Engineering Fracture Mechanics, in press.
PROCESS ZONE RESOLUTION BY EXTENDED FINITE ELEMENTS
Borek Patzák and
Milan
Jirásek
Swiss Federal Institute of Technology
LSC - ENAC,
EPFL,
1015 Lausanne,
Switzerland
Abstract
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 / milan.jirasek@epfl.ch