Abstract :
[en] Accurate numerical prediction of the whole ductile failure process is still a challenge. The adequate numerical scheme has to concord with the physical reality composed of an initial diffuse damage step followed by ultimate localised crack initiation and propagation. Currently, two main modelling philosophies exist. On the one hand, continuous approaches, described by damage models, are suited for diffuse damage, but are unable to represent physical discontinuities. On the other hand, discontinuous approaches are suitable to describe crack propagation behaviour and other localised processes, but fail in diffuse damage prediction of ductile materials. Moreover, they do not usually capture triaxiality effects or in other words, in-plane stretch effects, which are mandatory for accurate ductile failure simulations.
To describe the ductile failure process, the numerical scheme proposed here combines both approaches and by this way, their respective advantages: an implicit non-local damage model combined with an extrinsic cohesive law in a discontinuous Galerkin finite element framework [1]. An application example of this scheme is shown on the attached figure with a comparison of the experimental force-displacement curve [2]. An implicit non-local model [3] is involved to model the initial diffuse damage stage. Upon damage to crack transition, a cohesive band [4] is used as cohesive law in order to introduce in-plane stretch effects during the crack propagation. This model is based on the assumption that all the damaging process occurs inside a band of small but finite thickness ahead of the crack surface. The strains inside this band is obtained from the neighbouring strains and from the cohesive jump. Then, the stress-state inside the band and the cohesive traction forces on the crack lips are deduced from the underlying continuum damage model. The band thickness is not a new material parameter but it is computed to ensure the energetic consistency of the numerical scheme [5].
[1] Wu L, Becker G, Noels L. Elastic damage to crack transition in a coupled non-local implicit discontinuous Galerkin/extrinsic cohesive law framework. Comput. Methods Appl. Mech. Eng. 279 (2014): 379–409
[2] Geers M., de Borst R., Brekelmans W., Peerlings R. Validation and internal length scale determination for a gradient damage model: application to short glass-fibre-reinforced polypropylene. Int. J. of Sol. and Struct. 36 (1999): 2557‑2583.
[3] Peerlings R., de Borst R., Brekelmans W., Ayyapureddi S. Gradient-enhanced damage for quasi-brittle materials, Int. J. for Num. Methods in Eng. 39 (1996): 3391-3403
[4] Remmers J. J. C., de Borst R., Verhoosel C. V., Needleman A. The cohesive band model: a cohesive surface formulation with stress triaxiality. Int. J. Fract. 181 (2013): 177–18
[5] Leclerc J., Wu L., Nguyen V.D., Noels L. Cohesive band model: a cohesive model with triaxiality for crack transition in a coupled non-local implicit discontinuous Galerkin/extrinsic cohesive law framework. Int. J. for Num. Methods in Eng. (2017): In preparation.
