Journal
COMPUTATIONAL MATERIALS SCIENCE
Volume 44, Issue 2, Pages 733-749Publisher
ELSEVIER
DOI: 10.1016/j.commatsci.2008.05.019
Keywords
Localization phenomena; Extended-FEM; Partition of unity; Cosserat theory; Strain-softening
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The standard finite element models, i.e. the finite element methods that use the classical continuum models, suffer from the excessive mesh dependence when a strain-softening model is used. It cannot converge to a meaningful solution and the governing differential equation loses the ellipticity. This paper presents an enriched finite element algorithm for simulation of localization phenomenon using a higher order continuum model based on the Cosserat continuum theory. The governing equations are regularized by adding the rotational degrees-of-freedom to the conventional degrees-of-freedom and including the internal length parameter in the model. The extended finite element method (X-FEM) is employed, in which the discontinuity interfaces are represented independent of element boundaries and the process is accomplished by partitioning the domain with some triangular sub-elements whose Gauss points are used for integration of the domain of elements. Finally, several numerical examples are analyzed to demonstrate the efficiency of the mixed XFEM-Cosserat continuum model in shear band localization. (C) 2008 Elsevier B.V. All rights reserved.
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