[en] The cohesive method can be combined easily with Finite Element method to simulate a fracture
problem which can contains fracture initiation and propagation. Nevertheless, the insertion of
cohesive elements is not straightforward. Indeed, the two classical approaches suffer from severe
limitations. On one hand, in the intrinsic approach, as the cohesive element is inserted at the
beginning, this element has to model the continuum stage of deformation before fracture. This is
ensured by an initial slope in the cohesive law which leads to a stiffness modification and to an
alteration of propagation of wave. On the other hand, the introduction of the cohesive element during
the simulation in extrinsic approach requests a dynamic modification of mesh. This operation is very
difficult to implement especially in the case of a parallel implementation which is almost mandatory
due to the very important number of degrees of freedom inherent to a fine mesh used to track the
crack path.
A solution to these limitations, pioneered by J. Mergheim and R. Radovitzky is to recourse to a
discontinuous Galerkin formulation. Indeed this one used discontinuous test functions and integration
at the interface of elements to discretize a structure with discontinuous elements. The integration on
the boundary of elements allows ensuring weakly the continuity of displacements in a stable and
consistent manner. As interface elements are present they can be easily substituted by cohesive
elements when a fracture criterion is reached. The interest of the method has been recently proved by
R. Radovitzky etal. for 3D elements and by the authors for Euler-Bernoulli beams. An
extension of the formulation to Kirchhoff-Love shell is presented here.
A novel extrinsic cohesive law is developed to model a through the thickness fracture. In fact, as in
thin bodies formulation the thickness is not “discretized” this operation is not straightforward.
Indeed, as the fracture occurs only in tension, in a pure bending case the position of neutral axis has
to be move to propagate the fracture. To avoid this complicated step, it is suggested to integrate on
the thickness the cohesive law which is then applies on resultant efforts. The coupling between the
openings in displacement and rotation is performed in a way which guarantees a proper release of
energy for any loading. Furthermore, the combination between fracture modes I and II is realized as
suggested by M. Ortiz etal.
Some numerical quasi-static and dynamic benchmarks are simulated to show the interest and the
good performance of the presented framework.
