Abstract :
[en] One current challenge related to computational fracture mechanics is the modelization of ductile fracture and in particular the damage to crack transition.
In this paper we propose to achieve this goal by combining
1. A non-local damage model
2. The hybrid discontinuous Galerkin (DG)/extrinsic cohesive law (ECL) formulation
As classical damage models for finite element formulations lose the solution uniqueness and face the strain localization problem when strain softening of materials is involved, the damage model is herein formulated in a so-called implicit non-local approach, following the developments in [1]. In this formulation, a new non-local variable, the non-local
accumulated plastic strain eg, representative of an internal variable and its derivatives, results from the resolution of a new boundary value problem. Besides the advantage of using C0 elements, although the elements have now one additional degree of freedom
per node, this approach also possesses the feature of being fully non-local.
The hybrid DG/ECL method was recently proposed [2] to circumvent the drawbacks of the cohesive element methods. Indeed, with this DG/ECL method, prior to fracture, the flux and stabilization terms arising from the DG formulation at interelement boundaries are enforced via interface elements in a way that guarantees consistency and stability, contrarily
to traditional extrinsic cohesive zone methods. Upon the onset of fracture, the traction–separation law (TSL) governing the fracture process becomes operative without the need to modify the mesh topology as the the cohesive elements required to integrate the TSL are already present. This DG/ECL method has been shown to be an efficient numerical framework
that can easily be implement in parallel with excellent scalability properties to model fragmentation, dynamic crack propagation in brittle and smallscale yielding materials, for 3D problems and for thin structures [3,4]. In this work, the DG/ECL method is extended to
account for the damage process, as described in the non-local setting. One main advantage of the DG/ECL formulation is the existence of interface elements in which the damage model can be solved, the hydrostatic pressure can be resolved, and through which discontinuities can easily be introduced with a physically-based criterion.
