Physics-informed Neural Networks (PINN) for computational solid mechanics: Numerical frameworks and applications

Thin-Walled Structures, Journal Year: 2024, Volume and Issue: 205, P. 112495 - 112495

Published: Sept. 24, 2024

Language: Английский

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Mixed formulation of physics‐informed neural networks for thermo‐mechanically coupled systems and heterogeneous domains

International Journal for Numerical Methods in Engineering, Journal Year: 2023, Volume and Issue: 125(4)

Published: Nov. 8, 2023

Abstract Physics‐informed neural networks (PINNs) are a new tool for solving boundary value problems by defining loss functions of based on governing equations, conditions, and initial conditions. Recent investigations have shown that when designing many engineering problems, using first‐order derivatives combining equations from both strong weak forms can lead to much better accuracy, especially there heterogeneity variable jumps in the domain. This approach is called mixed formulation PINNs, which takes ideas finite element method. In this method, PDE reformulated as system where primary unknowns fluxes or gradients solution, secondary solution itself. work, we propose applying solve multi‐physical specifically stationary thermo‐mechanically coupled equations. Additionally, discuss sequential fully unsupervised training compare their accuracy computational cost. To improve network, incorporate hard constraints ensure valid predictions. We then investigate how different optimizers architectures affect efficiency. Finally, introduce simple parametric learning similar transfer learning. combines data physics address limitations PINNs regarding cost improves network's ability predict response unseen cases. The outcomes work will be useful other applications deep employed multiple systems fast reliable computations.

Language: Английский

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Viscoelasticty with physics-augmented neural networks: model formulation and training methods without prescribed internal variables

Computational Mechanics, Journal Year: 2024, Volume and Issue: 74(6), P. 1279 - 1301

Published: May 6, 2024

Abstract We present an approach for the data-driven modeling of nonlinear viscoelastic materials at small strains which is based on physics-augmented neural networks (NNs) and requires only stress strain paths training. The model built concept generalized standard therefore thermodynamically consistent by construction. It consists a free energy dissipation potential, can be either expressed components their tensor arguments or suitable set invariants. two potentials are described fully/partially input convex networks. For training NN strain, efficient flexible method long short-term memory cell developed to automatically generate internal variable(s) during process. proposed benchmarked thoroughly compared with existing approaches. Different databases ideal noisy data generated using conventional reference model. coordinate-based invariant-based formulation advantages latter demonstrated. Afterwards, calibrated applying three methods data. All yield good results, but differ in computation time usability large sets. presented recurrent turns out particularly robust widely applicable. show that together complete accurate 3D constitutive models even sparse bi- uniaxial

Language: Английский

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Boundary integrated neural networks for 2D elastostatic and piezoelectric problems

International Journal of Mechanical Sciences, Journal Year: 2024, Volume and Issue: 280, P. 109525 - 109525

Published: July 6, 2024

In this paper, we make the first attempt to adopt boundary integrated neural networks (BINNs) for numerical solution of two-dimensional (2D) elastostatic and piezoelectric problems. The proposed BINNs combine artificial with exact integral equations (BIEs) effectively solve value problems based on corresponding partial differential (PDEs). BIEs are utilized localize all unknown physical quantities boundary, which approximated by using resolved via a training process. contrast many traditional network methods domain discretization, present offer several distinct advantages. Firstly, embedding analytical into learning procedure, only need discretize problem domain, reduces number unknowns can lead faster more stable Secondly, operators in original PDEs substituted operators, eliminate additional differentiations (high-order derivatives may instabilities process). Thirdly, loss function contains residuals BIEs, as conditions have been inherently incorporated within formulation. Therefore, there is no necessity employing any weighting functions, commonly used most balance gradients among different objective functions. Extensive experiments show that much easier train usually provide accurate solutions compared methods.

Language: Английский

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A novel surrogate model for hydro-mechanical coupling in unsaturated soil with incomplete physical constraints

Computers and Geotechnics, Journal Year: 2025, Volume and Issue: 180, P. 107091 - 107091

Published: Jan. 27, 2025

Language: Английский

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A two-scale computational homogenization approach for elastoplastic truss-based lattice structures

Results in Engineering, Journal Year: 2025, Volume and Issue: unknown, P. 103976 - 103976

Published: Jan. 1, 2025

Language: Английский

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t-PiNet: A Thermodynamics-informed Hierarchical Learning for Discovering Constitutive Relations of Geomaterials

Journal of the Mechanics and Physics of Solids, Journal Year: 2025, Volume and Issue: unknown, P. 106049 - 106049

Published: Jan. 1, 2025

Language: Английский

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A Comprehensive Investigation of Physics-Informed Learning in Forward and Inverse Analysis of Elastic and Elastoplastic Footing

Computers and Geotechnics, Journal Year: 2025, Volume and Issue: 181, P. 107110 - 107110

Published: Feb. 5, 2025

Language: Английский

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Machine learning-based constitutive modelling for material non-linearity: A review

Mechanics of Advanced Materials and Structures, Journal Year: 2024, Volume and Issue: unknown, P. 1 - 19

Published: Dec. 17, 2024

Machine learning (ML) models are widely used across numerous scientific and engineering disciplines due to their exceptional performance, flexibility, prediction quality, ability handle highly complex problems if appropriate data available. One example of such areas which has attracted a lot attentions in the last couple years is integration data-driven approaches material modeling. There been several successful researches implementing ML-based constitutive instead classical phenomenological for various materials, particularly those with non-linear mechanical behaviors. This review paper aims systematically investigate literature on materials classify these based suitability non-linearity including Non-linear elasticity (hyperelasticity), plasticity, visco-elasticity, visco-plasticity. Furthermore, we also reviewed compared that have applied architectured as groups designed represent specific behaviors might not exist conventional categories. The other goal this provide initial steps understanding modeling, artificial neural networks (ANN), Gaussian processes, random forests (RF), generated adversarial (GANs), support vector machines (SVM), different regression physics-informed (PINN). outlines collection methods, types data, processing approaches, theoretical background ML models, advantage limitations potential future research directions. comprehensive will researchers knowledge necessary develop high-fidelity, robust, adaptable, flexible, accurate advanced materials.

Language: Английский

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A Finite Operator Learning Technique for Mapping the Elastic Properties of Microstructures to Their Mechanical Deformations

International Journal for Numerical Methods in Engineering, Journal Year: 2024, Volume and Issue: unknown

Published: Dec. 9, 2024

ABSTRACT To obtain fast solutions for governing physical equations in solid mechanics, we introduce a method that integrates the core ideas of finite element with physics‐informed neural networks and concept operators. We propose directly utilizing available discretized weak form packages to construct loss functions algebraically, thereby demonstrating ability find even presence sharp discontinuities. Our focus is on micromechanics as an example, where knowledge deformation stress fields given heterogeneous microstructure crucial further design applications. The primary parameter under investigation Young's modulus distribution within system. investigations reveal physics‐based training yields higher accuracy compared purely data‐driven approaches unseen microstructures. Additionally, offer two methods improve process obtaining high‐resolution solutions, avoiding need use basic interpolation techniques. first one based autoencoder approach enhance efficiency calculation high resolution grid points. Next, Fourier‐based parametrization utilized address complex 2D 3D problems micromechanics. latter idea aims represent microstructures efficiently using Fourier coefficients. proposed draws from deep energy but generalizes enhances them by learning parametric without relying external data. Compared other operator frameworks, it leverages domain decomposition several ways: (1) uses shape derivatives instead automatic differentiation; (2) automatically includes node connectivity, making solver flexible approximating jumps solution fields; (3) can handle arbitrary shapes enforce boundary conditions. provided some initial comparisons well‐known algorithms, emphasize advantages newly method.

Language: Английский

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