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An Adaptive Finite Element Approach for Brittle Fracture
Author(s) -
Geißler Gordon,
Kaliske Michael
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610062
Subject(s) - finite element method , computation , a priori and a posteriori , element (criminal law) , discrete element method , extended discrete element method , extended finite element method , brittleness , computer science , brittle fracture , fracture (geology) , structural engineering , mathematics , finite element limit analysis , mechanics , materials science , algorithm , engineering , physics , philosophy , epistemology , law , political science , composite material
The extension of the finite element method to take discrete fracture and failure modes into account is a current field of research. In recent times, first results in terms of cohesive element formulations have been introduced into commercial applications. Such element formulations are able to cover the discrete behaviour of interfaces between different materials or the mechanical processes of thin layers. These approaches are not suitable for simulations with unknown crack paths in homogeneous materials, due to the initial elastic phase of the material formulation and the necessity to define potential crack paths a priori. The presented strategy starts with an unextended model and modifies the structure during the computations in terms of an adaptive procedure. The idea is to generate additional elements, based on the cohesive element formulation, to approximate arbitrary crack paths. For this purpose, a failure criterion is introduced. For nodes where the limiting value is reached, cohesive elements are introduced between the volume element boundaries of accordingly facets and corresponding nodes are duplicated. Necessary modifications for this application on system level as well as the element and the material formulation are introduced. By means of some numerical examples, the functionality of the presented procedure is demonstrated. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)