This paper deals with the elastic energy induced by systems of straight edge dislocations in the framework of linearized plane elasticity. The dislocations are introduced as point topological defects of the displacement-gradient fields. Following the core radius approach, we introduce a parameter ε > 0 representing the lattice spacing of the crystal, we remove a disc of radius ε around each dislocation and compute the elastic energy stored outside the union of such discs, namely outside the core region. Then, we analyze the asymptotic behaviour of the elastic energy as ε → 0, in terms of Γ-convergence. We focus on the self energy regime of order log 1/ε; we show that configurations with logarithmic diverging energy converge, up to a subsequence, to a finite number of multiple dislocations and we compute the corresponding Γ-limit. © 2012 Springer-Verlag.
Γ-Convergence Analysis of Systems of Edge Dislocations: the Self Energy Regime / DE LUCA, Lucia; Garroni, Adriana; Ponsiglione, Marcello. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - STAMPA. - 206:3(2012), pp. 885-910. [10.1007/s00205-012-0546-z]
Γ-Convergence Analysis of Systems of Edge Dislocations: the Self Energy Regime
DE LUCA, LUCIA;GARRONI, Adriana;PONSIGLIONE, Marcello
2012
Abstract
This paper deals with the elastic energy induced by systems of straight edge dislocations in the framework of linearized plane elasticity. The dislocations are introduced as point topological defects of the displacement-gradient fields. Following the core radius approach, we introduce a parameter ε > 0 representing the lattice spacing of the crystal, we remove a disc of radius ε around each dislocation and compute the elastic energy stored outside the union of such discs, namely outside the core region. Then, we analyze the asymptotic behaviour of the elastic energy as ε → 0, in terms of Γ-convergence. We focus on the self energy regime of order log 1/ε; we show that configurations with logarithmic diverging energy converge, up to a subsequence, to a finite number of multiple dislocations and we compute the corresponding Γ-limit. © 2012 Springer-Verlag.File | Dimensione | Formato | |
---|---|---|---|
DeLuca_Γ-Convergence-analysis_2012.pdf.pdf
solo gestori archivio
Tipologia:
Documento in Post-print (versione successiva alla peer review e accettata per la pubblicazione)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
296.77 kB
Formato
Adobe PDF
|
296.77 kB | Adobe PDF | Contatta l'autore |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.