Validating Theories for Brittle Damage

Brannon, Rebecca M.; Wells, Joseph M.; Strack, Otto D. L.

doi:10.1007/s11661-007-9310-7

Cited by 37 publications

(35 citation statements)

References 16 publications

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“…Becker [1] accurately predicted the fragmentation of an expanding ring using the Gurson plasticity model [13] by randomly varying the initial porosity and introducing geometric imperfections by restricting the number of digits on the initial nodal coordinates. Brannon et al [10] discussed the issues associated with the validation of theories for brittle damage. They perturbed the material strength field to seed cracks, and employed the Weibull theory to reduce the mesh dependency of the solution.…”

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confidence: 99%

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Modeling localized failure with arbitrary Lagrangian Eulerian methods

Vitali

2011

Comput Mech

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Constitutive models incorporating damage are frequently used in finite element analyses of structural failure. Regions in a structure undergoing homogeneous deformation fail simultaneously with these models, producing an unrealistic response. A simple, and usually successful, solution to this problem in Lagrangian finite element analyses is to introduce spatially random variations in the material failure parameters. Using the same approach in multi-material arbitrary Lagrangian Eulerian (MMALE) formulations often fails because the material transport smears out the high frequency random variations in the failure parameters. A simple, novel approach to overcoming this difficulty is presented here. Example calculations of a tension test, spall in impacting plates, and shear band formation in the thick walled cylinder test are presented.

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confidence: 99%

“…We leave the evaluation of the appropriateness of using random perturbations in particular applications to others [1,10]. Section 2 reviews the transport algorithm used in our research code Raven [8,[30][31][32].…”

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confidence: 99%

Modeling localized failure with arbitrary Lagrangian Eulerian methods

Vitali

2011

Comput Mech

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“…Here, m is the Weibull modulus, implying that this theory would require revision for nonWeibull distributions, perhaps replacing m with a micro-physically based X.T/ function, as in the delocalization proposal of Equation (16). Also, is the pre-failure analytical principal stress invariant field over the finite element, which is known for the Brazilian test and the other simple cases studied by Kamojjala and Brannon.…”

Section: Nonlocal Corrections Of Discretization Errorsmentioning

confidence: 99%

Aleatory uncertainty and scale effects in computational damage models for failure and fragmentation

Strack

Leavy

Brannon

2014

Numerical Meth Engineering

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SUMMARYStress concentrations near grain boundaries, precipitates, and similar micro-heterogeneities nucleate instabilities leading to macroscale fracture. As it is not practical to model each flaw explicitly, their ensemble effect is modeled statistically. Accounting for this aleatory uncertainty requires smaller specimens (e.g., small finite elements) to have generally higher and more variable strengths, which is necessary for the initial failure probability of a finite domain to be unaffected by its discretization into elements. Localization itself, which might be attributed to constitutive instability, requires realistic numerical perturbations to predict bifurcations such as radial cracking in axisymmetric problems. These perturbations, stemming from microscale heterogeneity, are incorporated in simulations by imposing statistical spatial variability in the parameters of an otherwise conventional (deterministic and scale-independent) damage model. This approach is attractive for its algorithmic simplicity and straightforward calibration from standard strength tests. In addition, it results in virtually no loss of efficiency or robustness relative to deterministic models and accommodates general three-dimensional loading. Despite these advantages, some significant challenges remain and are discussed. However, it is demonstrated that including aleatory uncertainty with associated scale effects significantly improves predictiveness on large-scale computational domains, where it is impractical to resolve each crack or localization zone.

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“…Several researchers have suggested seeding material properties with variability in numerical simulations to capture such effects (e.g. [42][43][44]). For this example, the initial yield stress is perturbed.…”

Section: Example: Fragmenting Ringmentioning

confidence: 99%

A statistical method for verifying mesh convergence in Monte Carlo simulations with application to fragmentation

Bishop

Strack

2011

Numerical Meth Engineering

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SUMMARYA novel method is presented for assessing the convergence of a sequence of statistical distributions generated by direct Monte Carlo sampling. The primary application is to assess the mesh or grid convergence, and possibly divergence, of stochastic outputs from non-linear continuum systems. Example systems include those from fluid or solid mechanics, particularly those with instabilities and sensitive dependence on initial conditions or system parameters. The convergence assessment is based on demonstrating empirically that a sequence of cumulative distribution functions converges in the L ∞ norm. The effect of finite sample sizes is quantified using confidence levels from the Kolmogorov-Smirnov statistic. The statistical method is independent of the underlying distributions.The statistical method is demonstrated using two examples: (1) the logistic map in the chaotic regime, and (2) a fragmenting ductile ring modeled with an explicit-dynamics finite element code. In the fragmenting ring example the convergence of the distribution describing neck spacing is investigated. The initial yield strength is treated as a random field. Two different random fields are considered, one with spatial correlation and the other without. Both cases converged, albeit to different distributions. The case with spatial correlation exhibited a significantly higher convergence rate compared with the one without spatial correlation.

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Validating Theories for Brittle Damage

Cited by 37 publications

References 16 publications

Modeling localized failure with arbitrary Lagrangian Eulerian methods

Modeling localized failure with arbitrary Lagrangian Eulerian methods

Aleatory uncertainty and scale effects in computational damage models for failure and fragmentation

A statistical method for verifying mesh convergence in Monte Carlo simulations with application to fragmentation

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