In this paper we derive a line tension model for dislocations in 3D starting from a geometrically nonlinear elastic energy with quadratic growth. In the asymptotic analysis, as the amplitude of the Burgers vectors (proportional to the lattice spacing) tends to zero, we show that the elastic energy linearizes and the line tension energy density, up to an overall constant rotation, is identi_ed by the linearized cell problem formula given in [S. Conti, A. Garroni, and M. Ortiz, Arch. Ration. Mech. Anal., 218 (2015), pp. 699{755].
Derivation of a line-tension model for dislocations from a nonlinear three-dimensional energy: The case of quadratic growth / Garroni, A.; Marziani, R.; Scala, R.. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 53:4(2021), pp. 4252-4302. [10.1137/20M1330117]
Derivation of a line-tension model for dislocations from a nonlinear three-dimensional energy: The case of quadratic growth
GARRONI A.
;MARZIANI R.;SCALA R.
2021
Abstract
In this paper we derive a line tension model for dislocations in 3D starting from a geometrically nonlinear elastic energy with quadratic growth. In the asymptotic analysis, as the amplitude of the Burgers vectors (proportional to the lattice spacing) tends to zero, we show that the elastic energy linearizes and the line tension energy density, up to an overall constant rotation, is identi_ed by the linearized cell problem formula given in [S. Conti, A. Garroni, and M. Ortiz, Arch. Ration. Mech. Anal., 218 (2015), pp. 699{755].| File | Dimensione | Formato | |
|---|---|---|---|
|
Garroni_Derivation_2021.pdf
accesso aperto
Tipologia:
Documento in Post-print (versione successiva alla peer review e accettata per la pubblicazione)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
609.48 kB
Formato
Adobe PDF
|
609.48 kB | Adobe PDF |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
