Statistically informed upscaling of damage evolution in brittle materials

Vaughn, Nathan; Kononov, Alina; Moore, Bryan A.; Rougier, Esteban; Viswanathan, Hari; Hunter, Abigail

doi:10.1016/j.tafmec.2019.04.012

Cited by 10 publications

(2 citation statements)

References 52 publications

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“…This implies that the material response we obtain at macro-scale scale includes crack interactions at micro-scale, which are typically lost if one employs traditional mechanistic or homogenization approaches [57,66,67,90]. An example of an upscaling method, which could make use of the proposed surrogate models to calculate effective elastic moduli, is described in reference [91].…”

Section: Estimating Failure Pathsmentioning

confidence: 99%

Surrogate Models for Estimating Failure in Brittle and Quasi-Brittle Materials

et al. 2019

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In brittle fracture applications, failure paths, regions where the failure occurs and damage statistics, are some of the key quantities of interest (QoI). High-fidelity models for brittle failure that accurately predict these QoI exist but are highly computationally intensive, making them infeasible to incorporate in upscaling and uncertainty quantification frameworks. The goal of this paper is to provide a fast heuristic to reasonably estimate quantities such as failure path and damage in the process of brittle failure. Towards this goal, we first present a method to predict failure paths under tensile loading conditions and low-strain rates. The method uses a k-nearest neighbors algorithm built on fracture process zone theory, and identifies the set of all possible pre-existing cracks that are likely to join early to form a large crack. The method then identifies zone of failure and failure paths using weighted graphs algorithms. We compare these failure paths to those computed with a high-fidelity fracture mechanics model called the Hybrid Optimization Software Simulation Suite (HOSS). A probabilistic evolution model for average damage in a system is also developed that is trained using 150 HOSS simulations and tested on 40 simulations. A non-parametric approach based on confidence intervals is used to determine the damage evolution over time along the dominant failure path. For upscaling, damage is the key QoI needed as an input by the continuum models. This needs to be informed accurately by the surrogate models for calculating effective moduli at continuum-scale. We show that for the proposed average damage evolution model, the prediction accuracy on the test data is more than 90%. In terms of the computational time, the proposed models are ≈ O ( 10 6 ) times faster compared to high-fidelity fracture simulations by HOSS. These aspects make the proposed surrogate model attractive for upscaling damage from micro-scale models to continuum models. We would like to emphasize that the surrogate models are not a replacement of physical understanding of fracture propagation. The proposed method in this paper is limited to tensile loading conditions at low-strain rates. This loading condition corresponds to a dominant fracture perpendicular to tensile direction. The proposed method is not applicable for in-plane shear, out-of-plane shear, and higher strain rate loading conditions.

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Section: Estimating Failure Pathsmentioning

confidence: 99%

Surrogate Models for Estimating Failure in Brittle and Quasi-Brittle Materials

et al. 2019

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“…The evolution, growth, and interaction of cracks is key to modeling damage behavior in several brittle materials such as granite, concrete, metals, and ceramics [24,31,10,16]. A recent novel alternative is to bridge continuum and mesoscales by developing and implementing a continuum-scale effective-moduli constitutive model that is informed by crack statistics generated from the mesoscale simulations in low-strain-rate [43] or highstrain-rate [23] conditions. However, the cost of generating large datasets can also be prohibitive if this comes from computationally intensive high-fidelity simulations.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty Bounds for Multivariate Machine Learning Predictions on High-Strain Brittle Fracture

Garcia-Cardona¹,

Fernández-Godino²,

O’Malley³

et al. 2020

Preprint

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Simulation of the crack network evolution on high strain rate impact experiments performed in brittle materials is very compute-intensive. The cost increases even more if multiple simulations are needed to account for the randomness in crack length, location, and orientation, which is inherently found in real-world materials. Constructing a machine learning emulator can make the process faster by orders of magnitude. There has been little work, however, on assessing the error associated with their predictions. Estimating these errors is imperative for meaningful overall uncertainty quantification. In this work, we extend the heteroscedastic uncertainty estimates to bound a multiple output machine learning emulator. We find that the response prediction is robust with a somewhat conservative estimate of uncertainty.

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