Calculus of Variations and Geometric Measure Theory

L. Lussardi - M. Negri

Convergence of non-local finite element energies for fracture mechanics

created by negri on 28 Sep 2006
modified by lussardi on 10 Nov 2008


Published Paper

Inserted: 28 sep 2006
Last Updated: 10 nov 2008

Journal: Numer. Funct. Anal. Optim.
Volume: 28
Pages: 83-109
Year: 2007


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.