Numerical simulations of brittle and elasto-plastic fracture for thin structures subjected to dynamic loadings

The main purpose of this thesis is the development of a framework to model fracture initiation and propagation in thin bodies. This is achieved by the combination of two original models.
On one hand, (full) discontinuous Galerkin formulations of Euler-Bernoulli beams as well as Kirchhoff-Love shells are established. These formulations allow modeling a thin structure with discontinuous elements, the continuity being ensured weakly by addition of interface terms. The first advantage of the recourse to a discontinuous method is an easy insertion of cohesive elements during the simulation without a modification of the mesh topology. In fact with a continuous method, the insertion of the cohesive elements at the beginning of the simulation leads to numerical issues and their insertion at onset of fracture requires a complex implementation to duplicate the nodes. By contrast, as interface elements are naturally present in a discontinuous formulation their substitution at fracture initiation is straightforward. The second advantage of the discontinuous Galerkin formulation is a simple parallel implementation obtained in this work by exploiting, the discontinuity of the mesh in an original manner. Finally, last advantage of the recourse to a discontinuous Galerkin method for thin bodies is to obtain a one field formulation. In fact, the C1 continuity is ensured weakly by interface terms without considering rotational degrees of freedom.
On the other hand, the through-the-thickness crack propagation is complicated by the implicit thickness model inherent to thin bodies formulations. Therefore we suggest an original cohesive model based on reduced tresses. Our model combines the different reduced stresses in such a way that the expected amount of energy is released during the crack process leading to a model which respects the energetic balance whatever the applied loadings.
The efficiency of the obtained framework is demonstrated through the simulation of several benchmarks whose results are in agreement with numerical and experimental data coming from the literature. Furthermore, the versatility of our framework is shown by simulating 2 very different fracture phenomena: the crack propagation for elastic as well as for elasto-plastic behavior and the fragmentation of brittle materials. This demonstrates that our framework is a powerful tool to study dynamics crack phenomena in thin structure problems involving a large number of degrees of freedom.