Identifying Constitutive Parameters of Complex Hyperelastic Materials using Physics-Informed Neural Networks

Core Concepts

A robust Physics-Informed Neural Network (PINN) framework can accurately identify constitutive parameters of complex hyperelastic materials, such as the Arruda-Boyce model, under large deformation in plane stress conditions, even with noisy experimental data.

Abstract

The paper introduces a PINN-based framework to identify constitutive parameters of complex hyperelastic materials, specifically those exhibiting strain-stiffening behavior, under large deformation in plane stress conditions.
The key highlights are:

The framework integrates full-field deformation data from Digital Image Correlation (DIC) and loading history as additional boundary conditions for PINN training, ensuring robustness even with noisy experimental data.

The framework is validated on a prototype problem of a rectangular sample with a central hole, demonstrating the PINN's ability to accurately predict the deformation field and loading history compared to finite element analysis.

The framework is then applied to identify the constitutive parameters of the Arruda-Boyce model for a more complex geometry with multiple internal circular inhomogeneities. The results show the framework can maintain an error below 5% in parameter identification, even with 5% experimental noise.

The study investigates the effects of speckle density and noise level of the DIC data on the convergence and accuracy of the parameter identification. Increasing the speckle density is found to be crucial, especially when dealing with high noise levels.

Overall, the proposed PINN-based framework provides a robust approach for identifying constitutive parameters of complex hyperelastic solids, particularly those with intricate geometries and constitutive behaviors, using direct experimental measurements.

Stats

The sample has a length of 2a and width of 2b, with a central hole of radius r.
The constitutive model is the incompressible Arruda-Boyce (AB) model with shear modulus μ and strain hardening parameter λm.

Quotes

"Distinctively, our model emphasizes training PINNs with multi-modal synthetic experimental datasets consisting of full-field deformation and loading history, ensuring algorithm robustness even with noisy data."
"Our results reveal that the PINNs framework can accurately identify constitutive parameters of the incompressible Arruda-Boyce model for samples with intricate geometries, maintaining an error below 5%, even with an experimental noise level of 5%."

Key Insights Distilled From

Identifying Constitutive Parameters for Complex Hyperelastic Materials using Physics-Informed Neural Networks

by Siyuan Song,... at arxiv.org 04-10-2024

https://arxiv.org/pdf/2308.15640.pdf

Deeper Inquiries

How can the proposed PINN framework be extended to identify constitutive parameters for other complex hyperelastic models, such as the Holzapfel-Gasser-Ogden (HGO) model

The proposed Physics-Informed Neural Networks (PINN) framework can be extended to identify constitutive parameters for other complex hyperelastic models, such as the Holzapfel-Gasser-Ogden (HGO) model, by adapting the formulation of the strain energy density function and the constitutive relations specific to the HGO model. The HGO model is commonly used to describe the hyperelastic behavior of soft biological tissues with fiber-reinforced structures.
To apply the PINN framework to the HGO model, the strain energy density function and the corresponding stress-strain relationships of the HGO model need to be incorporated into the PINN architecture. This involves defining the material parameters unique to the HGO model, such as the fiber orientation distribution and material constants. The PINN framework can then be trained using synthetic experimental data, including full-field deformation and loading history, to accurately identify the constitutive parameters of the HGO model.

What are the potential challenges and limitations of the PINN approach when dealing with highly anisotropic materials or materials exhibiting history-dependent behaviors

When dealing with highly anisotropic materials or materials exhibiting history-dependent behaviors, the PINN approach may face several challenges and limitations.

Model Complexity: Highly anisotropic materials require more complex constitutive models to capture the directional dependence of material properties accurately. Implementing these complex models in the PINN framework may increase the computational cost and training time.

Data Requirement: History-dependent materials exhibit behavior that depends on the loading history, making it challenging to capture these nonlinearities accurately. The PINN framework may require a large amount of training data to effectively learn the complex material behavior.

Model Interpretability: Highly anisotropic or history-dependent materials may have intricate stress-strain relationships that are challenging to interpret. The black-box nature of neural networks in the PINN framework may limit the understanding of the underlying physics governing the material behavior.

Overfitting: The PINN framework may be prone to overfitting when dealing with highly complex material behaviors, leading to poor generalization to unseen data and inaccurate parameter identification.

Can the PINN framework be integrated with other experimental techniques, such as digital volume correlation, to enable 3D parameter identification for complex biological tissues

The PINN framework can be integrated with other experimental techniques, such as digital volume correlation (DVC), to enable 3D parameter identification for complex biological tissues. DVC is a non-contact optical technique used to measure full-field 3D displacements and strains in materials undergoing deformation. By combining DVC data with the PINN framework, researchers can enhance the accuracy and robustness of parameter identification for complex biological tissues in three dimensions.
The integration of DVC data into the PINN framework can provide additional constraints and boundary conditions for training the neural network. The 3D displacement fields obtained from DVC measurements can be used to validate the predictions of the PINN model and improve the accuracy of parameter identification. This multi-modal approach allows for a more comprehensive understanding of the material behavior and properties in complex biological tissues.