Local and non-local Gurson-based ductile damage and failure modelling at large deformation

Reusch, F.; Svendsen, Bob; Klingbeil, Dietmar

doi:10.1016/s0997-7538(03)00070-6

Cited by 92 publications

(34 citation statements)

References 17 publications

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“…Equation (10) results in a slow initial and final damage growth, which can be computationally more robust, since it does not show any discontinuities in the damage growth ( Figure 2). To avoid pathological localization effects due to material softening, the damage driving variable is computed from a non-local variablez via a separate set of Kuhn-Tucker loadingunloading conditions˙…”

Section: Continuum Modelmentioning

confidence: 99%

“…and can be well adapted to a (numerical) finite strain setting [9]. Gradient models are especially interesting to model ductile failure, since they can account for non-local microvoid interactions [10]. Gradient models can be classified into implicit and explicit models, depending on whether the non-local variable is an explicit functional of its local counterpart or not [11,12].…”

Section: Introductionmentioning

confidence: 99%

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Discrete crack modelling of ductile fracture driven by non‐local softening plasticity

Mediavilla

Peerlings

Geers

2006

Numerical Meth Engineering

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SUMMARYA combined approach towards ductile damage and fracture is presented, in the sense that a continuous material degradation is coupled with a discrete crack description for large deformations. Material degradation is modelled by a gradient enhanced damage-hyperelastoplasticity model. It is assumed that failure occurs solely due to plastic straining, which is particularly relevant for shear dominated problems, where the effect of the hydrostatic stress in triggering failure is less important. The gradient enhancement eliminates pathological localization effects which would normally result from the damage influence. Discrete cracks appear in the final stage of local material failure, when the damage has become critical. The rate and the direction of crack propagation depend on the evolution of the damage field variable, which in turn depends on the type of loading. In a large strain finite element framework, remeshing allows to incorporate the changing crack geometry and prevents severe element distortion. Attention is focused on the robustness of the computations, where the transfer of variables, which is needed after each remeshing, plays a crucial role. Numerical examples are shown and comparisons are made with published experimental results.

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Section: Continuum Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Discrete crack modelling of ductile fracture driven by non‐local softening plasticity

Mediavilla

Peerlings

Geers

2006

Numerical Meth Engineering

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“…As documented in the literature [6,7], the global behavior like the R-curve is adequately captured by relatively coarse meshes, fig. 2a.…”

Section: Resultsmentioning

confidence: 77%

“…. 2.5Õ l nl used in the literature [6,7] where numerical problems with distorted elements were reported for finer meshes [7]. For comparison, simulations without rounded crack tip were performed as well.…”

mentioning

confidence: 99%

Simulation of Crack Propagation under Small‐Scale Yielding by means of a Non‐local GTN‐Model

Hütter

Linse

Mühlich

et al. 2011

Proc Appl Math and Mech

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Today, the local approach to fracture is widely applied to simulate the failure of specimens. For ductile damage processes the Gurson-Tvergaard-Needleman model is the quasi-standard. In the last time non-local extensions allowed a mesh-size independent simulation of crack growth. However, most publications dealing with this subject focus upon the convergence regarding global quantities such as the load-displacement relation. Minor attention is paid to the fields directly at the crack tip. Correspondingly, the interrelationship between the intrinsic length of the model and relevant microscopic damage processes at the crack tip is only partly established until now. In the present study the crack propagation is simulated for an implicitly gradient enriched GTN-model within a boundary layer in order to overcome influences of the specimen geometry. The different stages of damage evolution are resolved by a fine mesh. ModelIn order to describe the ductile crack initiation and propagation a non-local extension of the widely used GURSON [1] model with the modifications of TVERGAARD and NEEDLEMAN (GTN,[2,3]) is employed. For this purpose, the volumetric plastic strain rate ε vol in the evolution equation of the local model for the void volume fraction f is replaced by its non-local counterpart ε nl using an implicit gradient enrichment [4]:Thereby, an intrinsic length scale l nl is introduced via the prefactor of the LAPLACE-operator ∆Ô Õ. The formulation can be interpreted as a spatial average over the local volumetric plastic strain ε vol around the actual point. The crack propagation behavior of the model is investigated under small-scale yielding conditions by means of a boundary layer approach. This has the advantage that a possible influence of the specimen geometry can be excluded. The hardening is described by a power law (exponent N ). In the FE-model elements with quadratic shape functions for the displacements and linear ones for the non-local strains are used, for details see [4]. Dynamic simulations are performed with implicit time integration under quasi-static loading [5].In the initial loading stages the plastic deformations occur within a region much smaller than the intrinsic length scale l nl . Hence, at this stage no void growth but pure crack tip blunting is predicted by the model which is physically reasonable. In order to handle the strain singularity at the crack tip coinciding with blunting of an ideal sharp crack, an initial radius is used at the crack tip, see fig. 1. This procedure allows to use elements with edge lengths h lig considerably smaller than the value of h lig Ô0.5 . . . 2.5Õ l nl used in the literature [6,7] where numerical problems with distorted elements were reported for finer meshes [7]. For comparison, simulations without rounded crack tip were performed as well. Fig. 1 Details of the finite element mesh at the crack tip with initial radius l nl ResultsFirst, simulations with a common set of parameters (f 0 0.01, f c 0.15, f f 0.25, N 0.1, E 250 σ y , ν 0.3) and several spat...

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“…For this reason several ideas were published to regularize the numerical model. In this work the implicit gradient formulation is used which has been proven to be efficient and numerically attractive to get a transition to non-local CDM as for example shown in [2], [3] or [4]. In the case of complete failure these methods will lead to ill conditioned equation systems and additionally are only able to represent evolving cracks in a smeared way.…”

Section: Introductionmentioning

confidence: 99%

3D Ductile crack propagation with the XFEM

Beese

Löhnert

Wriggers

2015

Proc Appl Math and Mech

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Local and non-local Gurson-based ductile damage and failure modelling at large deformation

Cited by 92 publications

References 17 publications

Discrete crack modelling of ductile fracture driven by non‐local softening plasticity

Discrete crack modelling of ductile fracture driven by non‐local softening plasticity

Simulation of Crack Propagation under Small‐Scale Yielding by means of a Non‐local GTN‐Model

3D Ductile crack propagation with the XFEM

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