Continuous and Discontinuous Modelling of Cohesive Frictional
Lecture Notes in Physics 568, ed. P.A. Vermeer et al., Springer,
Berlin, 2001, pp. 17-29.
MODELLING OF LOCALIZED DAMAGE AND FRACTURE IN QUASIBRITTLE MATERIALS
Swiss Federal Institute of Technology
This paper focuses on strain and damage localization due to propagation
and coalescence of microcracks in quasibrittle materials such as concrete
or rock. The mathematical description and numerical simulation of such
phenomena can be based on an indirect representation of the cracking-induced
deformation by inelastic strain, or on a direct representation by discontinuities
in the displacement field. The first part of the paper gives a general
overview and classification of modeling approaches and numerical techniques
related to both types of representations and discusses their possible combination.
The second part proposes a new technique for computational resolution of
localization zones in regularized softening continua, based on special
enrichments of the standard finite element approximations.
This paper has briefly sketched the idea of finite elements with embedded
localization zones and illustrated it with a simple one-dimensional example.
Of course, much additional work is needed to make the proposed concept
useful in practical applications. The most difficult step is no doubt the
extension to multiple dimensions. In one dimension, the weak compatibility
condition (vanishing integral of the enhanced strain mode over the element)
is equivalent to the strong compatibility condition (continuity of displacements).
In multiple dimensions, this is no longer the case, and the exact way in
which weak compatibility is enforced has an important influence on the
kinematic properties of the enriched model. For instance, the elements
with embedded discontinuities that are derived in a variationally consistent
manner from the stress continuity condition are inherently incapable of
reproducing a clean separation with no stress transfer across a widely
open crack; see Jirasek (2000) for a discussion.
Other issues to be addressed in the future include the optimal choice
of enrichment functions and efficient integration schemes. Finally, it
is desirable to develop the technique into a truly adaptive
approach, in which the parameters of the enhanced modes are continuously
adapted to the evolving shape of the localization profile. These topics
are the subject of an ongoing research.
The complete paper can be downloaded in PostScript
format (320 kB).
EPFL / 1 February 2001 / firstname.lastname@example.org