Existence for constrained dynamic Griffith fracture with a weak maximal dissipation condition

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...

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Bibliographic Details
Published inJournal of the mechanics and physics of solids Vol. 95; pp. 697 - 707
Main Authors Dal Maso, Gianni, Larsen, Christopher J., Toader, Rodica
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.10.2016
Subjects
Cracking domains
Dynamic fracture mechanics
Wave equation
Wave equation
Dynamic fracture mechanics
Cracking domains
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ISSN0022-5096
DOI10.1016/j.jmps.2016.04.033

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Summary: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.
ISSN:0022-5096
DOI:10.1016/j.jmps.2016.04.033