A data-driven computational homogenization method based on neural networks for the nonlinear anisotropic electrical response of graphene/polymer nanocomposites

Lu, Xiaoxin; Giovanis, Dimitris G.; Yvonnet, Julien; Papadopoulos, Vissarion; Detrez, Fabrice; Bai, Jinbo

doi:10.1007/s00466-018-1643-0

Cited by 138 publications

(82 citation statements)

References 47 publications

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“…In macroscopic approaches, the stressstrain relations, or strain energy density functions, are directly fitted by regression methods, like deep neural network (DNN) [23,24,25,26] and Kriging methods [26,27]. Enabled by recent progresses in computer hardware systems, DNN becomes one of the most popular tools due to its large model generalities [28,29], and has also stimulated applications across different engineering disciplines [30,31,32,33]. However, the extrapolation capability of the macroscopic approaches to unknown material and loading spaces is usually limited by the lack of microscale physics.…”

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confidence: 99%

Exploring the 3D architectures of deep material network in data-driven multiscale mechanics

Liu

2019

Journal of the Mechanics and Physics of Solids

141

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This paper extends the deep material network (DMN) proposed by Liu et al. (2019) [1] to tackle general 3-dimensional (3D) problems with arbitrary material and geometric nonlinearities. It discovers a new way of describing multiscale heterogeneous materials by a multi-layer network structure and mechanistic building blocks. The data-driven framework of DMN is discussed in detail about the offline training and online extrapolation stages. Analytical solutions of the 3D building block with a two-layer structure in both small-and finite-strain formulations are derived based on interfacial equilibrium conditions and kinematic constraints. With linear elastic data generated by direct numerical simulations on a representative volume element (RVE), the network can be effectively trained in the offline stage using stochastic gradient descent and advanced model compression algorithms. Efficiency and accuracy of DMN on addressing the long-standing 3D RVE challenges with complex morphologies and material laws are validated through numerical experiments, including 1) hyperelastic particle-reinforced rubber composite with Mullins effect; 2) polycrystalline materials with rate-dependent crystal plasticity; 3) carbon fiber reinforced polymer (CFRP) composites with fiber anisotropic elasticity and matrix plasticity. In particular, we demonstrate a threescale homogenization procedure of CFRP system by concatenating the microscale and mesoscale material networks. The complete learning and extrapolation procedures of DMN establish a reliable data-driven framework for multiscale material modeling and design.anisotropic responses, and may require burdensome calibration to find the model parameters. As a result, homogenization based on the concept of representative volume element (RVE) [11] has become an important approach to model multiscale materials [12]. Many analytical methods have been proposed, which adopt some micromechanics assumptions to simplify the full-field RVE problem, such as Hashin-Shtrikman bounds [13,14], the Mori-Tanaka method [15] and self-consistent methods [16]. Since most analytical methods are derived based on the solution for regular geometries and simple material models (e.g. Eshelby's solution for isotropic elastic materials [17]), it is usually difficult for them to consider complex microstructural morphologies, history-dependent materials and large deformations. Additionally, direct numerical simulation (DNS) tools, such as finite element [18], meshfree [19,20] and fast Fourier transform (FFT)-based micromechanics methods [21,22], are both flexible and accurate. However, a DNS model involves a detailed meshing of the RVE microstructures and requires tremendous computational cost, especially for 3D problems. Therefore, one of the fundamental issues in multiscale material modeling and design is how to find an accurate low-dimensional representation of the RVE for arbitrary morphologies and nonlinearities.In the past decade, a plethora of data-driven material modeling methods have been proposed based on exist...

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confidence: 99%

Exploring the 3D architectures of deep material network in data-driven multiscale mechanics

Liu

2019

Journal of the Mechanics and Physics of Solids

141

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“…In [55], ANNs are used in combination with FE simulations in order to capture the hydro-mechanical coupling of porous media. Based on FE simulations, trained ANNs can show excellent results in predicting the effective electrical response of graphene/polymer nanocomposites and in macroscopic computations [56]. An on-the-fly adaptive scheme with error estimators is developed in [57], allowing the flexible switching between highly efficient microscaletrained ANNs and the physics-driven reduced-order model in macroscopic mechanical FE simulations.…”

Section: Machine Learning Methods As An Alternative To Materials Modelsmentioning

confidence: 99%

Application of artificial neural networks for the prediction of interface mechanics: a study on grain boundary constitutive behavior

Fernández

Rezaei

Mianroodi

et al. 2020

Adv. Model. and Simul. in Eng. Sci.

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The present work aims at the identification of the effective constitutive behavior of 5 aluminum grain boundaries (GB) for proportional loading by using machine learning (ML) techniques. The input for the ML approach is high accuracy data gathered in challenging molecular dynamics (MD) simulations at the atomic scale for varying temperatures and loading conditions. The effective traction-separation relation is recorded during the MD simulations. The raw MD data then serves for the training of an artificial neural network (ANN) as a surrogate model of the constitutive behavior at the grain boundary. Despite the extremely fluctuating nature of the MD data and its inhomogeneous distribution in the traction-separation space, the ANN surrogate trained on the raw MD data shows a very good agreement in the average behavior without any data-smoothing or pre-processing. Further, it is shown that the trained traction-separation ANN captures important physical properties and is able to predict traction values for given separations not contained in the training data. For example, MD simulations show a transition in traction-separation behaviour from pure sliding mode under shear load to combined GB sliding and decohesion with intermediate hardening regime at mixed load directions. These changes in GB behaviour are fully captured in the ANN predictions. Furthermore, by construction, the ANN surrogate is differentiable for arbitrary separation and also temperature, such that a thermo-mechanical tangent stiffness operator can always be evaluated. The trained ANN can then serve for large-scale FE simulation as an alternative to direct MD-FE coupling which is often infeasible in practical applications.

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“…The training itself may be computationally expensive, but it can be done offline, whereas the required online computation of the response function is not more expensive than conventional phenomenological models. Either experimental data can be used for training [1,13,19,45] or RVE simulations [11,15,23,27,28,34,43].…”

Section: Introductionmentioning

confidence: 99%

“…Several authors [11,34,37,45] trained the non-linear stress-strain relationship, corresponding to a pseudo-plastic Cauchy-elastic material behavior. In a similar way, a non-linear conductivity problem was addressed by neural networks [28]. Kirchdoerfer and Ortiz [22] minimized the distance between actual states (of stress and strain) and training data directly within their "data-driven computing" approach, assuming that the material possesses an inherent Cauchy-elastic relation.…”

Section: Introductionmentioning

confidence: 99%

A hybrid approach to simulate the homogenized irreversible elastic–plastic deformations and damage of foams by neural networks

Settgast

Hütter

Kuna

et al. 2020

International Journal of Plasticity

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Classically, the constitutive behavior of materials is described either phenomenologically, or by homogenization approaches. Phenomenological approaches are computationally very efficient, but are limited for complex non-linear and irreversible mechanisms. Such complex mechanisms can be described well by computational homogenization, but respective FE 2 computations are very expensive.As an alternative way, neural networks have been proposed for constitutive modeling, using either experiments or computational homogenization results for training. However, the application of this method to irreversible material behavior is not trivial.The present contribution presents a hybrid methodology to embed neural networks into the established framework of rate-independent plasticity. Both, the yield function and the evolution equations of internal state variables are represented by neural networks. Respective training data for a foam material are generated from RVE-simulations under monotonic loading. It is demonstrated that this hybrid multi-scale neural network approach (HyMNNA) allows to simulate efficiently even the anisotropic elastic-plastic behavior of foam structures with coupled anisotropic evolution of damage and non-associated plastic flow.

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A data-driven computational homogenization method based on neural networks for the nonlinear anisotropic electrical response of graphene/polymer nanocomposites

Cited by 138 publications

References 47 publications

Exploring the 3D architectures of deep material network in data-driven multiscale mechanics

Exploring the 3D architectures of deep material network in data-driven multiscale mechanics

Application of artificial neural networks for the prediction of interface mechanics: a study on grain boundary constitutive behavior

A hybrid approach to simulate the homogenized irreversible elastic–plastic deformations and damage of foams by neural networks

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