Inserted: 28 sep 2006
Last Updated: 10 nov 2008
Journal: Numer. Funct. Anal. Optim.
Usually smeared crack techniques are based on the following features: the fracture is represented geometrically by means of a band of finite elements and mechanically by a softening constitutive law of damage type. Often these methods are implemented by means of non-local operators (such as convolution kernels) which control the localization effects and reduce the mesh bias. In this work we consider a non-local energy of smeared crack type defined for a finite element space on a structured grid. Our goal is the characterization of the limit energy as the mesh size $h$ tends to zero. In this way we will establish a precise link between the discrete and continuum formulations of the fracture energies, showing in particular the correct scaling and the explicit form of the mesh bias.