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Symmetry
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Recent Advances in the Study of Symmetry and Continuum Mechanics...
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Recent Advances in the Study of Symmetry and Continuum Mechanics II

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (20 December 2022) | Viewed by 6403

Special Issue Editor

Dr. Victor A. Eremeyev

E-Mail Website
Guest Editor
Department of Civil and Environmental Engineering and Architecture (DICAAR), University of Cagliari, Via Marengo, 2, 09123 Cagliari, Italy
Interests: plates and shells; media with complex properties; surface elasticity; generalized continua
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

This Special Issue is the continuation of the previous one recently published in Symmetry with the same title (https://www.mdpi.com/journal/symmetry/special_issues/Continuum_Mechanics).

Symmetry plays an important role in continuum mechanics as it may represent the crucial properties of material behavior as well as properties of solutions of corresponding boundary-value problems. For example, variational symmetries results in appearance of new conservative laws in continuum mechanics and mechanics of structures.

The presented special issue is devoted to recent advances in continuum mechanics related to symmetries analysis. Among the topics of the issue are the following: 1) symmetry-based analysis of constitutive equations of complex materials including generalized media; 2) invariant properties of solutions of boundary-value problems; 3) variational symmetries and relative conservation laws followed from the Noether theorem; 4) anisotropic and composite materials and structures including metamaterials; 5) application of the local material symmetry group to formulation of reduced constitutive relations; 6) chirality in continuum mechanics; 7) any topics used the concept of symmetry in continuum mechanics.

Dr. Victor A. Eremeyev
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

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 2400 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

  • symmetry
  • generalized media
  • invariance
  • metamaterials
  • anisotropy
  • material symmetry group

Published Papers (3 papers)

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Research

11 pages, 2622 KiB  
Article
Symmetrization of Mechanical Response in Fibrous Metamaterials through Micro-Shear Deformability
by Mario Spagnuolo
Symmetry 2022, 14(12), 2660; https://doi.org/10.3390/sym14122660 - 16 Dec 2022
Cited by 4 | Viewed by 1077
Abstract
The basic concept of this study consists of the investigation of symmetrization of the mechanical response in extension and compression for fibrous metamaterials endowed with a symmetric microstructure relative to the axial direction. It is known that generally, this response is non-symmetric due [...] Read more.
The basic concept of this study consists of the investigation of symmetrization of the mechanical response in extension and compression for fibrous metamaterials endowed with a symmetric microstructure relative to the axial direction. It is known that generally, this response is non-symmetric due to the different deformation mechanisms activated in the two tests. If a further deformation mechanism based on the micro-shearing of connective elements is taken into account, the global mechanical response is observed to be symmetric for given sets of stiffnesses. The studied problem is addressed with the help of numerical simulations. Full article
(This article belongs to the Special Issue Recent Advances in the Study of Symmetry and Continuum Mechanics II)
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14 pages, 319 KiB  
Article
Displacements and Stress Functions of Straight Dislocations and Line Forces in Anisotropic Elasticity: A New Derivation and Its Relation to the Integral Formalism
by Markus Lazar
Symmetry 2021, 13(9), 1721; https://doi.org/10.3390/sym13091721 - 17 Sep 2021
Cited by 3 | Viewed by 2341
Abstract
The displacement and stress function fields of straight dislocations and lines forces are derived based on three-dimensional anisotropic incompatible elasticity. Using the two-dimensional anisotropic Green tensor of generalized plane strain, a Burgers-like formula for straight dislocations and body forces is derived and its [...] Read more.
The displacement and stress function fields of straight dislocations and lines forces are derived based on three-dimensional anisotropic incompatible elasticity. Using the two-dimensional anisotropic Green tensor of generalized plane strain, a Burgers-like formula for straight dislocations and body forces is derived and its relation to the solution of the displacement and stress function fields in the integral formalism is given. Moreover, the stress functions of a point force are calculated and the relation to the potential of a Dirac string is pointed out. Full article
(This article belongs to the Special Issue Recent Advances in the Study of Symmetry and Continuum Mechanics II)
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27 pages, 785 KiB  
Article
Spherically Symmetric Tensor Fields and Their Application in Nonlinear Theory of Dislocations
by Evgeniya V. Goloveshkina and Leonid M. Zubov
Symmetry 2021, 13(5), 830; https://doi.org/10.3390/sym13050830 - 09 May 2021
Cited by 6 | Viewed by 1979
Abstract
The concept of a spherically symmetric second-rank tensor field is formulated. A general representation of such a tensor field is derived. Results related to tensor analysis of spherically symmetric fields and their geometric properties are presented. Using these results, a formulation of the [...] Read more.
The concept of a spherically symmetric second-rank tensor field is formulated. A general representation of such a tensor field is derived. Results related to tensor analysis of spherically symmetric fields and their geometric properties are presented. Using these results, a formulation of the spherically symmetric problem of the nonlinear theory of dislocations is given. For an isotropic nonlinear elastic material with an arbitrary spherically symmetric distribution of dislocations, this problem is reduced to a nonlinear boundary value problem for a system of ordinary differential equations. In the case of an incompressible isotropic material and a spherically symmetric distribution of screw dislocations in the radial direction, an exact analytical solution is found for the equilibrium of a hollow sphere loaded from the outside and from the inside by hydrostatic pressures. This solution is suitable for any models of an isotropic incompressible body, i.e., universal in the specified class of materials. Based on the obtained solution, numerical calculations on the effect of dislocations on the stress state of an elastic hollow sphere at large deformations are carried out. Full article
(This article belongs to the Special Issue Recent Advances in the Study of Symmetry and Continuum Mechanics II)
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