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A finite element method for the computational modelling of cohesive cracks
Author(s) -
Mergheim J.,
Kuhl E.,
Steinmann P.
Publication year - 2005
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1286
Subject(s) - discontinuity (linguistics) , finite element method , displacement (psychology) , basis (linear algebra) , brittleness , constitutive equation , degrees of freedom (physics and chemistry) , set (abstract data type) , structural engineering , mathematics , mathematical analysis , geometry , computer science , engineering , physics , quantum mechanics , psychology , psychotherapist , thermodynamics , programming language
The present contribution is concerned with the computational modelling of cohesive cracks in quasi‐brittle materials, whereby the discontinuity is not limited to interelement boundaries, but is allowed to propagate freely through the elements. In the elements, which are intersected by the discontinuity, additional displacement degrees of freedom are introduced at the existing nodes. Therefore, two independent copies of the standard basis functions are used. One set is put to zero on one side of the discontinuity, while it takes its usual values on the opposite side, and vice versa for the other set. To model inelastic material behaviour, a discrete damage‐type constitutive model is applied, formulated in terms of displacements and tractions at the surface. Some details on the numerical implementation are given, concerning the failure criterion, the determination of the direction of the discontinuity and the integration scheme. Finally, numerical examples show the performance of the method. Copyright © 2005 John Wiley & Sons, Ltd.