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A discrete model for elasticity with microstructure.

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Title: A discrete model for elasticity with microstructure.
Authors: Polyzos, D.1 (AUTHOR) polyzos@upatras.gr, Gortsas, T.V.1 (AUTHOR), Tsinopoulos, S.V.2 (AUTHOR), Beskos, D.E.3,4 (AUTHOR)
Source: Mechanics Research Communications. Oct2025, Vol. 149, pN.PAG-N.PAG. 1p.
Subjects: Elasticity, Microstructure, Mechanical behavior of materials, Dispersion relations, Lattice models (Statistical physics), Strains & stresses (Mechanics)
Abstract: • Derivation of Mindlin's strain gradient elastic theory through lattice models. • Presentation Mindlin's theory for 1D problems. • Determination of nonclassical material properties and internal length scale parameters. • Dispersion curves with acoustic and optical branches. In the mid-1960s, Mindlin introduced his theory of strain gradient elasticity (SGE), along with one of its most widely recognized simplified versions, known as SGE-Form II. These enhanced theories were motivated by the need to capture dynamic phenomena that classical elasticity fails to address. Although theoretically elegant, the inclusion of numerous material constants and internal length scale parameters makes the practical application of both SGE and SGE-Form II challenging—even for one-dimensional (1D) problems. A practical approach for identifying these parameters involves validating the theories through lattice models, where both the microstructure and macrostructure are materially and geometrically well-defined. Using a simple 1D lattice model with nearest and next-nearest neighbor spring connections and distributed mass, Polyzos and Fotiadis (Int. J. Solids Struct. 49, 470–480, 2012) were the first to successfully validate Mindlin's SGE-Form II and to interpret the intrinsic parameters introduced by the theory. Despite significant efforts, no lattice model has yet been shown to fully replicate the behavior described by the general SGE theory, even in 1D cases. This gap is addressed in the present work through the use of a simple 1D lattice model and the implementation of a continualization process similar to that employed by Polyzos and Fotiadis (2012). [ABSTRACT FROM AUTHOR]
Copyright of Mechanics Research Communications is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 188944310
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PubTypeId: academicJournal
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  Data: A discrete model for elasticity with microstructure.
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  Data: <searchLink fieldCode="AR" term="%22Polyzos%2C+D%2E%22">Polyzos, D.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> polyzos@upatras.gr</i><br /><searchLink fieldCode="AR" term="%22Gortsas%2C+T%2EV%2E%22">Gortsas, T.V.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Tsinopoulos%2C+S%2EV%2E%22">Tsinopoulos, S.V.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Beskos%2C+D%2EE%2E%22">Beskos, D.E.</searchLink><relatesTo>3,4</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Mechanics+Research+Communications%22">Mechanics Research Communications</searchLink>. Oct2025, Vol. 149, pN.PAG-N.PAG. 1p.
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  Data: <searchLink fieldCode="DE" term="%22Elasticity%22">Elasticity</searchLink><br /><searchLink fieldCode="DE" term="%22Microstructure%22">Microstructure</searchLink><br /><searchLink fieldCode="DE" term="%22Mechanical+behavior+of+materials%22">Mechanical behavior of materials</searchLink><br /><searchLink fieldCode="DE" term="%22Dispersion+relations%22">Dispersion relations</searchLink><br /><searchLink fieldCode="DE" term="%22Lattice+models+%28Statistical+physics%29%22">Lattice models (Statistical physics)</searchLink><br /><searchLink fieldCode="DE" term="%22Strains+%26+stresses+%28Mechanics%29%22">Strains & stresses (Mechanics)</searchLink>
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  Label: Abstract
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  Data: • Derivation of Mindlin's strain gradient elastic theory through lattice models. • Presentation Mindlin's theory for 1D problems. • Determination of nonclassical material properties and internal length scale parameters. • Dispersion curves with acoustic and optical branches. In the mid-1960s, Mindlin introduced his theory of strain gradient elasticity (SGE), along with one of its most widely recognized simplified versions, known as SGE-Form II. These enhanced theories were motivated by the need to capture dynamic phenomena that classical elasticity fails to address. Although theoretically elegant, the inclusion of numerous material constants and internal length scale parameters makes the practical application of both SGE and SGE-Form II challenging—even for one-dimensional (1D) problems. A practical approach for identifying these parameters involves validating the theories through lattice models, where both the microstructure and macrostructure are materially and geometrically well-defined. Using a simple 1D lattice model with nearest and next-nearest neighbor spring connections and distributed mass, Polyzos and Fotiadis (Int. J. Solids Struct. 49, 470–480, 2012) were the first to successfully validate Mindlin's SGE-Form II and to interpret the intrinsic parameters introduced by the theory. Despite significant efforts, no lattice model has yet been shown to fully replicate the behavior described by the general SGE theory, even in 1D cases. This gap is addressed in the present work through the use of a simple 1D lattice model and the implementation of a continualization process similar to that employed by Polyzos and Fotiadis (2012). [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Mechanics Research Communications is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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        Value: 10.1016/j.mechrescom.2025.104510
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        Text: English
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      – SubjectFull: Elasticity
        Type: general
      – SubjectFull: Microstructure
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      – SubjectFull: Mechanical behavior of materials
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      – SubjectFull: Dispersion relations
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      – SubjectFull: Lattice models (Statistical physics)
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      – SubjectFull: Strains & stresses (Mechanics)
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      – TitleFull: A discrete model for elasticity with microstructure.
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              M: 10
              Text: Oct2025
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              Y: 2025
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