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24.12.2024 | Original Article

Differentiable neural-integrated meshfree method for forward and inverse modeling of finite strain hyperelasticity

verfasst von: Honghui Du, Binyao Guo, QiZhi He

Erschienen in: Engineering with Computers

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Abstract

The present study aims to extend the novel physics-informed machine learning approach, specifically the neural-integrated meshfree (NIM) method, to model finite-strain problems characterized by nonlinear elasticity and large deformations. To this end, the hyperelastic material models are integrated into the loss function of the NIM method by employing a consistent local variational formulation. Thanks to the inherent differentiable programming capabilities, NIM can circumvent the need for derivation of Newton–Raphson linearization of the variational form and the resulting tangent stiffness matrix, which are typically required in traditional numerical methods. Additionally, NIM utilizes a hybrid neural-numerical approximation encoded with partition-of-unity basis functions, coined NeuroPU, to effectively represent the displacement solution and streamline the model training process. NeuroPU can also be used for approximating the unknown material fields, enabling NIM a unified framework for both forward and inverse modeling. For the imposition of displacement boundary conditions, this study introduces a new approach based on singular kernel functions into the NeuroPU approximation, leveraging its unique feature that allows for customized basis functions. Numerical experiments demonstrate the NIM method’s capability in forward hyperelasticity modeling, achieving desirable accuracy, with errors among \(10^{-3} \,\text{to}\, 10^{-5}\) in the relative \(L_2\) norm, comparable to the well-established finite element solvers. Furthermore, NIM is applied to address the complex task of identifying heterogeneous mechanical properties of hyperelastic materials from strain data, validating its effectiveness in the inverse modeling of nonlinear materials. To leverage GPU acceleration, NIM is fully implemented on the JAX deep learning framework in this study, utilizing the accelerator-oriented array computation capabilities offered by JAX.

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Fußnoten
1
With a slight abuse of notation, the symbol \(\varvec{\epsilon }\) is used to denote the Green-Lagrangian strain tensor instead of the commonly used \(\varvec{E}\), to avoid confusion with elastic modulus E.
 
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Metadaten
Titel
Differentiable neural-integrated meshfree method for forward and inverse modeling of finite strain hyperelasticity
verfasst von
Honghui Du
Binyao Guo
QiZhi He
Publikationsdatum
24.12.2024
Verlag
Springer London
Erschienen in
Engineering with Computers
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-024-02090-z