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See detailA damage to crack transition model accounting for stress triaxiality formulated in a hybrid non-local implicit discontinuous Galerkin - cohesive band model framework
Leclerc, Julien ULg; Wu, Ling ULg; Nguyen, Van Dung ULg et al

in International Journal for Numerical Methods in Engineering (in press)

Modelling the entire ductile fracture process remains a challenge. On the one hand, continuous damage models succeed in capturing the initial diffuse damage stage but are not able to represent ... [more ▼]

Modelling the entire ductile fracture process remains a challenge. On the one hand, continuous damage models succeed in capturing the initial diffuse damage stage but are not able to represent discontinuities or cracks. On the other hand, discontinuous methods, as the cohesive zones, which model the crack propagation behaviour, are suited to represent the localised damaging process. However, they are unable to represent diffuse damage. Moreover, most of the cohesive models do not capture triaxiality effect. In this paper, the advantages of the two approaches are combined in a single damage to crack transition framework. In a small deformation setting, a non-local elastic damage model is associated with a cohesive model in a discontinuous Galerkin finite element framework. A cohesive band model is used to naturally introduce a triaxiality-dependent behaviour inside the cohesive law. Practically, a numerical thickness is introduced to recover a 3D-state, mandatory to incorporate the in-plane stretch effects. This thickness is evaluated to ensure the energy consistency of the method and is not a new numerical parameter. The traction-separation law is then built from the underlying damage model. [less ▲]

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See detailCohesive Band Model: a triaxiality-dependent cohesive model inside an implicit non-local damage to crack transition framework
Leclerc, Julien ULg; Wu, Ling ULg; Nguyen, Van Dung ULg et al

Conference (2017, June 14)

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 ... [more ▼]

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. [less ▲]

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See detailCohesive band model: a triaxiality-dependent cohesive model for damage to crack transition in a non-local implicit discontinuous Galerkin framework
Leclerc, Julien ULg; Wu, Ling ULg; Noels, Ludovic ULg et al

Conference (2016, June 07)

Numerical modelling of the complete ductile failure process is still a challenge. On the one hand, continuous approaches, described by damage models, succeed in the initial diffuse damage stage but are ... [more ▼]

Numerical modelling of the complete ductile failure process is still a challenge. On the one hand, continuous approaches, described by damage models, succeed in the initial diffuse damage stage but are still unable to represent physical discontinuities. On the other hand, discontinuous approaches, such as the cohesive zone models, are able to represent the crack propagation behaviour. They are suited for local damaging processes as crack initiation and propagation, and so, fail in diffuse damage prediction of ductile materials. Moreover, they do not usually capture triaxiality effects, mandatory for accurate ductile failure simulations. To describe the ductile failure process, the numerical scheme proposed here combines both approaches [1] in order to beneficiate from their respective advantages: a non-local damage model combined with an extrinsic cohesive law in a discontinuous Galerkin finite element framework. An application example of this scheme is shown on the attached figure. The initial diffuse damage stage is modelled by an implicit nonlocal damage model as suggested by [2]. Upon damage to crack transition, a cohesive band [3] is used to introduce in-plane stretch effects inside the cohesive law or in other words, a triaxiality-dependent behaviour. Indeed, these in-plane strains play an important role during the ductile failure process and have to be considered. Concretely, when crack appears in the last failure stage, all the damaging process is assumed to occur inside a thin band ahead of the crack surface. Thanks to the small but finite numerical band thickness, the strains inside this band can be obtained from the in-plane 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 is computed to ensure the energetic consistency during the transition. [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] 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 [3] 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): 177–188 [less ▲]

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