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Titel: Positive definiteness in coupled strain gradient elasticity
Autor(en): Nazarenko, Lidiia
Glüge, RainerIn der Gemeinsamen Normdatei der DNB nachschlagen
Altenbach, HolmIn der Gemeinsamen Normdatei der DNB nachschlagen
Erscheinungsdatum: 2021
Art: Artikel
Sprache: Englisch
URN: urn:nbn:de:gbv:ma9:1-1981185920-449473
Schlagwörter: Linear theory of coupled gradient elasticity
Strain and strain gradient energy density
Fifth-rank coupling term
Zusammenfassung: The linear theory of coupled gradient elasticity has been considered for hemitropic second gradient materials, specifically the positive definiteness of the strain and strain gradient energy density, which is assumed to be a quadratic form of the strain and of the second gradient of the displacement. The existence of the mixed, fifth-rank coupling term significantly complicates the problem. To obtain inequalities for the positive definiteness including the coupling term, a diagonalization in terms of block matrices is given, such that the potential energy density is obtained in an uncoupled quadratic form of a modified strain and the second gradient of displacement. Using orthonormal bases for the second-rank strain tensor and third-rank strain gradient tensor results in matrix representations for the modified fourth-rank and the sixth-rank tensors, such that Sylvester’s formula and eigenvalue criteria can be applied to yield conditions for positive definiteness. Both criteria result in the same constraints on the constitutive parameters. A comparison with results available in the literature was possible only for the special case that the coupling term vanishes. These coincide with our results.
URI: https://opendata.uni-halle.de//handle/1981185920/44947
http://dx.doi.org/10.25673/42993
Open-Access: Open-Access-Publikation
Nutzungslizenz: (CC BY-SA 4.0) Creative Commons Namensnennung - Weitergabe unter gleichen Bedingungen 4.0 International(CC BY-SA 4.0) Creative Commons Namensnennung - Weitergabe unter gleichen Bedingungen 4.0 International
Sponsor/Geldgeber: Projekt DEAL 2020
Journal Titel: Continuum mechanics and thermodynamics
Verlag: Springer
Verlagsort: Berlin
Band: 33
Originalveröffentlichung: 10.1007/s00161-020-00949-2
Seitenanfang: 713
Seitenende: 725
Enthalten in den Sammlungen:Fakultät für Maschinenbau (OA)

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