A weak penalty formulation remedying traction oscillations in interface elements
Journal article, 2016

A frequently used approach to modeling of fracture along predefined paths (e.g. grain boundaries in metals) is to use intrinsic interface elements. Despite their popularity, it is well known that the use of such elements in combination with a stiff cohesive zone model may result in traction oscillations. A common strategy to alleviate this problem is to employ reduced Lobatto integration along the cohesive surface. Even though such reduced integration has been demonstrated to work well for some cases, the present work shows that there are situations where the use of this integration method results in severe traction oscillations. More precisely, it is shown that intrinsic interface elements (with full or reduced integration) share stability properties with an equivalent mixed formulation, and hence oscillations result from the violation of the inf–sup (LBB) condition for the mixed formulation. As a remedy for these oscillations, the interface elements are modified using a weak penalty formulation, based on a traction approximation fulfilling the inf–sup condition. Using this method, oscillation free results can be obtained without modifying the cohesive zone law or introducing additional unknowns. These oscillation free results are demonstrated by several numerical examples, including straight, curved and intersecting cracks.

Weak penalty


Traction oscillations

Interface elements



Erik Svenning

Chalmers, Applied Mechanics, Material and Computational Mechanics

Computer Methods in Applied Mechanics and Engineering

0045-7825 (ISSN)

Vol. 310 460-474

Computational modelling of ductile fracture on multiple geometrical scales

Swedish Research Council (VR) (2012-03006), 2013-01-01 -- 2016-12-31.

Subject Categories

Applied Mechanics

Computational Mathematics



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