Negri, Matteo and Ortner, Christoph (2008) Quasi-static crack propagation by Griffith's criterion. Mathematical Models and Methods in Applied Sciences, Volume 18 (Number 11). pp. 1895-1925. doi:10.1142/S0218202508003236

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Abstract

We consider the propagation of a crack in a brittle material along a prescribed crack path and define a quasi-static evolution by means of stationary points of the free energy. We show that this evolution satisfies Griffith's criterion in a suitable form which takes into account both stable and unstable propagations, as well as an energy balance formula which accounts for dissipation in the unstable regime. If the load is monotonically increasing, this solution is explicit and almost everywhere unique. For more general loads we construct a solution via time discretization. Finally, we consider a finite element discretization of the problem and prove convergence of the discrete solutions.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General)
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Fracture mechanics, Brittleness -- Mathematical models
Journal or Publication Title:	Mathematical Models and Methods in Applied Sciences
Publisher:	World Scientific Publishing Co. Pte. Ltd.
ISSN:	0218-2025
Official Date:	November 2008
Dates:	Date Event November 2008 Published
Volume:	Volume 18
Number:	Number 11
Page Range:	pp. 1895-1925
DOI:	10.1142/S0218202508003236
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Fifth Framework Programme (European Commission) (FP5)
Grant number:	HPRN-CT-2002-00284 (FP5)

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