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4 pages, 190 KiB

Open AccessEditorial

Empowering Materials Processing and Performance from Data and AI

by Francisco Chinesta, Elias Cueto and Benjamin Klusemann

Materials 2021, 14(16), 4409; https://doi.org/10.3390/ma14164409 - 6 Aug 2021

Cited by 1 | Viewed by 1255

Abstract

Third millennium engineering is addressing new challenges in materials sciences and engineering [...] Full article

(This article belongs to the Special Issue Empowering Materials Processing and Performance from Data and AI)

Research

Jump to: Editorial

23 pages, 7936 KiB

Open AccessArticle

A Stochastic FE² Data-Driven Method for Nonlinear Multiscale Modeling

by Xiaoxin Lu, Julien Yvonnet, Leonidas Papadopoulos, Ioannis Kalogeris and Vissarion Papadopoulos

Materials 2021, 14(11), 2875; https://doi.org/10.3390/ma14112875 - 27 May 2021

Cited by 21 | Viewed by 2986

Abstract

A stochastic data-driven multilevel finite-element (FE

^{2}

) method is introduced for random nonlinear multiscale calculations. A hybrid neural-network–interpolation (NN–I) scheme is proposed to construct a surrogate model of the macroscopic nonlinear constitutive law from representative-volume-element calculations, whose results are used as input [...] Read more.

A stochastic data-driven multilevel finite-element (FE

^{2}

) method is introduced for random nonlinear multiscale calculations. A hybrid neural-network–interpolation (NN–I) scheme is proposed to construct a surrogate model of the macroscopic nonlinear constitutive law from representative-volume-element calculations, whose results are used as input data. Then, a FE

^{2}

method replacing the nonlinear multiscale calculations by the NN–I is developed. The NN–I scheme improved the accuracy of the neural-network surrogate model when insufficient data were available. Due to the achieved reduction in computational time, which was several orders of magnitude less than that to direct FE

^{2}

, the use of such a machine-learning method is demonstrated for performing Monte Carlo simulations in nonlinear heterogeneous structures and propagating uncertainties in this context, and the identification of probabilistic models at the macroscale on some quantities of interest. Applications to nonlinear electric conduction in graphene–polymer composites are presented. Full article

(This article belongs to the Special Issue Empowering Materials Processing and Performance from Data and AI)

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19 pages, 1613 KiB

Open AccessArticle

Hybrid Modelling by Machine Learning Corrections of Analytical Model Predictions towards High-Fidelity Simulation Solutions

by Frederic E. Bock, Sören Keller, Norbert Huber and Benjamin Klusemann

Materials 2021, 14(8), 1883; https://doi.org/10.3390/ma14081883 - 10 Apr 2021

Cited by 12 | Viewed by 3308

Abstract

Within the fields of materials mechanics, the consideration of physical laws in machine learning predictions besides the use of data can enable low prediction errors and robustness as opposed to predictions only based on data. On the one hand, exclusive utilization of fundamental [...] Read more.

Within the fields of materials mechanics, the consideration of physical laws in machine learning predictions besides the use of data can enable low prediction errors and robustness as opposed to predictions only based on data. On the one hand, exclusive utilization of fundamental physical relationships might show significant deviations in their predictions compared to reality, due to simplifications and assumptions. On the other hand, using only data and neglecting well-established physical laws can create the need for unreasonably large data sets that are required to exhibit low bias and are usually expensive to collect. However, fundamental but simplified physics in combination with a corrective model that compensates for possible deviations, e.g., to experimental data, can lead to physics-based predictions with low prediction errors, also despite scarce data. In this article, it is demonstrated that a hybrid model approach consisting of a physics-based model that is corrected via an artificial neural network represents an efficient prediction tool as opposed to a purely data-driven model. In particular, a semi-analytical model serves as an efficient low-fidelity model with noticeable prediction errors outside its calibration domain. An artificial neural network is used to correct the semi-analytical solution towards a desired reference solution provided by high-fidelity finite element simulations, while the efficiency of the semi-analytical model is maintained and the applicability range enhanced. We utilize residual stresses that are induced by laser shock peening as a use-case example. In addition, it is shown that non-unique relationships between model inputs and outputs lead to high prediction errors and the identification of salient input features via dimensionality analysis is highly beneficial to achieve low prediction errors. In a generalization task, predictions are also outside the process parameter space of the training region while remaining in the trained range of corrections. The corrective model predictions show substantially smaller errors than purely data-driven model predictions, which illustrates one of the benefits of the hybrid modelling approach. Ultimately, when the amount of samples in the data set is reduced, the generalization of the physics-related corrective model outperforms the purely data-driven model, which also demonstrates efficient applicability of the proposed hybrid modelling approach to problems where data is scarce. Full article

(This article belongs to the Special Issue Empowering Materials Processing and Performance from Data and AI)

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23 pages, 16401 KiB

Open AccessArticle

A Strategy for Dimensionality Reduction and Data Analysis Applied to Microstructure–Property Relationships of Nanoporous Metals

by Norbert Huber

Materials 2021, 14(8), 1822; https://doi.org/10.3390/ma14081822 - 7 Apr 2021

Cited by 10 | Viewed by 3054

Abstract

Nanoporous metals, with their complex microstructure, represent an ideal candidate for the development of methods that combine physics, data, and machine learning. The preparation of nanporous metals via dealloying allows for tuning of the microstructure and macroscopic mechanical properties within a large design [...] Read more.

Nanoporous metals, with their complex microstructure, represent an ideal candidate for the development of methods that combine physics, data, and machine learning. The preparation of nanporous metals via dealloying allows for tuning of the microstructure and macroscopic mechanical properties within a large design space, dependent on the chosen dealloying conditions. Specifically, it is possible to define the solid fraction, ligament size, and connectivity density within a large range. These microstructural parameters have a large impact on the macroscopic mechanical behavior. This makes this class of materials an ideal science case for the development of strategies for dimensionality reduction, supporting the analysis and visualization of the underlying structure–property relationships. Efficient finite element beam modeling techniques were used to generate ~200 data sets for macroscopic compression and nanoindentation of open pore nanofoams. A strategy consisting of dimensional analysis, principal component analysis, and machine learning allowed for data mining of the microstructure–property relationships. It turned out that the scaling law of the work hardening rate has the same exponent as the Young’s modulus. Simple linear relationships are derived for the normalized work hardening rate and hardness. The hardness to yield stress ratio is not limited to 1, as commonly assumed for foams, but spreads over a large range of values from 0.5 to 3. Full article

(This article belongs to the Special Issue Empowering Materials Processing and Performance from Data and AI)

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19 pages, 3557 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Evaluation of Ti–Mn Alloys for Additive Manufacturing Using High-Throughput Experimental Assays and Gaussian Process Regression

by Xinyi Gong, Yuksel C. Yabansu, Peter C. Collins and Surya R. Kalidindi

Materials 2020, 13(20), 4641; https://doi.org/10.3390/ma13204641 - 17 Oct 2020

Cited by 16 | Viewed by 3892

Abstract

Compositionally graded cylinders of Ti–Mn alloys were produced using the Laser Engineered Net Shaping (LENS™) technique, with Mn content varying from 0 to 12 wt.% along the cylinder axis. The cylinders were subjected to different post-build heat treatments to produce a large sample [...] Read more.

Compositionally graded cylinders of Ti–Mn alloys were produced using the Laser Engineered Net Shaping (LENS™) technique, with Mn content varying from 0 to 12 wt.% along the cylinder axis. The cylinders were subjected to different post-build heat treatments to produce a large sample library of α–β microstructures. The microstructures in the sample library were studied using back-scattered electron (BSE) imaging in a scanning electron microscope (SEM), and their mechanical properties were evaluated using spherical indentation stress–strain protocols. These protocols revealed that the microstructures exhibited features with averaged chord lengths in the range of 0.17–1.78 μm, and beta content in the range of 20–83 vol.%. The estimated values of the Young’s moduli and tensile yield strengths from spherical indentation were found to vary in the ranges of 97–130 GPa and 828–1864 MPa, respectively. The combined use of the LENS technique along with the spherical indentation protocols was found to facilitate the rapid exploration of material and process spaces. Analyses of the correlations between the process conditions, several key microstructural features, and the measured material properties were performed via Gaussian process regression (GPR). These data-driven statistical models provided valuable insights into the underlying correlations between these variables. Full article

(This article belongs to the Special Issue Empowering Materials Processing and Performance from Data and AI)

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21 pages, 3159 KiB

Open AccessArticle

A Methodology for the Statistical Calibration of Complex Constitutive Material Models: Application to Temperature-Dependent Elasto-Visco-Plastic Materials

by Juan Luis de Pablos, Edoardo Menga and Ignacio Romero

Materials 2020, 13(19), 4402; https://doi.org/10.3390/ma13194402 - 2 Oct 2020

Cited by 7 | Viewed by 2289

Abstract

The calibration of any sophisticated model, and in particular a constitutive relation, is a complex problem that has a direct impact in the cost of generating experimental data and the accuracy of its prediction capacity. In this work, we address this common situation [...] Read more.

The calibration of any sophisticated model, and in particular a constitutive relation, is a complex problem that has a direct impact in the cost of generating experimental data and the accuracy of its prediction capacity. In this work, we address this common situation using a two-stage procedure. In order to evaluate the sensitivity of the model to its parameters, the first step in our approach consists of formulating a meta-model and employing it to identify the most relevant parameters. In the second step, a Bayesian calibration is performed on the most influential parameters of the model in order to obtain an optimal mean value and its associated uncertainty. We claim that this strategy is very efficient for a wide range of applications and can guide the design of experiments, thus reducing test campaigns and computational costs. Moreover, the use of Gaussian processes together with Bayesian calibration effectively combines the information coming from experiments and numerical simulations. The framework described is applied to the calibration of three widely employed material constitutive relations for metals under high strain rates and temperatures, namely, the Johnson–Cook, Zerilli–Armstrong, and Arrhenius models. Full article

(This article belongs to the Special Issue Empowering Materials Processing and Performance from Data and AI)

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12 pages, 1166 KiB

Open AccessArticle

Nonlinear Regression Operating on Microstructures Described from Topological Data Analysis for the Real-Time Prediction of Effective Properties

by Minyoung Yun, Clara Argerich, Elias Cueto, Jean Louis Duval and Francisco Chinesta

Materials 2020, 13(10), 2335; https://doi.org/10.3390/ma13102335 - 19 May 2020

Cited by 13 | Viewed by 2365

Abstract

Real-time decision making needs evaluating quantities of interest (QoI) in almost real time. When these QoI are related to models based on physics, the use of Model Order Reduction techniques allows speeding-up calculations, enabling fast and accurate evaluations. To accommodate real-time constraints, a [...] Read more.

Real-time decision making needs evaluating quantities of interest (QoI) in almost real time. When these QoI are related to models based on physics, the use of Model Order Reduction techniques allows speeding-up calculations, enabling fast and accurate evaluations. To accommodate real-time constraints, a valuable route consists of computing parametric solutions—the so-called computational vademecums—that constructed off-line, can be inspected on-line. However, when dealing with shapes and topologies (complex or rich microstructures) their parametric description constitutes a major difficulty. In this paper, we propose using Topological Data Analysis for describing those rich topologies and morphologies in a concise way, and then using the associated topological descriptions for generating accurate supervised classification and nonlinear regression, enabling an almost real-time evaluation of QoI and the associated decision making. Full article

(This article belongs to the Special Issue Empowering Materials Processing and Performance from Data and AI)

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17 pages, 547 KiB

Open AccessArticle

A Data-Driven Learning Method for Constitutive Modeling: Application to Vascular Hyperelastic Soft Tissues

by David González, Alberto García-González, Francisco Chinesta and Elías Cueto

Materials 2020, 13(10), 2319; https://doi.org/10.3390/ma13102319 - 18 May 2020

Cited by 12 | Viewed by 2768

Abstract

We address the problem of machine learning of constitutive laws when large experimental deviations are present. This is particularly important in soft living tissue modeling, for instance, where large patient-dependent data is found. We focus on two aspects that complicate the problem, namely, [...] Read more.

We address the problem of machine learning of constitutive laws when large experimental deviations are present. This is particularly important in soft living tissue modeling, for instance, where large patient-dependent data is found. We focus on two aspects that complicate the problem, namely, the presence of an important dispersion in the experimental results and the need for a rigorous compliance to thermodynamic settings. To address these difficulties, we propose to use, respectively, Topological Data Analysis techniques and a regression over the so-called General Equation for the Nonequilibrium Reversible-Irreversible Coupling (GENERIC) formalism (M. Grmela and H. Ch. Oettinger, Dynamics and thermodynamics of complex fluids. I. Development of a general formalism. Phys. Rev. E 56, 6620, 1997). This allows us, on one hand, to unveil the true “shape” of the data and, on the other, to guarantee the fulfillment of basic principles such as the conservation of energy and the production of entropy as a consequence of viscous dissipation. Examples are provided over pseudo-experimental and experimental data that demonstrate the feasibility of the proposed approach. Full article

(This article belongs to the Special Issue Empowering Materials Processing and Performance from Data and AI)

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18 pages, 1437 KiB

Open AccessArticle

Data-Oriented Constitutive Modeling of Plasticity in Metals

by Alexander Hartmaier

Materials 2020, 13(7), 1600; https://doi.org/10.3390/ma13071600 - 1 Apr 2020

Cited by 23 | Viewed by 4482

Abstract

Constitutive models for plastic deformation of metals are typically based on flow rules determining the transition from elastic to plastic response of a material as function of the applied mechanical load. These flow rules are commonly formulated as a yield function, based on [...] Read more.

Constitutive models for plastic deformation of metals are typically based on flow rules determining the transition from elastic to plastic response of a material as function of the applied mechanical load. These flow rules are commonly formulated as a yield function, based on the equivalent stress and the yield strength of the material, and its derivatives. In this work, a novel mathematical formulation is developed that allows the efficient use of machine learning algorithms describing the elastic-plastic deformation of a solid under arbitrary mechanical loads and that can replace the standard yield functions with more flexible algorithms. By exploiting basic physical principles of elastic-plastic deformation, the dimensionality of the problem is reduced without loss of generality. The data-oriented approach inherently offers a great flexibility to handle different kinds of material anisotropy without the need for explicitly calculating a large number of model parameters. The applicability of this formulation in finite element analysis is demonstrated, and the results are compared to formulations based on Hill-like anisotropic plasticity as reference model. In future applications, the machine learning algorithm can be trained by hybrid experimental and numerical data, as for example obtained from fundamental micromechanical simulations based on crystal plasticity models. In this way, data-oriented constitutive modeling will also provide a new way to homogenize numerical results in a scale-bridging approach. Full article

(This article belongs to the Special Issue Empowering Materials Processing and Performance from Data and AI)

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