Geometric deep learning for computational mechanics Part I: anisotropic hyperelasticity

Vlassis, Nikolaos N.; Ma, Rong; Sun, WaiChing

doi:10.1016/j.cma.2020.113299

Cited by 172 publications

(89 citation statements)

References 99 publications

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“…Following this line, Ref. [49] introduced a graph convolutional deep neural network, incorporating the non-Euclidean weighted graph data to predict the elastic response of materials with complex microstructures. For recent works on CNNs, we refer to [50][51][52], and the citations therein.…”

Section: Deep Learning (Dl) Architecturesmentioning

confidence: 99%

Feed-Forward Neural Networks for Failure Mechanics Problems

2021

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This work addresses an efficient neural network (NN) representation for the phase-field modeling of isotropic brittle fracture. In recent years, data-driven approaches, such as neural networks, have become an active research field in mechanics. In this contribution, deep neural networks—in particular, the feed-forward neural network (FFNN)—are utilized directly for the development of the failure model. The verification and generalization of the trained models for elasticity as well as fracture behavior are investigated by several representative numerical examples under different loading conditions. As an outcome, promising results close to the exact solutions are produced.

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Section: Deep Learning (Dl) Architecturesmentioning

confidence: 99%

Feed-Forward Neural Networks for Failure Mechanics Problems

2021

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“…(3) by setting γ 3 = 0. An H 1 norm loss function for a hyperelastic energy functional can be seen in Vlassis et al [18].…”

Section: Sobolev Training Of a Hyperelastic Energy Functionalmentioning

confidence: 99%

“…The major issue that limits the adaptations of neural network constitutive models is the lack of interpretability and the vulnerability to overfitting. While there are existing regularization techniques such as dropout layers [16], cross-validation [17,18], and/or increasing the size of the database that could be helpful, it remains difficult to assess their credibility without the interpretability of the underlying laws deduced from the neural network. Another approach could involve symbolic regression through reinforcement learning [3] or genetic algorithms [19] that may lead to explicitly written evolution laws, however, the fitness of these equations is often at the expense of readability.…”

Section: Introductionmentioning

confidence: 99%

“…In both cases, there are several key upshots brought by the existence of the yield function. For instance, the existence of a yield function facilitates the geometric interpretation of plasticity and, therefore, enables us to connect mechanics concepts, such as the thermodynamic law, with geometric concepts, such as convexity in the principal stress space [18,29,30]. Furthermore, the existence of a distinctive elastic region in the stress or strain space also allows introducing a multi-step transfer learning strategy.…”

Section: Introductionmentioning

confidence: 99%

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Sobolev training of thermodynamic-informed neural networks for interpretable elasto-plasticity models with level set hardening

Vlassis

Sun

2021

Computer Methods in Applied Mechanics and Engineering

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134

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We introduce a deep learning framework designed to train smoothed elastoplasticity models with interpretable components, such as the stored elastic energy function, yield surface, and plastic flow that evolve based on a set of deep neural network predictions. By recasting the yield function as an evolving level set, we introduce a deep learning approach to deduce the solutions of the Hamilton-Jacobi equation that governs the hardening/softening mechanism. This machine learning hardening law may recover any classical hand-crafted hardening rules and discover new mechanisms that are either unbeknownst or difficult to express with mathematical expressions. Leveraging Sobolev training to gain control over the derivatives of the learned functions, the resultant machine learning elastoplasticity models are thermodynamically consistent, interpretable, while exhibiting excellent learning capacity. Using a 3D FFT solver to create a polycrystal database, numerical experiments are conducted and the implementations of each component of the models are individually verified. Our numerical experiments reveal that this new approach provides more robust and accurate forward predictions of cyclic stress paths than those obtained from black-box deep neural network models such as the recurrent neural network, the 1D convolutional neural network, and the multi-step feed-forward model. c

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“…Other works have represented designs as graphs. [25] used a graph-based convolutional model to learn fluid dynamics on meshed surfaces, [27] used a similar approach to learn the structural behavior of a thin shell, and [28] learned material properties from graph-based microstructures. The closest existing work to this one is probably [29], in which graph representations of trusses were used to optimize cross section sizes for struc-tural loads.…”

Section: Surrogate Modeling Without Parametric Design Fea-mentioning

confidence: 99%

Toward Reusable Surrogate Models: Graph-Based Transfer Learning on Trusses

Whalen

Mueller

2021

Journal of Mechanical Design

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Surrogate models are often employed to speed up engineering design optimization; however, they typically require that all training data conform to the same parametrization (e.g. design variables), limiting design freedom and prohibiting the reuse of historical data. In response, this paper proposes Graph-based Surrogate Models (GSMs) for space frame structures. The GSM can accurately predict displacement fields from static loads given the structure's geometry as input, enabling training across multiple parametrizations. GSMs build upon recent advancements in geometric deep learning which have led to the ability to learn on undirected graphs: a natural representation for space frames. To further promote flexible surrogate models, the paper explores transfer learning within the context of engineering design, and demonstrates positive knowledge transfer across data sets of different topologies, complexities, loads and applications, resulting in more flexible and data-efficient surrogate models for space frame structures.

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Geometric deep learning for computational mechanics Part I: anisotropic hyperelasticity

Cited by 172 publications

References 99 publications

Feed-Forward Neural Networks for Failure Mechanics Problems

Feed-Forward Neural Networks for Failure Mechanics Problems

Sobolev training of thermodynamic-informed neural networks for interpretable elasto-plasticity models with level set hardening

Toward Reusable Surrogate Models: Graph-Based Transfer Learning on Trusses

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