Multiscale modeling of materials: Computing, data science, uncertainty and goal-oriented optimization

Kovachki, Nikola B.; Liu, Burigede; Sun, Xingsheng; Zhou, Hao; Bhattacharya, Kaushik; Ortiz, Michael; Stuart, Andrew M.

doi:10.1016/j.mechmat.2021.104156

Cited by 24 publications

(11 citation statements)

References 89 publications

(83 reference statements)

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“…Although these forward solver evaluations are embarrassingly parallel, the computational cost might be intractable when the number of parameters

N_{θ}

is large or the forward evaluation is expensive. The use of reduced‐order models, including but not limit to neural network surrogate models, 106‐110 projection‐based reduced order models, 111‐115 and Kernel‐based surrogate models, 116‐118 is worth exploring in the future. For the damage detection problem in Section 4.2, the sensors are uniformly located on the aircraft wing. Optimal sensor placement, 119‐121 which potentially makes data collection more efficient and makes the algorithm converge faster, is worth further investigation.…”

Section: Discussionmentioning

confidence: 99%

Bayesian calibration for large‐scale fluid structure interaction problems under embedded/immersed boundary framework

Cao

Huang

2022

Numerical Meth Engineering

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Bayesian calibration is widely used for inverse analysis and uncertainty analysis for complex systems in the presence of both computer models and observation data. In the present work, we focus on large-scale fluid-structure interaction systems characterized by large structural deformations. Numerical methods to solve these problems, including embedded/immersed boundary methods, are typically not differentiable and lack smoothness. We propose a framework that is built on unscented Kalman filter/inversion to efficiently calibrate and provide uncertainty estimations of such complicated models with noisy observation data. The approach is derivative-free and non-intrusive, and is of particular value for the forward model that is computationally expensive and provided as a black box which is impractical to differentiate. The framework is demonstrated and validated by successfully calibrating the model parameters of a piston problem and identifying the damage field of an aircraft wing under transonic buffeting.

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“…Although these forward solver evaluations are embarrassingly parallel, the computational cost might be intractable when the number of parameters

N_{θ}

Section: Discussionmentioning

confidence: 99%

Bayesian calibration for large‐scale fluid structure interaction problems under embedded/immersed boundary framework

Cao

Huang

2022

Numerical Meth Engineering

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“…The combination of topdown and bottom-up has been proposed as a way to make use of more sources of information at once while also finding compromise between the limitations of either pathway (Panchal et al, 2013;Arróyave and McDowell, 2019;Tallman et al, 2017Tallman et al, , 2020. Some recent work has investigated hierarchical multiscale modeling by generating uncertainty from the bottomup and constraining the variation in a top-down manner (Liu et al, 2021;Kovachki et al, 2022). In the current work, the experimental data provides a top-down constraint for variation, and the quantification of uncertainty from individual sources is left to future work.…”

Section: Discussionmentioning

confidence: 99%

Uncertainty Quantification of a High-Throughput Profilometry-Based Indentation Plasticity Test of Al 7075 T6 Alloy

et al. 2022

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The quantification of spatially variable mechanical response in structural materials remains a challenge. Additive manufacturing methods result in increased spatial property variations—the effect of which on component performance is of key interest. To assist iterative design of additively manufactured prototypes, lower-cost benchtop test methods with high precision and accuracy will be necessary. Profilometry-based indentation plastometry (PIP) promises to improve upon the instrumented indentation test in terms of the measurement uncertainty. PIP uses an isotropic Voce hardening model and inverse numerical methods to identify plasticity parameters. The determination of the baseline uncertainty of PIP test is fundamental to its use in characterizing spatial material property variability in advanced manufacturing. To quantify the uncertainty of the PIP test, ninety-nine PIP tests are performed on prepared portions of a traditionally manufactured Al 7075 plate sample. The profilometry data and the Voce parameter predictions are examined to distinguish contributions of noise, individual measurement uncertainty, and additional set-wide variations. Individual measurement uncertainty is estimated using paired profilometry measurements that are taken from each indentation. Principal component analysis is used to analyze and model the measurement uncertainty. The fitting procedure used within the testing device software is employed to examine the effect of profile variations on plasticity predictions. The expected value of the error in the plasticity parameters is given as a function of the number of tests taken, to support rigorous use of the PIP method. The modeling of variability in the presence of measurement uncertainty is discussed.

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“…Despite the achieved progress, currently available methods are still problematic due to their data-hungry and black-box nature. The state-of-the-art techniques [1][2][3][4][5][6][7][8][9] that either bypass (directly use data as look-up tables in a model-free fashion) or surrogate (encode in, e.g., artificial neural networks (ANNs) or Gaussian processes) material models are rooted in a supervised learning or curve-fitting setting. Hence, they need a large amount of data consisting of input-output, i.e., strain-stress pairs.…”

Section: Introductionmentioning

confidence: 99%

Discovering plasticity models without stress data

2022

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We propose an approach for data-driven automated discovery of material laws, which we call EUCLID (Efficient Unsupervised Constitutive Law Identification and Discovery), and we apply it here to the discovery of plasticity models, including arbitrarily shaped yield surfaces and isotropic and/or kinematic hardening laws. The approach is unsupervised, i.e., it requires no stress data but only full-field displacement and global force data; it delivers interpretable models, i.e., models that are embodied by parsimonious mathematical expressions discovered through sparse regression of a potentially large catalog of candidate functions; it is one-shot, i.e., discovery only needs one experiment. The material model library is constructed by expanding the yield function with a Fourier series, whereas isotropic and kinematic hardening is introduced by assuming a yield function dependency on internal history variables that evolve with the plastic deformation. For selecting the most relevant Fourier modes and identifying the hardening behavior, EUCLID employs physics knowledge, i.e., the optimization problem that governs the discovery enforces the equilibrium constraints in the bulk and at the loaded boundary of the domain. Sparsity promoting regularization is deployed to generate a set of solutions out of which a solution with low cost and high parsimony is automatically selected. Through virtual experiments, we demonstrate the ability of EUCLID to accurately discover several plastic yield surfaces and hardening mechanisms of different complexity.

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Multiscale modeling of materials: Computing, data science, uncertainty and goal-oriented optimization

Cited by 24 publications

References 89 publications

Bayesian calibration for large‐scale fluid structure interaction problems under embedded/immersed boundary framework

Bayesian calibration for large‐scale fluid structure interaction problems under embedded/immersed boundary framework

Uncertainty Quantification of a High-Throughput Profilometry-Based Indentation Plasticity Test of Al 7075 T6 Alloy

Discovering plasticity models without stress data

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