Is coupling PD with FEM the way forward to solve in an efficient way crack propagation problems?

Environmental, economic and safety concerns require more and more precise capabilities to perform the life cycle assessment of engineering structures. Therefore, structural engineers should be capable of describing all stages of the structural life even that involving the propagation of cracks and branching under complex loading conditions. The description of the propagation of cracks in structural materials, however, is still an open problem. The unavoidable presence of discontinuities prevents a direct application of the methods based on Classical Continuum Mechanics (CCM). Recently, Peridynamics (PD) has been proposed [1, 2] as a theory in which cracks are not part of the problem but part of the solution; PD is based on integral equations that do not make strong assumptions on the continuity of the displacement field. The integrals of the peridynamic theory are computed on a neighborhood of each material point, which is affected, in a nonlocal way, even by points that are not in direct contact with it. As a consequence of such a nonlocality, computational methods based on PD are usually more computationally expensive than those based on CCM. Several researchers are trying to couple computational methods based on CCM with those based on PD to obtain a computational tool able to simulate crack propagation in an efficient way [3-5]. Coupling two different continuum theories is not straightforward. In our presentation, coupling is realized at the discrete level between the standard displacement version of the Finite Element Method and a meshless version of the Ordinary State based PD. The domain is divided in two portions, one discretized with FEM and the other with OSBPD. If a perfect bonding between the displacements of the two portions is imposed, some out of balance forces are generated. The paper evaluates the magnitude of the out of balance forces and discusses some ways to reduce them.