On computational homogenization of microscale crack propagation
Journal article, 2016

© 2016 John Wiley and Sons, Ltd. The effective response of microstructures undergoing crack propagation is studied by homogenizing the response of statistical volume elements (SVEs). Because conventional boundary conditions (Dirichlet, Neumann and strong periodic) all are inaccurate when cracks intersect the SVE boundary, we herein use first order homogenization to compare the performance of these boundary conditions during the initial stage of crack propagation in the microstructure, prior to macroscopic localization. Using weakly periodic boundary conditions that lead to a mixed formulation with displacements and boundary tractions as unknowns, we can adapt the traction approximation to the problem at hand to obtain better convergence with increasing SVE size. In particular, we show that a piecewise constant traction approximation, which has previously been shown to be efficient for stationary cracks, is more efficient than the conventional boundary conditions in terms of convergence also when crack propagation occurs on the microscale. The performance of the method is demonstrated by examples involving grain boundary crack propagation modelled by conventional cohesive interface elements as well as crack propagation modelled by means of the extended finite element method in combination with the concept of material forces.


Weak periodicity

Multiscale modelling

Computational homogenization


Material forces


Erik Svenning

Chalmers, Applied Mechanics, Material and Computational Mechanics

Martin Fagerström

Chalmers, Applied Mechanics, Material and Computational Mechanics

Fredrik Larsson

Chalmers, Applied Mechanics, Material and Computational Mechanics

International Journal for Numerical Methods in Engineering

0029-5981 (ISSN) 1097-0207 (eISSN)

Vol. 108 1 76-90

Computational modelling of ductile fracture on multiple geometrical scales

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

Subject Categories

Materials Engineering

Applied Mechanics


C3SE (Chalmers Centre for Computational Science and Engineering)

Areas of Advance

Materials Science



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1/5/2023 1