A Full Discontinuous Galerkin Formulation Of Euler Bernoulli Beams In Linear Elasticity With Fractured Mechanic Applications

A full discontinuous Galerkin method is used to predict the fracture of beams thanks to insertion of an extrinsic cohesive element. In fact, The formulation developed originally by G. Wells etal. to guarantee weakly the high order derivatives of plates with only displacement field unknown and extended by L. Noels etal. for shells is derived for beam with full discontinuous elements. This new formulation can be advantageously combined, as shown first by J. Mergheim etal. , with an extrinsic cohesive approach as there is no need to modify dynamically the mesh, which is the major drawback of this approach. The pre-fractured stage is modeled by full discontinuous elements in a manner which is proved stable and consistent and the fracture is modeled by a cohesive law applied on stress resultant an stress couple defined by J.C. Simo etal. The suggested study produces two type of results. On one hand, it is shown analytically and verified by numerical examples that the presented framework has got the properties of consistency and convergence expected for a numerical scheme. On the other hand, it is proved by some test cases that the energy released during fracture process is equal to the fracture energy except in the case where the difference of internal energy between not fractured and fractured configurations is bigger than the fracture energy. In this case, the fracture occurs in one time step. The presented work proposed a novel interesting manner to take into account fracture in thin bodies. The verification made on the particularized case of beams suggested great perspectives for plates and shells which allow to simulate more complex problems