In this paper, we prove a compactness and semicontinuity result in GSBD for sequences with bounded Griffith energy. This generalises classical results in (G)SBV by Ambrosio and SBD by Bellettini-Coscia-Dal Maso. As a result, the static problem in Francfort-Marigo's variational approach to crack growth admits (weak) solutions. Moreover, we obtain a compactness property for minimisers of suitable Ambrosio-Tortorelli's type energies, for which we have recently shown the Γ-convergence to Griffith energy.
Compactness and lower semicontinuity in $GSBD$ / Chambolle, Antonin; Crismale, Vito. - In: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. - ISSN 1435-9855. - (2020). [10.4171/JEMS/1021]
Compactness and lower semicontinuity in $GSBD$
Crismale, Vito
2020
Abstract
In this paper, we prove a compactness and semicontinuity result in GSBD for sequences with bounded Griffith energy. This generalises classical results in (G)SBV by Ambrosio and SBD by Bellettini-Coscia-Dal Maso. As a result, the static problem in Francfort-Marigo's variational approach to crack growth admits (weak) solutions. Moreover, we obtain a compactness property for minimisers of suitable Ambrosio-Tortorelli's type energies, for which we have recently shown the Γ-convergence to Griffith energy.| File | Dimensione | Formato | |
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