Surrogate modeling of elasto-plastic problems via long short-term memory neural networks and proper orthogonal decomposition

Im, Sun-Young; Lee, Jonggeon; Cho, Maenghyo

doi:10.1016/j.cma.2021.114030

Cited by 53 publications

(18 citation statements)

References 47 publications

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“…Furthermore, because of their limited functionality, the newly introduced routines are easily verified. This is a significant advantage over existing non-intrusive surrogate models such as [50][51][52]58], which are powerful but relatively difficult to validate.…”

Section: Fig 4 Relative Error Of Numerical Integration For Different ...mentioning

confidence: 99%

“…deep-trained FE [49], that aim to resolve computational bottlenecks in FE. Furthermore, neural networks have demonstrated unprecedented efficiency in predicting the solutions of computationally expensive simulations, such as nonlinear finite element analysis [50,51], convective operation [52], asymptotic homogenization [53,54], and multiscale analysis [55].…”

Section: Introductionmentioning

confidence: 99%

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An ANN-assisted efficient enriched finite element method via the selective enrichment of moment fitting

Lee

Kang²,

Jung

et al. 2023

Engineering with Computers

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Enrichment techniques that employ nonconforming mesh are effective in modeling structures with discontinuities because numerical issues regarding mesh quality are avoided. However, the accurate integration of the bilinear and linear forms on the discretized domain, which is required in the standard Galerkin-based finite element method, is computationally expensive due to the complexity of the enriched basis function. In this paper, we present a fast and accurate alternative method of numerical integration using nonlinear regression enabled by a multiperceptron feedforward neural network. The relationship between an implicitly represented geometry and the quadrature rule derived from the moment fitting method is predicted by the neural network; the neural network-based regression model circumvents complex computation and significantly reduces the overall online time by avoiding expensive function evaluations. Through the selected numerical examples, we demonstrate the efficiency and accuracy of the current method, as well as the flexibility of the trained network to be used in different contexts.

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Section: Fig 4 Relative Error Of Numerical Integration For Different ...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An ANN-assisted efficient enriched finite element method via the selective enrichment of moment fitting

Lee

Kang²,

Jung

et al. 2023

Engineering with Computers

View full text Add to dashboard Cite

show abstract

“…Based on the history of plastic deformations, the incremental solution is derived from the connection between a tiny stress increment and a little strain increment corresponding to the stress state. [31]- [35] In this part, we first describe the mechanics of the dissolving process before rewriting the incremental relationships for an elastoplastic material in the form of a matrix. In the matrix form, the stress increment {dσ(𝑥, 𝜃)} can be expressed by the elastic strain increment term {𝑑𝜖 𝑒 (𝑥, 𝜃)} or the general strain increment, {d𝟄(𝑥, 𝜃)}, as follows:…”

Section: 4mentioning

confidence: 99%

Generalization of spectral stochastic finite element method for analysis of structures with elastoplastic materials

rahimibondarabadi¹,

mousaviamjad²

2022

Preprint

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The significance of the influence of uncertainty and stochastic approach-related problems on engineering system analysis is now evident and irrefutable. On the other hand, considering the factors that apply these uncertainties in the findings should need a significant amount of computing cost and effort, which is why researchers are always looking for approaches that combine high calculation accuracy with speed. One of the most useful tools for analyzing systems with uncertainty in computational stochastic mechanics is the spectral stochastic finite element method. In the present paper, by applying uncertainty to the applied loads and elastic modulus, this method has been developed to analyze the structures with nonlinear materials, and a method called the nonlinear spectral stochastic finite element method (NLSSFEM) has been proposed. The results obtained from the used method have been compared with the results obtained from the Monte Carlo simulation method. The accuracy of calculations and the speed of access to the solution of the proposed method are evaluated as desirable.

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“…Several recent studies also focused on adopting deep neural networks for multiscale simulations of heterogeneous solids [23][24][25]. As an example, a computational framework to establish a datadriven constitutive model for heterogeneous path-dependent composites has been implemented to predict the stress-strain relationships via the principal values [26], in which adopted separate data-driven models were adopted for elastic and plastic parts, respectively.…”

Section: Introductionmentioning

confidence: 99%

A single Long Short-Term Memory network for enhancing the prediction of path-dependent plasticity with material heterogeneity and anisotropy

Haghighi¹,

Na²

2022

Preprint

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This study presents applicability of conventional deep recurrent neural networks (RNN) to predict path-dependent plasticity associated with material heterogeneity and anisotropy. Although the architecture of RNN possess inductive biases toward information over time, it is a still challenging to to learn the path-dependent material behavior as a function of loading path considering the change from elastic to elasto-plastic regimes. Our attempt is to develop a simple machine-learning based model that can replicate elastoplastic behaviors considering material heterogeneity and anisotropy. The basic Long-Short Term Memory Unit (LSTM) is adopted for the modeling of plasticity in the two-dimensional space by enhancing the inductive bias toward the past information through manipulating input variables. Our results find that a single LSTM based model can capture the J2 plasticity responses under both monotonic and arbitrary loading paths provided the material heterogeneity. The proposed neural network architecture is then used to model elasto-plastic responses of a two-dimensional transversely anisotropic material associated with computational homogenization (FE 2 ). It is also found that a single LSTM model can be used to accurately and effectively capture the path-dependent responses of heterogeneous and anisotropic microstructures under arbitrary mechanical loading conditions.

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Surrogate modeling of elasto-plastic problems via long short-term memory neural networks and proper orthogonal decomposition

Cited by 53 publications

References 47 publications

An ANN-assisted efficient enriched finite element method via the selective enrichment of moment fitting

An ANN-assisted efficient enriched finite element method via the selective enrichment of moment fitting

Generalization of spectral stochastic finite element method for analysis of structures with elastoplastic materials

A single Long Short-Term Memory network for enhancing the prediction of path-dependent plasticity with material heterogeneity and anisotropy

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