material, take directly into account the material internal structure, and in particular material internal lengths. Field and boundary conditions of the equivalent continuum are also derived based on work equivalence between internal and external actions. The response of the obtained one-dimensional equivalent model and of a finite element model of a bar with pores are compared, showing a very good match between each other in a wide range of pore densities.

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“…In addition to those landmark studies cited in up to this point, the interested readers are kindly referred to [21,22] for relatively recent applications of Eringen's two-phase model, [23][24][25][26][27] for different approaches to the modelling of nanobars, and a review paper [28] for a better insight on classification, limitations, and mathematical aspects of nonlocal continuum models.…”

Section: Introductionmentioning

confidence: 99%

Some New Approximate Solutions in Closed-Form to Problems of Nanobars

Eroğlu

2021

European Mechanical Science

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Following recent technological advancements, a great attention has been paid to the mechanical behaviour of structural elements of nanosize. In this study, some solutions to mechanical problems of bars of nanosize are examined using Eringen's two-phase nonlocal elasticity. Assuming the fraction coefficient of nonlocal part of the material is small, a perturbation expansion with respect to it is performed. With this procedure, the original nonlocal problem is broken into a set of local elasticity problems. Solutions to some example problems of nanobars are provided in closed-form for the first time, and commented on. The new solutions provided herein may well serve for benchmark studies, as well as identification of material parameters of nano-sized structural elements, such as carbon nanotubes.

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Review on nonlocal continuum mechanics: Physics, material applicability, and mathematics

Cited by 69 publications

References 260 publications

Analytical solution of the uniaxial extension problem for the relaxed micromorphic continuum and other generalized continua (including full derivations)

Analytical solution of the uniaxial extension problem for the relaxed micromorphic continuum and other generalized continua (including full derivations)

A multifield continuum model for the description of the response of microporous/microcracked composite materials

Some New Approximate Solutions in Closed-Form to Problems of Nanobars

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