Learning nonlocal constitutive models with neural networks

We propose a machine learning embedded method of parameters determination in the constitutional models of hydrogels. It is found that the developed logistic regression-like algorithm for hydrogel swelling allows us to determine the fitting parameters based on known swelling ratio and chemical potential. We also put forward the neural networks-like algorithm, which, by its own property, can converge faster as the layer deepens. We then develop neural networks-like algorithm for hydrogel under uniaxial load for experimental application purpose. Finally, we propose several machine learning embedded potential applications for hydrogels, which would provide directions for machine learning-based hydrogel research.

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Nonlinear multiscale simulation of elastic beam lattices with anisotropic homogenized constitutive models based on artificial neural networks

Computational Mechanics ◽

10.1007/s00466-021-02061-x ◽

2021 ◽

Author(s):

Til Gärtner ◽

Mauricio Fernández ◽

Oliver Weeger

Keyword(s):

Neural Networks ◽

Artificial Neural Networks ◽

Lattice Structure ◽

Constitutive Models ◽

Multiscale Simulation ◽

Multiscale Approach ◽

Perturbation Approach ◽

Material Symmetry ◽

Highly Nonlinear ◽

Artificial Neural

AbstractA sequential nonlinear multiscale method for the simulation of elastic metamaterials subject to large deformations and instabilities is proposed. For the finite strain homogenization of cubic beam lattice unit cells, a stochastic perturbation approach is applied to induce buckling. Then, three variants of anisotropic effective constitutive models built upon artificial neural networks are trained on the homogenization data and investigated: one is hyperelastic and fulfills the material symmetry conditions by construction, while the other two are hyperelastic and elastic, respectively, and approximate the material symmetry through data augmentation based on strain energy densities and stresses. Finally, macroscopic nonlinear finite element simulations are conducted and compared to fully resolved simulations of a lattice structure. The good agreement between both approaches in tension and compression scenarios shows that the sequential multiscale approach based on anisotropic constitutive models can accurately reproduce the highly nonlinear behavior of buckling-driven 3D metamaterials at lesser computational effort.

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Prediction of Soil Deformation in Tunnelling Using Artificial Neural Networks

Computational Intelligence and Neuroscience ◽

10.1155/2016/6708183 ◽

2016 ◽

Vol 2016 ◽

pp. 1-16 ◽

Cited By ~ 34

Author(s):

Jinxing Lai ◽

Junling Qiu ◽

Zhihua Feng ◽

Jianxun Chen ◽

Haobo Fan

Keyword(s):

Neural Networks ◽

Artificial Neural Networks ◽

Rock Mass ◽

Constitutive Models ◽

Future Research ◽

Dynamic Prediction ◽

Regression Methods ◽

Ann Models ◽

Rock Mass Deformation ◽

Artificial Neural

In the past few decades, as a new tool for analysis of the tough geotechnical problems, artificial neural networks (ANNs) have been successfully applied to address a number of engineering problems, including deformation due to tunnelling in various types of rock mass. Unlike the classical regression methods in which a certain form for the approximation function must be presumed, ANNs do not require the complex constitutive models. Additionally, it is traced that the ANN prediction system is one of the most effective ways to predict the rock mass deformation. Furthermore, it could be envisaged that ANNs would be more feasible for the dynamic prediction of displacements in tunnelling in the future, especially if ANN models are combined with other research methods. In this paper, we summarized the state-of-the-art and future research challenges of ANNs on the tunnel deformation prediction. And the application cases as well as the improvement of ANN models were also presented. The presented ANN models can serve as a benchmark for effective prediction of the tunnel deformation with characters of nonlinearity, high parallelism, fault tolerance, learning, and generalization capability.

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Rheology-Informed Neural Networks (RhINNs) for forward and inverse metamodelling of complex fluids

Scientific Reports ◽

10.1038/s41598-021-91518-3 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Mohammadamin Mahmoudabadbozchelou ◽

Safa Jamali

Keyword(s):

Neural Networks ◽

Constitutive Equations ◽

Automatic Differentiation ◽

Complex Fluids ◽

Shear Banding ◽

Constitutive Models ◽

Soft Materials ◽

Specific Model ◽

Model Parameters ◽

Rate Dependent

AbstractReliable and accurate prediction of complex fluids’ response under flow is of great interest across many disciplines, from biological systems to virtually all soft materials. The challenge is to solve non-trivial time and rate dependent constitutive equations to describe these structured fluids under various flow protocols. We present Rheology-Informed Neural Networks (RhINNs) for solving systems of Ordinary Differential Equations (ODEs) adopted for complex fluids. The proposed RhINNs are employed to solve the constitutive models with multiple ODEs by benefiting from Automatic Differentiation in neural networks. In a direct solution, the RhINNs platform accurately predicts the fully resolved solution of constitutive equations for a Thixotropic-Elasto-Visco-Plastic (TEVP) complex fluid for a series of flow protocols. From a practical perspective, an exhaustive list of experiments are required to identify model parameters for a multi-variant constitutive TEVP model. RhINNs are found to learn these non-trivial model parameters for a complex material using a single flow protocol, enabling accurate modeling with limited number of experiments and at an unprecedented rate. We also show the RhINNs are not limited to a specific model and can be extended to include various models and recover complex manifestations of kinematic heterogeneities and transient shear banding of thixotropic fluids.

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