Calculus of Variations and Geometric Measure Theory

F. Acanfora - M. Ponsiglione

Quasi-static growth of brittle craks in a linearly elastic flexural plate

created on 04 Mar 2004
modified by ponsiglio on 09 Jan 2007


Published Paper

Inserted: 4 mar 2004
Last Updated: 9 jan 2007

Journal: Ann. Mat. Pura Appl.
Volume: 185
Number: 2
Pages: 293-317
Year: 2006


In this paper we propose a variational model for the irreversible quasi-static growth in brittle fractures for a linearly elastic homogeneous isotropic plate, subject to a time dependent vertical displacement on a part of its lateral surface. The model is based on the Griffith's criterion for crack growth and is inspired to the model proposed in \cite{FM} by G.A. Francfort and J.-J. Marigo in the case of $3$-D elasticity. We give a precise mathematical formulation of the model and in this framework we prove an existence result.

Keywords: Brittle fracture, free discontinuity problems, Plates, Higher order elliptic equations, Crack propagation, Quasi-static growth