Engineering Fracture Mechanics, in press.


Borek Patzák and Milan Jirásek
Swiss Federal Institute of Technology
LSC - ENAC, EPFL, 1015 Lausanne, Switzerland


A new numerical technique for the computational resolution of highly localized strains in narrow damage process zones of quasibrittle materials is proposed. Objective description of localization due to softening is provided by a nonlocal damage model. The extended finite element method (X-FEM) is exploited for an adaptive enrichment of the standard displacement approximation by regularized Heaviside functions that are close to the exact localization mode. An accurate closed-form expression for the width of the enriched zone is derived by localization analysis under uniaxial stress. Numerical examples show that satisfactory results can be obtained even on coarse basic meshes with only a few added degrees of freedom.

Summary and Conclusions

The extended finite element method has been successfully applied to the simulation of a propagating damage process zone using a nonlocal material model. The approximation of the displacement field has been improved by incorporating a set of special enrichments that correspond to regularized Heaviside functions.  The width of the enriched zone has been determined by localization analysis in one dimension. The method allows to accurately capture the localized nature of the solution even on coarse basic grids. Although tested only for the case when the crack trajectory is straight and known in advance, the methodology seems to be promising. The generalization to arbitrary curved crack trajectories and to three dimensions is the subject of an ongoing research.

The complete paper can be downloaded in an electronic form: PostScript, PDF

EPFL / 26 April 2002 /