Existence for constrained dynamic Griffith fracture with a weak maximal dissipation condition |
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| Affiliation: | 1. SISSA, Via Bonomea 265, 34136 Trieste, Italy;2. Department of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609-2280, USA;3. Dima, Università degli Studi di Udine, Via delle Scienze 206, 33100 Udine, Italy;1. Dipartimento di Matematica, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185 Roma, Italy;2. Dipartimento di Ingegneria Strutturale e Geotecnica, Sapienza Università di Roma, Via Eudossiana 18, 00184 Roma, Italy;3. IMSIA, ENSTA ParisTech, CNRS, CEA, EDF, Université Paris-Saclay, 828 Boulevard des Maréchaux, 91762 Palaiseau Cedex France;1. Université Paris-Est, Laboratoire Navier (UMR 8205), CNRS, ENPC, IFSTTAR, 6 & 8 avenue Blaise Pascal, 77455 Marne-la-Vallée, France;2. Université Grenoble Alpes, 3SR, CNRS, Domaine Universitaire BP53, 38041 Grenoble Cedex 9, France;1. Theoretical and Applied Mechanics, Northwestern University, Evanston, IL 60208, USA;2. Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94551, USA;3. Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA;1. Department of Civil-Environmental Engineering and Architecture, University of Parma, Parco Area delle Scienze 181/A, I 43124 Parma, Italy;2. Department of Industrial Engineering, University of Parma, Parco Area delle Scienze 181/A, I 43124 Parma, Italy;3. Construction Technologies Institute - Italian National Research Council (ITC-CNR), Via Lombardia 49, I 20098 San Giuliano Milanese, Milano, Italy |
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| Abstract: | The study of dynamic fracture is based on the dynamic energy-dissipation balance. It is easy to see that this condition is always satisfied by a stationary crack together with a displacement satisfying the system of elastodynamics. Therefore to predict crack growth a further principle is needed. In this paper we introduce a weak maximal dissipation condition that, together with elastodynamics and energy balance, provides a model for dynamic fracture, at least within a certain class of possible crack evolutions. In particular, we prove the existence of dynamic fracture evolutions satisfying this condition, subject to smoothness constraints, and exhibit an explicit example to show that maximal dissipation can indeed rule out stationary cracks. |
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| Keywords: | Wave equation Dynamic fracture mechanics Cracking domains |
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