Perspective: Machine learning in experimental solid mechanics

Brodnik, Neal R.; Muir, C.; Tulshibagwale, N.; Rossin, Jeff; Echlin, McLean P.; Hamel, Craig M.; Kramer, Sharlotte Lorraine Bolyard; Pollock, Tresa M.; Kiser, James D.; Smith, Christian W.; Daly, Samantha

doi:10.1016/j.jmps.2023.105231

Cited by 29 publications

(4 citation statements)

References 116 publications

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“…The entire system of non-linear equations is obtained by compiling macroscale Equations ( 10) and (11) and microscale Equations ( 26) and (27). The number of equations can be essentially reduced by assuming that constraint (10) is fulfilled after solving the entire system of non-linear equations and by employing Equation ( 23) on the microscale for periodic displacement boundary conditions.…”

Section: Microscalementioning

confidence: 99%

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FE2 Computations with Deep Neural Networks: Algorithmic Structure, Data Generation, and Implementation

Eivazi

Tröger

Wittek

et al. 2023

MCA

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Multiscale FE2 computations enable the consideration of the micro-mechanical material structure in macroscopical simulations. However, these computations are very time-consuming because of numerous evaluations of a representative volume element, which represents the microstructure. In contrast, neural networks as machine learning methods are very fast to evaluate once they are trained. Even the DNN-FE2 approach is currently a known procedure, where deep neural networks (DNNs) are applied as a surrogate model of the representative volume element. In this contribution, however, a clear description of the algorithmic FE2 structure and the particular integration of deep neural networks are explained in detail. This comprises a suitable training strategy, where particular knowledge of the material behavior is considered to reduce the required amount of training data, a study of the amount of training data required for reliable FE2 simulations with special focus on the errors compared to conventional FE2 simulations, and the implementation aspect to gain considerable speed-up. As it is known, the Sobolev training and automatic differentiation increase data efficiency, prediction accuracy and speed-up in comparison to using two different neural networks for stress and tangent matrix prediction. To gain a significant speed-up of the FE2 computations, an efficient implementation of the trained neural network in a finite element code is provided. This is achieved by drawing on state-of-the-art high-performance computing libraries and just-in-time compilation yielding a maximum speed-up of a factor of more than 5000 compared to a reference FE2 computation. Moreover, the deep neural network surrogate model is able to overcome load-step size limitations of the RVE computations in step-size controlled computations.

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Section: Microscalementioning

confidence: 99%

“…A comprehensive overview of applications in continuum material mechanics is given in [10]. Further reviews are provided in [11,12] for applications in experimental solid mechanics and [13] for material development in additive manufacturing employing machine learning methods. Ref.…”

Section: Introductionmentioning

confidence: 99%

FE2 Computations with Deep Neural Networks: Algorithmic Structure, Data Generation, and Implementation

Eivazi

Tröger

Wittek

et al. 2023

MCA

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“…In recent years, machine learning techniques have become increasingly popular, as they were successfully applied to a wide variety of problems and have also found multiple applications in the field of solid mechanics ( Kumar and Kochmann, 2022 ; Brodnik et al, 2023 ), including parameter identification. Kakaletsis et al (2023) tried to replace the whole identification routine with a neural network that was trained on pairs of simulation output and mechanical parameters but did not obtain satisfactory results.…”

Section: Introductionmentioning

confidence: 99%

Using dropout based active learning and surrogate models in the inverse viscoelastic parameter identification of human brain tissue

Hinrichsen,

Ferlay,

Reiter

et al. 2024

Front. Physiol.

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Inverse mechanical parameter identification enables the characterization of ultrasoft materials, for which it is difficult to achieve homogeneous deformation states. However, this usually involves high computational costs that are mainly determined by the complexity of the forward model. While simulation methods like finite element models can capture nearly arbitrary geometries and implement involved constitutive equations, they are also computationally expensive. Machine learning models, such as neural networks, can help mitigate this problem when they are used as surrogate models replacing the complex high fidelity models. Thereby, they serve as a reduced order model after an initial training phase, where they learn the relation of in- and outputs of the high fidelity model. The generation of the required training data is computationally expensive due to the necessary simulation runs. Here, active learning techniques enable the selection of the “most rewarding” training points in terms of estimated gained accuracy for the trained model. In this work, we present a recurrent neural network that can well approximate the output of a viscoelastic finite element simulation while significantly speeding up the evaluation times. Additionally, we use Monte-Carlo dropout based active learning to identify highly informative training data. Finally, we showcase the potential of the developed pipeline by identifying viscoelastic material parameters for human brain tissue.

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“…Moreover, the existing AI literature related to this field focuses primarily on structural mechanics [12][13][14]. On the other hand, gradient-based optimization approaches have been successfully applied to design responsive structures comprised of, for example, shape memory polymers [15,16], piezoelectric materials [10,17], and LCEs [18,19].…”

Section: Introductionmentioning

confidence: 99%

Liquid Crystal Orientation and Shape Optimization for the Active Response of Liquid Crystal Elastomers

Barrera,

Cook,

Lee

et al. 2024

Polymers

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Liquid crystal elastomers (LCEs) are responsive materials that can undergo large reversible deformations upon exposure to external stimuli, such as electrical and thermal fields. Controlling the alignment of their liquid crystals mesogens to achieve desired shape changes unlocks a new design paradigm that is unavailable when using traditional materials. While experimental measurements can provide valuable insights into their behavior, computational analysis is essential to exploit their full potential. Accurate simulation is not, however, the end goal; rather, it is the means to achieve their optimal design. Such design optimization problems are best solved with algorithms that require gradients, i.e., sensitivities, of the cost and constraint functions with respect to the design parameters, to efficiently traverse the design space. In this work, a nonlinear LCE model and adjoint sensitivity analysis are implemented in a scalable and flexible finite element-based open source framework and integrated into a gradient-based design optimization tool. To display the versatility of the computational framework, LCE design problems that optimize both the material, i.e., liquid crystal orientation, and structural shape to reach a target actuated shapes or maximize energy absorption are solved. Multiple parameterizations, customized to address fabrication limitations, are investigated in both 2D and 3D. The case studies are followed by a discussion on the simulation and design optimization hurdles, as well as potential avenues for improving the robustness of similar computational frameworks for applications of interest.

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Perspective: Machine learning in experimental solid mechanics

Cited by 29 publications

References 116 publications

FE2 Computations with Deep Neural Networks: Algorithmic Structure, Data Generation, and Implementation

FE2 Computations with Deep Neural Networks: Algorithmic Structure, Data Generation, and Implementation

Using dropout based active learning and surrogate models in the inverse viscoelastic parameter identification of human brain tissue

Liquid Crystal Orientation and Shape Optimization for the Active Response of Liquid Crystal Elastomers

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