Bayesian-EUCLID: Discovering hyperelastic material laws with uncertainties

Joshi, Akshay; Thakolkaran, Prakash; Zheng, Yiwen; Escande, Maxime; Flaschel, Moritz; Lorenzis, Laura De; Kumar, Siddhant

doi:10.1016/j.cma.2022.115225

Cited by 29 publications

(5 citation statements)

References 60 publications

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“…The weak form is then minimized with respect to θ using a fixed-point iteration scheme (inspired by [422]), where a L p -regularization is used to promote sparsity in θ. Despite its young age, the approach has already been applied to plasticity [423], viscoelasticity [424], combinations [425], and has been extended to incorporate uncertainties through a Bayesian model [426]. Furthermore, the approach has been extended with an ensemble of input-convex NNs [413], yielding a more accurate, but less interpretable model.…”

Section: Model Identificationmentioning

confidence: 99%

Deep learning in computational mechanics: a review

Herrmann,

Kollmannsberger

2024

Comput Mech

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The rapid growth of deep learning research, including within the field of computational mechanics, has resulted in an extensive and diverse body of literature. To help researchers identify key concepts and promising methodologies within this field, we provide an overview of deep learning in deterministic computational mechanics. Five main categories are identified and explored: simulation substitution, simulation enhancement, discretizations as neural networks, generative approaches, and deep reinforcement learning. This review focuses on deep learning methods rather than applications for computational mechanics, thereby enabling researchers to explore this field more effectively. As such, the review is not necessarily aimed at researchers with extensive knowledge of deep learning—instead, the primary audience is researchers on the verge of entering this field or those attempting to gain an overview of deep learning in computational mechanics. The discussed concepts are, therefore, explained as simple as possible.

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Section: Model Identificationmentioning

confidence: 99%

Deep learning in computational mechanics: a review

Herrmann,

Kollmannsberger

2024

Comput Mech

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“…In the following, we describe our novel approach to automatically discover generalized standard (hence, stable and thermodynamically consistent) material models based on full-field displacement and global force data. The backbone of the approach, which we denote as EUCLID in line with our previous work [18,30,32,41], can be outlined as follows: we start from a very wide material model space, which we construct by exploiting the flexibility and a priori thermodynamic consistency of the generalized standard material model framework; we constrain this model space by enforcing the satisfaction of momentum balance (in weak sense) on the source data; we exploit sparse regression to ensure parsimonity of the discovered model. Through these three key ingredients, we end up simultaneously performing model selection and identification of the unknown material parameters.…”

Section: Automated Discovery Of Generalized Standard Materials Modelsmentioning

confidence: 99%

“…By leveraging sparse regression [29,39,40], it is ensured that a parsimonious and interpretable material model, i.e., one with a small number of terms and parameters, is discovered. Later works on EUCLID include a study of the problem from a Bayesian perspective for quantifying the uncertainty in the discovered models [41] and an unsupervised training framework for artificial neural networks [18]. For related works that aim to identify material parameters of an a priori known constitutive model or train uninterpretable blackbox machine learning models in an unsupervised fashion, the reader is referred to works by Man and Furukawa [42], Huang et al [43], Liu et al [44], Amores et al [45], Anton and Wessels [46].…”

Section: Introductionmentioning

confidence: 99%

Automated discovery of generalized standard material models with EUCLID

Flaschel

Kumar

Lorenzis

2023

Computer Methods in Applied Mechanics and Engineering

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“…EUCLID can automatically discover the target model from a large library of interpretable candidate material models, with the input of full-field displacements and global reaction forces instead of labeled stress-strain data pairs. Until now, EUCLID has been successfully demonstrated for hyperelasticity (Flaschel et al, 2021c,b,a;Joshi et al, 2022;Flaschel et al, 2023b), viscoelasticity (Marino et al, 2023), pressure-insensitive associated plasticity (Flaschel et al, 2022a,c,b), and generalized standard material models (Flaschel et al, 2023a).…”

Section: Introductionmentioning

confidence: 99%

Discovering non-associated pressure-sensitive plasticity models with EUCLID

Xu,

Flaschel,

De Lorenzis

2024

Preprint

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We extend EUCLID (Efficient Unsupervised Constitutive Law Identification and Discovery) – a data-driven framework for automated material model discovery – to pressure-sensitive plasticity models, encompassing arbitrarily shaped yield surfaces with convexity constraints and non-associated flow rules. The method only requires full-field displacement and boundary force data from one single experiment and delivers constitutive laws as interpretable mathematical expressions. We construct a material model library for pressure-sensitive plasticity models with nonassociated flow rules in four steps: (1) a Fourier series describes an arbitrary yield surface shape in the deviatoric stress plane; (2) a pressure-sensitive term in the yield function defines the shape of the shear failure surface and determines plastic deformation under tension; (3) a compression cap term determines plastic deformation under compression; (4) a non-associated flow rule may be adopted to avoid the excessive dilatancy induced by plastic deformations. In contrast to traditional parameter identification methods, EUCLID is equipped with a sparsity promoting regularization to restrain the number of model parameters (and thus modeling features) to the minimum needed to accurately interpret the data, thus achieving a compromise between model simplicity and accuracy. The convexity of the learned yield surface is guaranteed by a set of constraints in the inverse optimization problem. We demonstrate the proposed approach in multiple numerical experiments with noisy data, and show the ability of EUCLID to accurately select a suitable material model from the starting library.

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Bayesian-EUCLID: Discovering hyperelastic material laws with uncertainties

Cited by 29 publications

References 60 publications

Deep learning in computational mechanics: a review

Deep learning in computational mechanics: a review

Automated discovery of generalized standard material models with EUCLID

Discovering non-associated pressure-sensitive plasticity models with EUCLID

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