Quasi static growth of brittle cracks in a linearly elastic flexural plate

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 11] by Francfort and 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. Mathematics Subject Classification (2000) 74K20, 35J35, 74G65, 35R35, 35A35, 74R10