On the convergence of 3D free discontinuity models in variational fracture
Free discontinuity problems arising in the variational theory for fracture mechanics are considered. A Γ -convergence proof for an r-adaptive 3D finite element discretization is given in the case of a brittle material. The optimal displacement field, crack pattern and mesh geometry are obtained through a variational procedure that encompasses both mechanical and configurational forces. Possible extensions to cohesive fracture and quasi-static evolutions are discussed.
© 2010 Springer Science+Business Media B.V. Received: 18 December 2009; Accepted: 10 February 2010; Published online: 4 March 2010. F. F. greatly acknowledges the support of the Italian MIUR through the FARB 2009 grant "Mechanics of Innovative Multiscale Composite Systems", and the Laboratory for Parallel Computing (LAPC) of the University Centre for Risk Prediction and Prevention (CUGRI) between the University of Salerno and the University of Naples "Federico II".M.N. acknowledges the support of the Italian CNR through the CNRShort Term Mobility Program. F.F. and M.N. thank the Graduate Aerospace Laboratories at Caltech (GALCIT) for the hospitality during their visits.