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Abstract
The extended finite element (XFEM) enriches the standard local FE approximations
with known information about the problem, with the use of the partition of unity.
This allows the use of meshes that do not conform to a discontinuity and avoids
adaptive re-meshing as the discontinuity grows as required with the conventional
FEM. When the crack tip asymptotic field is available and used as the enrichment
function, XFEM is more accurate than FEM allowing the use of a much coarser
mesh around the crack tip. Such asymptotic fields have been known for a
long time for traction-free cracks (the Williams expansions) but have only
recently been derived for cohesive cracks (Karihaloo–Xiao expansions). In
this paper an overview of latter expansions is given for a range of cohesive
laws and their usefulness in the simulation of cohesive crack propagation is
demonstrated on two examples of concrete and fibre-reinforced concrete flexural
members.
Keywords
Asymptotic displacement field, asymptotic stress field,
cohesive crack, extended finite element (XFEM)
Milestones
Received: 28 May 2010
Revised: 27 August 2010
Accepted: 8 September 2010
Published: 28 June 2011