Use of neural networks to model structures of hyperelastic materials

Write in the journal Materials, a team of Chinese scientists reported the use of neural networks to model structures of hyperelastic materials to identify material parameters. The authors stated that their proposed approach is universal and has high accuracy.

Study: Parameter identification of a rubber-like hyperelastic material based on the general regression neural network. Image Credit: Gorodenkoff/Shutterstock.com

Research background

Hyperelastic materials possess several excellent qualities such as wearability, impact resistance and elasticity, and can undergo extreme deformations, which makes them extremely durable. Many hyperelastic materials, including gels and rubbers, have found commercial use in engineering applications such as insulation materials.

In recent years, researchers have explored the use of simulations and numerical models to predict and describe experimental phenomena in these materials. Establishing a constitutive model has become a key research concern for the design of advanced hyperelastic materials.

Studies have shown that hyperelastic materials have nonlinear characteristics and their properties depend on their strain energy function. Several models such as Gent model, Ogden model, Mooney-Rivlin model and Gent-Thomas model have been developed to provide suitable strain energy density for these materials.

The sample and its geometry used in a uniaxial tensile test: (a) Image of a sample of silicone rubber with aluminum foils bonded;  (b) The dimensions of the silicone rubber specimen and aluminum foils.

The specimen and its geometry used in a uniaxial tensile test: (a) An image of a silicone rubber specimen with aluminum foils glued on; (b) The dimensions of the silicone rubber specimen and aluminum sheets. Image Credit: Hou, J et al., Materials

Incompressible models have become a key variant of the model due to their ability to simplify theoretical work and, therefore, provide crucial information about the properties of hyperelastic materials. There has been an increased focus on the study of hyperelastic models to facilitate the subsequent application of these commercially important materials.

Common approaches to determining the parameters of these materials include experiments, numerical calculations, and the use of artificial intelligence. Artificial intelligence has received increased research attention in recent years due to its ability to predict the parameters and behavior of materials, which experiments and simulations find difficult.

Artificial intelligence methods can use existing data to establish the relationship between variables. This gives these methods a significant advantage over traditional analysis. AI has been successfully used to optimize mechanical models, predict mechanical parameters, and monitor the health of materials and components along with several other aspects.

The study

The study investigated the use of neural networks to improve the modeling of mechanical parameters of hyperelastic materials. The authors used an approach based on the General Regression Neural Network (GRNN), a type of radial basis function neural network.

GRNN has been widely applied in many fields and has several advantages over conventional neural networks. It has a simpler network structure than feedforward neural networks. Model training is straightforward and simple – as soon as the training samples pass through the hidden layer of the model, training is complete. This reduces both training time and costs.

Moreover, GRNN calculations have better global convergence capabilities than feedforward networks, which generally achieve only local convergence.

The goal of this article is to create a simple, effective, and practical GRNN approach. The goal of the proposed neural network-based approach is to accurately identify the model parameters of hyperelastic materials. The approach combines experimental analysis, numerical modelling, simulations and GRNN learning.

The experimental device of a uniaxial tensile test.

The experimental device of a uniaxial tensile test. Image Credit: Hou, J et al., Materials

The theoretical basis of GRNN and its architecture were discussed in depth in the study, as well as the application of this approach to determine the parameters of materials. A brief introduction of the hyperelastic model is provided by the researchers, along with prediction schemes based on GRNN, finite element analysis, and uniaxial tests.

Additionally, the document provided an example of validation using silicone rubber. Uniaxial tensile tests were used to measure the force-displacement curve of the material. The experimental results demonstrated nonlinear characteristics of the material. A numerical model based on finite element simulation was used to obtain training samples for the neural network to identify the parameters.

Results and conclusions

The authors have devised a simple, practical and efficient method for identifying parameters in hyperelastic models. The approach combined experimental observations, numerical modeling and GRNN. Target values ​​were provided by experiments, with the numerical models being used to provide training samples for the neural network. GRNN was used to identify the parameters.

The GRNN-based approach improved the accuracy of parameter prediction for three commonly used models: the MR model, the polynomial model, and the Ogden model. However, while the results from the three hyperelastic models met the accuracy requirements, the Ogden model produced a force-displacement curve that was closest to the experimental data.

Finite element mesh and boundary conditions of a sample of silicone rubber.

Finite element mesh and boundary conditions of a sample of silicone rubber. Image Credit: Hou, J et al., Materials

Based on this, the authors concluded that the Ogden model was the most suitable for characterizing the mechanical properties of silicone rubber. The authors stated that this GRNN-based approach could be considered a universal approach to solving problems when identifying multiple parameters. GRNN is therefore a powerful forecasting tool capable of automatically optimizing material parameters.

Further reading

Hou, J et al. (2022) Parameter identification of a rubber-like hyperelastic material based on the general regression neural network Materials 15(11) 3776 [online] mdpi.com. Available at: https://www.mdpi.com/1996-1944/15/11/3776

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