Learning viscoelasticity models from indirect data using deep neural networks

Xu, Kailai; Tartakovsky, Alexandre M.; Burghardt, Jeffrey; Darve, Eric

doi:10.1016/j.cma.2021.114124

Cited by 42 publications

(19 citation statements)

References 25 publications

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“…Both Huang et al [56] and Xu et al [57] proposed a method to use an ANN to replace the constitutive model in a FEM solver in order to impose the physical constraints during training, enabling the ANN to learn material behaviour based on the experimental measurement. Nonetheless, the approach highly depends on a full-field data for force and displacements, while, in most experiments, only partially observed data are usually available, limiting its application to more complex three-dimensional bodies.…”

Section: Indirect/inverse Trainingmentioning

confidence: 99%

The Use of Machine-Learning Techniques in Material Constitutive Modelling for Metal Forming Processes

Lourenço

Andrade‐Campos

Georgieva

2022

Metals

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Accurate numerical simulations require constitutive models capable of providing precise material data. Several calibration methodologies have been developed to improve the accuracy of constitutive models. Nevertheless, a model’s performance is always constrained by its mathematical formulation. Machine learning (ML) techniques, such as artificial neural networks (ANNs), have the potential to overcome these limitations. Nevertheless, the use of ML for material constitutive modelling is very recent and not fully explored. Difficulties related to data requirements and training are still open problems. This work explores and discusses the use of ML techniques regarding the accuracy of material constitutive models in metal plasticity, particularly contributing (i) a parameter identification inverse methodology, (ii) a constitutive model corrector, (iii) a data-driven constitutive model using empirical known concepts and (iv) a general implicit constitutive model using a data-driven learning approach. These approaches are discussed, and examples are given in the framework of non-linear elastoplasticity. To conveniently train these ML approaches, a large amount of data concerning material behaviour must be used. Therefore, non-homogeneous strain field and complex strain path tests measured with digital image correlation (DIC) techniques must be used for that purpose.

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Section: Indirect/inverse Trainingmentioning

confidence: 99%

The Use of Machine-Learning Techniques in Material Constitutive Modelling for Metal Forming Processes

Lourenço

Andrade‐Campos

Georgieva

2022

Metals

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“…Some authors recently reported different approaches to tackle this issue. For example, Xu et al [11] presented a method for an ANN to model viscoelasticity, based on displacement data, using partial differential equations to introduce the physical constraints during training, and Liu et al [10] addressed the issue via coupling the ANN model with the Finite Element Method (FEM) to learn constitutive laws based on force and displacement data (Fig. 2).…”

Section: Key Engineering Materials Vol 926mentioning

confidence: 99%

The Virtual Fields Method to Indirectly Train Artificial Neural Networks for Implicit Constitutive Modelling

Lourenço¹,

Andrade‐Campos

Georgieva³

2022

KEM

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Artificial Neural Networks (ANNs) have the potential to provide a different approach to constitutive modelling, with the main advantage that these do not require to postulate a mathematical formulation or identify empirical parameters. Currently, the training of an ANN for implicit constitutive modelling mostly relies on paired data, usually stress-strain however, stress cannot be directly measured in a real experiment. As such, the training should be carried out indirectly using measurable variables from the experimental setting, such as displacements and the applied force. In the current work, displacements and global force data are used to indirectly train an ANN to predict the stress state of a material. An experimental test is recreated numerically in order to obtain displacement and global force data for different load distributions, i.e. obtaining synthetic data using a virtual experiment. The strain from the current and previous time increments are obtained from the corresponding displacements and used as inputs for the ANN to predict the current state of stress. Training is carried out without stress labels to compute the loss. Instead, the local and global equilibrium conditions, corresponding to the application of the Virtual Fields Method (VFM) to the physical model, are employed to compute the loss and update the network parameters, until the predicted stress state is accurate.

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“…Calculation of the derivatives for the [G] matrix is less straightforward since u is an implicit function of θ through the Newton-Raphson iteration procedure. Following the approach presented by Xu et al [13], this obstacle is overcome through application of the implicit function theorem, which allows [G] to be expressed as…”

Section: Back Propagation Through Finite Element Calculationsmentioning

confidence: 99%

Autonomous Inversion of In Situ Deformation Measurement Data for CO2 Storage Decision Support

Burghardt,

Bao,

et al. 2021

Preprint

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Geologic carbon storage (GCS) is likely to play a key part of the global effort to dramatically reduce CO 2 emissions and perhaps even reduce atmospheric CO 2 concentrations through carbon negative operations. A critical part of effort to commercialize and widely deploy this technology is developing the capability to rapidly assimilate real-time monitoring data into a form that will enable site operators to make decisions to manage the safe and efficient operations. Two of the risks associate with GCS are the risk of inducing fractures in the sealing formations that can create leakage pathways and the risk of inducing earthquakes of sufficient magnitude to cause public concern, property damage, or safety risks. To properly manage these risks the site operator needs to know the initial state of stress, the change in stress induced by injection, and the relationship between operational parameters such as injection rate and pressure and the change in stress. Current methods of estimating the change in stress require choosing the type of constitutive model and the model parameters based on core, log, and geophysical data during the characterization phase, with little feedback from operational observations to validate or refine these choices. These characterization methods interrogate the geologic formations using length scales, loading rates or magnitudes that are quite different from those encountered by the actual storage system. It is shown that errors in the assumed constitutive response, even when informed by laboratory tests on core samples, are likely to be common, large, and underestimate the magnitude of stress change caused by injection. Recent advances in borehole-based strain instruments and borehole and surface-based tilt and displacement instruments have now enabled monitoring of the deformation of the storage system throughout its operational lifespan. This data can enable validation and refinement of the knowledge of the geomechanical properties and state of the system, but brings with it a challenge to transform the raw data into actionable knowledge. We demonstrate a method that uses automatic differentiation and a finite-element based geomechanical model perform a gradient-based deterministic inversion of geomechanical monitoring data. This

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Learning viscoelasticity models from indirect data using deep neural networks

Cited by 42 publications

References 25 publications

The Use of Machine-Learning Techniques in Material Constitutive Modelling for Metal Forming Processes

The Use of Machine-Learning Techniques in Material Constitutive Modelling for Metal Forming Processes

The Virtual Fields Method to Indirectly Train Artificial Neural Networks for Implicit Constitutive Modelling

Autonomous Inversion of In Situ Deformation Measurement Data for CO2 Storage Decision Support

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