Data-Driven multiscale modeling in mechanics

Karapiperis, Konstantinos; Stainier, Laurent; Ortiz, Michael; Andrade, José E.

doi:10.1016/j.jmps.2020.104239

Cited by 127 publications

(62 citation statements)

References 68 publications

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“…These data could be collected from experiments or, due to the steadily increasing computing power, generated in silicio from lower scale simulations. Within the data-driven formalism the latter one has been applied by Karapiperis et al [30] for sand recently. In order to enable the collection of data from experiments, Leygue et al [38] and Stainier et al [55] have introduced the data-driven identification which allows to collect strain-stress tuples from displacement fields and boundary conditions in inhomogeneous samples.…”

Section: Introductionmentioning

confidence: 99%

Automated constitutive modeling of isotropic hyperelasticity based on artificial neural networks

et al. 2021

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Herein, an artificial neural network (ANN)-based approach for the efficient automated modeling and simulation of isotropic hyperelastic solids is presented. Starting from a large data set comprising deformations and corresponding stresses, a simple, physically based reduction of the problem’s dimensionality is performed in a data processing step. More specifically, three deformation type invariants serve as the input instead of the deformation tensor itself. In the same way, three corresponding stress coefficients replace the stress tensor in the output layer. These initially unknown values are calculated from a linear least square optimization problem for each data tuple. Using the reduced data set, an ANN-based constitutive model is trained by using standard machine learning methods. Furthermore, in order to ensure thermodynamic consistency, the previously trained network is modified by constructing a pseudo-potential within an integration step and a subsequent derivation which leads to a further ANN-based model. In the second part of this work, the proposed method is exemplarily used for the description of a highly nonlinear Ogden type material. Thereby, the necessary data set is collected from virtual experiments of discs with holes in pure plane stress modes, where influences of different loading types and specimen geometries on the resulting data sets are investigated. Afterwards, the collected data are used for the ANN training within the reduced data space, whereby an excellent approximation quality could be achieved with only one hidden layer comprising a low number of neurons. Finally, the application of the trained constitutive ANN for the simulation of two three-dimensional samples is shown. Thereby, a rather high accuracy could be achieved, although the occurring stresses are fully three-dimensional whereas the training data are taken from pure two-dimensional plane stress states.

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Section: Introductionmentioning

confidence: 99%

Automated constitutive modeling of isotropic hyperelasticity based on artificial neural networks

et al. 2021

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“…Recent work, such as Leygue et al [33] and Karapiperis et al [35] have explored options to address the demand of data. In [33], collections of non-homogeneous strain data, and the applied face of a specimen, which could be obtained from digital image correlation, are used to constitute database.…”

Section: Introductionmentioning

confidence: 99%

“…This database can then be used to compute admissible stress-strain pairs from experimental data. Meanwhile, Karapiperis et al [35] explore the possibility of introducing an on-the-fly sampling technique to generate data from sub-scale computations with no prior information needed as well as employ an offline goal-oriented sampling technique to incorporate high-fidelity simulations and high-resolution experiments in the material database.…”

Section: Introductionmentioning

confidence: 99%

A kd-tree-accelerated hybrid data-driven/model-based approach for poroelasticity problems with multi-fidelity multi-physics data

Bahmani

Sun

2021

Computer Methods in Applied Mechanics and Engineering

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We present a hybrid model/model-free data-driven approach to solve poroelasticity problems. Extending the data-driven modeling framework originated from Kirchdoerfer and Ortiz (2016), we introduce one model-free and two hybrid modelbased/data-driven formulations capable of simulating the coupled diffusion-deformation of fluid-infiltrating porous media with different amounts of available data. To improve the efficiency of the model-free data search, we introduce a distance-minimized algorithm accelerated by a k-dimensional tree search. To handle the different fidelities of the solid elasticity and fluid hydraulic constitutive responses, we introduce a hybridized model in which either the solid and the fluid solver can switch from a model-based to a model-free approach depending on the availability and the properties of the data. Numerical experiments are designed to verify the implementation and compare the performance of the proposed model to other alternatives. c

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“…It was also successfully extended to large strain and assessed with raw experimental data in [15], which provides encouraging prospects. Alternatively, the DDCM can also be employed with numerically generated databases from multiple simulations at finer scales [16,17]. Yet, in the current stages of development, including the present work, the use of in silico data, generated by a sampling of a constitutive model later discarded in the data-driven simulations, allows to assess the approach by comparing to standard finite element (FE) analyses.…”

Section: State Of the Artmentioning

confidence: 99%

“…The definition of the functional space for the FE stress field in the data-driven setting is out of the scope of the present work. Instead, the stresses are merely evaluated at the integration points, using (17), as…”

Section: Discretization Of Local State Fieldsmentioning

confidence: 99%