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Cited by 91 publications
(142 citation statements)
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“…This subsection is devoted to prove a compactness result for sequences (β ε ) ⊂ AS (2) ε with equi-bounded energy E (2) ε . To this purpose, we start proving a suitable version of the Friesecke, James and Müller Rigidity Estimate [15, Theorem 3.1] in a domain with"small holes" (see [23,Section 4] for analogous results in the linear setting).…”
Section: 1mentioning
confidence: 99%
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“…This subsection is devoted to prove a compactness result for sequences (β ε ) ⊂ AS (2) ε with equi-bounded energy E (2) ε . To this purpose, we start proving a suitable version of the Friesecke, James and Müller Rigidity Estimate [15, Theorem 3.1] in a domain with"small holes" (see [23,Section 4] for analogous results in the linear setting).…”
Section: 1mentioning
confidence: 99%
“…Nevertheless, this lemma cannot be directly applied to a sequence of strains (β ε ) ⊂ AS (2) ε , as it is not a sequence of gradients. Then, we achieve the compactness result Proposition 3.5 by exploiting the specific singularity of the strains belonging to AS (2) ε , and by applying Lemma 3.1 to a new curl-free field β ε −β ε , withβ ε suitably chosen. Another possible strategy to prove compactness is suggested by observing that β ε are in fact gradients in a suitable simply connected subset of Ω ε obtained removing from Ω ε a finite number of segments.…”
Section: Notice That For Everymentioning
confidence: 99%
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“…In view of the anti-plane assumption, all the relevant quantities are defined in a cross section of the crystal, i.e., on a square lattice. Following the formalism in [4], we have introduced screw dislocations in the model, as point topological singularities of the discrete displacement field. First, we have analysed by means of a Γ-convergence expansion the elastic energy induced by dislocations, as the lattice spacing ε tends to zero, showing that the energy concentrates on points which interact through the so-called renormalised energy.…”
Section: Introductionmentioning
confidence: 99%