Special Issue "Time and Space Nonlocal Operators in Structural Mechanics"

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Computer and Engineering Science and Symmetry".

Deadline for manuscript submissions: 31 May 2021.

Special Issue Editors

Prof. Dr. Raffaele Barretta
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Guest Editor
Department of Structures for Engineering and Architecture, University of Naples Federico II, Via Claudio 21 - 80125 Naples, Italy
Interests: solid and structural mechanics; advanced materials; nonlocal constitutive models; functionally graded materials; generalized continua; nanostructures and nanocomposites; MEMS and NEMS
Special Issues and Collections in MDPI journals
Dr. Francesco Paolo Pinnola
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Guest Editor
Department of Structures for Engineering and Architecture, University of Naples Federico II, Via Claudio 21 - 80125 Naples, Italy

Special Issue Information

Dear Colleagues,

This Special Issue aims to collect advanced developments in the application of nonlocal operators to various engineering and physics problems with special regard to structural mechanics. The authors could contribute to expanding the knowledge about structural modeling by advanced mathematical operators. The manuscripts could consider time-dependent mechanical behaviors, nonlocal elasticity, size effects, peridynamics, and all those problems in which nonlocal operators can be used. Contributions in physics, materials science, solids mechanics, biomechanics, dynamics of structures, nanomechanics, diffusion or transport problems are particularly encouraged. Authors may discuss theoretical aspects, computational methods, modeling techniques, interpretation of experimental data, and simulation issues. All papers providing an interesting improvement of the application of nonlocal operators in engineering problems will be welcome. Suggested topics: • statics and dynamics of systems ruled by nonlocal operators; • constitutive laws of advanced materials; • linear and nonlinear viscoelasticity; • nonlocal elasticity; • micro- and nanomechanics; • strain gradient formulations; • multiscale phenomena in physics; • mechanics of composites and laminated materials; • size effects and stress/strain localization; • long range interactions; • fractional calculus in mechanics.

Prof. Raffaele Barretta
Dr. Francesco Paolo Pinnola
Guest Editors

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • viscoelasticity and hereditariness
  • nonlocal elasticity
  • constitutive laws
  • size effects
  • mechanical models

Published Papers (7 papers)

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Research

Open AccessArticle
Effect of Axial Porosities on Flexomagnetic Response of In-Plane Compressed Piezomagnetic Nanobeams
Symmetry 2020, 12(12), 1935; https://doi.org/10.3390/sym12121935 - 24 Nov 2020
Cited by 6 | Viewed by 608
Abstract
We investigated the stability of an axially loaded Euler–Bernoulli porous nanobeam considering the flexomagnetic material properties. The flexomagneticity relates to the magnetization with strain gradients. Here we assume both piezomagnetic and flexomagnetic phenomena are coupled simultaneously with elastic relations in an inverse magnetization. [...] Read more.
We investigated the stability of an axially loaded Euler–Bernoulli porous nanobeam considering the flexomagnetic material properties. The flexomagneticity relates to the magnetization with strain gradients. Here we assume both piezomagnetic and flexomagnetic phenomena are coupled simultaneously with elastic relations in an inverse magnetization. Similar to flexoelectricity, the flexomagneticity is a size-dependent property. Therefore, its effect is more pronounced at small scales. We merge the stability equation with a nonlocal model of the strain gradient elasticity. The Navier sinusoidal transverse deflection is employed to attain the critical buckling load. Furthermore, different types of axial symmetric and asymmetric porosity distributions are studied. It was revealed that regardless of the high magnetic field, one can realize the flexomagnetic effect at a small scale. We demonstrate as well that for the larger thicknesses a difference between responses of piezomagnetic and piezo-flexomagnetic nanobeams would not be significant. Full article
(This article belongs to the Special Issue Time and Space Nonlocal Operators in Structural Mechanics)
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Open AccessArticle
Dynamics of Nonlocal Rod by Means of Fractional Laplacian
Symmetry 2020, 12(12), 1933; https://doi.org/10.3390/sym12121933 - 24 Nov 2020
Viewed by 317
Abstract
The use of fractional models to analyse nonlocal behaviour of solids has acquired great importance in recent years. The aim of this paper is to propose a model that uses the fractional Laplacian in order to obtain the equation ruling the dynamics of [...] Read more.
The use of fractional models to analyse nonlocal behaviour of solids has acquired great importance in recent years. The aim of this paper is to propose a model that uses the fractional Laplacian in order to obtain the equation ruling the dynamics of nonlocal rods. The solution is found by means of numerical techniques with a discretisation in the space domain. At first, the proposed model is compared to a model that uses Eringen’s classical approach to derive the differential equation ruling the problem, showing how the parameters used in the proposed fractional model can be estimated. Moreover, the physical meaning of the model parameters is assessed. The model is then extended in dynamics by means of a discretisation in the time domain using Newmark’s method, and the responses to different dynamic conditions, such as an external load varying with time and free vibrations due to an initial deformation, are estimated, showing the difference of behaviour between the local response and the nonlocal response. The obtained results show that the proposed model can be used efficiently to estimate the response of the nonlocal rod both to static and dynamic loads. Full article
(This article belongs to the Special Issue Time and Space Nonlocal Operators in Structural Mechanics)
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Open AccessArticle
Propagation of Flexural Waves in Anisotropic Fluid-Conveying Cylindrical Shells
Symmetry 2020, 12(6), 901; https://doi.org/10.3390/sym12060901 - 01 Jun 2020
Cited by 1 | Viewed by 541
Abstract
In the present article, first-order shear deformation theory (FSDT) of the shell has been employed, for the first time, in order to analyze the propagation of the flexural waves in anisotropic fluid-conveying cylindrical shells. Four various anisotropic materials are utilized and their wave [...] Read more.
In the present article, first-order shear deformation theory (FSDT) of the shell has been employed, for the first time, in order to analyze the propagation of the flexural waves in anisotropic fluid-conveying cylindrical shells. Four various anisotropic materials are utilized and their wave propagation behavior surveyed. Viscous fluid flow has been regarded to be laminar, fully developed, Newtonian, and axially symmetric. The Navier–Stokes equation can be utilized to explore the flow velocity effect. FSDT of the shell and Hamilton’s principle have been employed in order to achieve governing equations of anisotropic fluid-conveying cylindrical shells and finally, the obtained governing equations have been solved via an analytical method. In addition, the influences of different variables such as flow velocity, radius to thickness ratio, and longitudinal and circumferential wave numbers have been investigated and indicated within the framework of a detailed set of figures. Full article
(This article belongs to the Special Issue Time and Space Nonlocal Operators in Structural Mechanics)
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Open AccessArticle
Nonlocal Mechanical Behavior of Layered Nanobeams
Symmetry 2020, 12(5), 717; https://doi.org/10.3390/sym12050717 - 02 May 2020
Cited by 4 | Viewed by 595
Abstract
The research at hand deals with the mechanical behavior of beam-like nanostructures. Nanobeams are assembled of multiple layers of different materials and geometry giving a layered nanobeam. To properly address experimentally noticed size effects in structures of this type, an adequate nonlocal elasticity [...] Read more.
The research at hand deals with the mechanical behavior of beam-like nanostructures. Nanobeams are assembled of multiple layers of different materials and geometry giving a layered nanobeam. To properly address experimentally noticed size effects in structures of this type, an adequate nonlocal elasticity formulation must be applied. The present model relies on the stress-driven integral methodology that effectively circumvents known deficiencies of other approaches. As a main contribution, a set of differential equations and boundary conditions governing the underlaying mechanics is proposed and applied to two benchmark examples. The obtained results show the expected stiffening nonlocal behavior exhibiting most of smaller and smaller structures and modern devices. Full article
(This article belongs to the Special Issue Time and Space Nonlocal Operators in Structural Mechanics)
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Open AccessArticle
Exact Mechanical Hierarchy of Non-Linear Fractional-Order Hereditariness
Symmetry 2020, 12(4), 673; https://doi.org/10.3390/sym12040673 - 23 Apr 2020
Cited by 1 | Viewed by 555
Abstract
Non-local time evolution of material stress/strain is often referred to as material hereditariness. In this paper, the widely used non-linear approach to single integral time non-local mechanics named quasi-linear approach is proposed in the context of fractional differential calculus. The non-linear model of [...] Read more.
Non-local time evolution of material stress/strain is often referred to as material hereditariness. In this paper, the widely used non-linear approach to single integral time non-local mechanics named quasi-linear approach is proposed in the context of fractional differential calculus. The non-linear model of the springpot is defined in terms of a single integral with separable kernel endowed with a non-linear transform of the state variable that allows for the use of Boltzmann superposition. The model represents a self-similar hierarchy that allows for a time-invariance as the result of the application of the conservation laws at any resolution scale. It is shown that the non-linear springpot possess an equivalent mechanical hierarchy in terms of a functionally-graded elastic column resting on viscous dashpots with power-law decay of the material properties. Some numerical applications are reported to show the capabilities of the proposed model. Full article
(This article belongs to the Special Issue Time and Space Nonlocal Operators in Structural Mechanics)
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Open AccessArticle
Nonlocal Elasticity Response of Doubly-Curved Nanoshells
Symmetry 2020, 12(3), 466; https://doi.org/10.3390/sym12030466 - 16 Mar 2020
Cited by 10 | Viewed by 763
Abstract
In this paper, we focus on the bending behavior of isotropic doubly-curved nanoshells based on a high-order shear deformation theory, whose shape functions are selected as an accurate combination of exponential and trigonometric functions instead of the classical polynomial functions. The small-scale effect [...] Read more.
In this paper, we focus on the bending behavior of isotropic doubly-curved nanoshells based on a high-order shear deformation theory, whose shape functions are selected as an accurate combination of exponential and trigonometric functions instead of the classical polynomial functions. The small-scale effect of the nanostructure is modeled according to the differential law consequent, but is not equivalent to the strain-driven nonlocal integral theory of elasticity equipped with Helmholtz’s averaging kernel. The governing equations of the problem are obtained from the Hamilton’s principle, whereas the Navier’s series are proposed for a closed form solution of the structural problem involving simply-supported nanostructures. The work provides a unified framework for the bending study of both thin and thick symmetric doubly-curved shallow and deep nanoshells, while investigating spherical and cylindrical panels subjected to a point or a sinusoidal loading condition. The effect of several parameters, such as the nonlocal parameter, as well as the mechanical and geometrical properties, is investigated on the bending deflection of isotropic doubly-curved shallow and deep nanoshells. The numerical results from our investigation could be considered as valid benchmarks in the literature for possible further analyses of doubly-curved applications in nanotechnology. Full article
(This article belongs to the Special Issue Time and Space Nonlocal Operators in Structural Mechanics)
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Open AccessArticle
Material Symmetries in Homogenized Hexagonal-Shaped Composites as Cosserat Continua
Symmetry 2020, 12(3), 441; https://doi.org/10.3390/sym12030441 - 10 Mar 2020
Cited by 6 | Viewed by 1125
Abstract
In this work, material symmetries in homogenized composites are analyzed. Composite materials are described as materials made of rigid particles and elastic interfaces. Rigid particles of arbitrary hexagonal shape are considered and their geometry described by a limited set of parameters. The purpose [...] Read more.
In this work, material symmetries in homogenized composites are analyzed. Composite materials are described as materials made of rigid particles and elastic interfaces. Rigid particles of arbitrary hexagonal shape are considered and their geometry described by a limited set of parameters. The purpose of this study is to analyze different geometrical configurations of the assemblies corresponding to various material symmetries such as orthotetragonal, auxetic and chiral. The problem is investigated through a homogenization technique which is able to carry out constitutive parameters using a principle of energetic equivalence. The constitutive law of the homogenized continuum has been derived within the framework of Cosserat elasticity, wherein the continuum has additional degrees of freedom with respect to classical elasticity. A panel composed of material with various symmetries, corresponding to some particular hexagonal geometries defined, is analyzed under the effect of localized loads. The results obtained show the difference of the micropolar response for the considered material symmetries, which depends on the non-symmetries of the strain and stress tensor as well as on the additional kinematical and work-conjugated statical descriptors. This work underlines the importance of resorting to the Cosserat theory when analyzing anisotropic materials. Full article
(This article belongs to the Special Issue Time and Space Nonlocal Operators in Structural Mechanics)
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