NOTICE: this is the author's version of a work that was accepted for publication in Computer Methods in Applied Mechanics and Engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computer Methods in Applied Mechanics and Engineering 200:45-46, 2011, 3223-3241, 10.1016/j.cma.2011.07.008
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Discontinuous Galerkin method; shells; Kirchhoff-Love; finite-elements; fracture mechanics; cohesive element
Abstract :
[en] In order to model fracture, the cohesive zone method can be coupled in a very efficient way with the Finite Element method. Nevertheless, there are some drawbacks with the classical insertion of cohesive elements. It is well known that, on one the hand, if these elements are present before fracture there is a modification of the structure stiffness, and that, on the other hand, their insertion during the simulation requires very complex implementation, especially with parallel codes. These drawbacks can be avoided by combining the cohesive method with the use of a discontinuous Galerkin formulation. In such a formulation, all the elements are discontinuous and the continuity is weakly ensured in a stable and consistent way by inserting extra terms on the boundary of elements. The recourse to interface elements allows to substitute them by cohesive elements at the onset of fracture.
The purpose of this paper is to develop this formulation for Kirchhoff-Love plates and shells. It is achieved by the establishment of a full DG formulation of shell combined with a cohesive model, which is adapted to the special thickness discretization of shell formulation. In fact, this cohesive model is applied on resulting reduced stresses which are the basis of thin structures formulations.
Finally, numerical examples demonstrate the efficiency of the method.
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