A fracture framework for Euler Bernoulli beams based on a full discontinuous Galerkin formulation/extrinsic cohesive law combination

A new full Discontinuous Galerkin discretization of Euler Bernoulli beam is presented. The main
interest of this framework is its ability to simulate fracture problems by inserting a cohesive zone model in the formulation. With a classical Continuous Galerkin method the use of the cohesive zone model is di cult because as insert a cohesive element between bulk elements is not straightforward. On one hand if the cohesive element is inserted at the beginning of the simulation there is a modification of the structure stiffness and on the other hand inserting the cohesive element during the simulation requires modification of the mesh during computation. These drawbacks are avoided with the presented formulation as the structure is discretized in a stable and consistent way with full discontinuous elements and inserting cohesive elements during the simulation becomes straightforward. A new cohesive law based on the resultant stresses (bending moment and membrane) of the thin structure discretization is also presented. This model allows propagating fracture while avoiding through-the-thickness integration of the cohesive law. Tests are performed to show that the proposed model releases,
during the fracture process, an energy quantity equal to the fracture energy for any combination of tension-bending loadings.