Non-interpenetration conditions in the passage from nonlinear to linearized Griffith fracture

Almi S, Davoli E, Friedrich M (2023)

Publication Type: Journal article

Publication year: 2023

Journal

Journal De Mathematiques Pures Et Appliquees Elsevier

DOI: 10.1016/j.matpur.2023.05.001

Abstract

We characterize the passage from nonlinear to linearized Griffith-fracture theories under non-interpenetration constraints. In particular, sequences of deformations satisfying a Ciarlet-Nečas condition in SBV2 and for which a convergence of the energies is ensured, are shown to admit asymptotic representations in GSBD2 satisfying a suitable contact condition. With an explicit counterexample, we prove that this result fails if convergence of the energies does not hold. We further prove that each limiting displacement satisfying the contact condition can be approximated by an energy-convergent sequence of deformations fulfilling a Ciarlet-Nečas condition. The proof relies on a piecewise Korn-Poincaré inequality in GSBD2, on a careful blow-up analysis around jump points, as well as on a refined GSBD2-density result guaranteeing enhanced contact conditions for the approximants.

Authors with CRIS profile

Manuel Friedrich Professur für Angewandte Mathematik (Angewandte Analysis)

Involved external institutions

Università degli Studi di Napoli Federico II IT Italy (IT) Technische Universität Wien / Vienna University of Technology AT Austria (AT)

How to cite

APA:

Almi, S., Davoli, E., & Friedrich, M. (2023). Non-interpenetration conditions in the passage from nonlinear to linearized Griffith fracture. Journal De Mathematiques Pures Et Appliquees. https://dx.doi.org/10.1016/j.matpur.2023.05.001

MLA:

Almi, Stefano, Elisa Davoli, and Manuel Friedrich. "Non-interpenetration conditions in the passage from nonlinear to linearized Griffith fracture." Journal De Mathematiques Pures Et Appliquees (2023).

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