Finite element formulation of a new nonlocal damage model

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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“…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: 74%

“…. 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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“…Samal developed a nonlocal damage law trying to overcome the drawbacks of the local Roussellier model [Samal et al, 2008[Samal et al, , 2009 where the damage growth law is defined in terms of the local void volume fraction but keeping a local definition for strain. This is the new trend for the Rousselier model as well as for the GTN model.…”

Section: The Rousselier Modelmentioning

confidence: 99%

Numerical Simulation and Experimental Investigation of the Fracture Behaviour of an Electron Beam Welded Steel Joint

Tu¹

2018

Springer Theses

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“…More recently, Samal et al (2008) have enhanced Rousselier's constitutive model by adopting a similar approach to the one proposed by Reusch et al (2003a), i.e., a new damage variable has been incorporated through a gradient implicit formulation.…”

Section: Nonlocal Formulation Of a Gurson-based Damage Modelmentioning

confidence: 99%

Ductile Failure Modelling: Stress Dependence, Nonlocality, and Damage to Fracture Transition

Pires

Andrade³

et al. 2013

Handbook of Damage Mechanics

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In this chapter, some recent developments and proposals for improvement of material models at the constitutive level to deal with ductile damage at large plastic strains are addressed. Numerical tests are carried out to test their performance on shear-dominated stress states where their main differences lie. Subsequently, aspects of the use of nonlocal models for the regularization of the numerical values associated with damage models, namely, discretization dependency, are reviewed. Different approaches on the choice of the regulation variable or variables are tested at different stress states characterized by different values of triaxiality and third invariant of the deviatoric stress tensor. Finally, a simple strategy on how to handle the transition from damage to fracture by means of the extended finite element method is described.

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Finite element formulation of a new nonlocal damage model

Cited by 52 publications

References 66 publications

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

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

Numerical Simulation and Experimental Investigation of the Fracture Behaviour of an Electron Beam Welded Steel Joint

Ductile Failure Modelling: Stress Dependence, Nonlocality, and Damage to Fracture Transition

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