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Inverse Identification of Elastic Constants of Thin Hyper-Elastic Isotropic Plates using the Dispersion Curve and Neural Network

Dehghan Tezerjani, Alireza | 2025

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 57960 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Fallah Rajabzadeh, Famida
  7. Abstract:
  8. Non-destructive methods using ultrasound waves, including elastography, have gained special attention in recent years for determining the mechanical and geometric properties of materials. Due to the hyperelastic nature of body tissues, this research aims to determine the mechanical and geometric properties (thickness) of a hyperelastic plate immersed in fluid, considered as a simplified model of arteries. In this study, the mechanical and geometric properties (thickness) of an incompressible, isotropic, single-layer hyperelastic plate are investigated through an inverse method based on a neural network using the wave dispersion curve. To this end, the wave propagation equations in incompressible hyperelastic plates are presented and numerically solved based on the theory of incremental elasticity. Through this approach, the wave dispersion curves are extracted. Then, using the inverse method based on a convolutional neural network (CNN), the mechanical properties and thickness of the plate are evaluated with high accuracy and in real-time. In this research, the hyperelastic plate is modeled using two strain energy functions: Neo-Hookean and Mooney-Rivlin. In the Neo-Hookean model, a parametric study showed that thickness, stretch, and shear modulus significantly affect the dispersion curves of the fundamental symmetric and antisymmetric wave modes. The dispersion curves for the fundamental antisymmetric wave mode were extracted, and the mechanical properties and thickness of the plate were predicted using the proposed inverse method. The results indicated that the mean squared error (MSE) for the test data was . For validation, the neural network was trained with experimental data, initially showing a % error. However, by combining the symmetric and antisymmetric wave modes, the accuracy of the inverse method improved by times, and the MSE decreased to . These results demonstrated that utilizing the dispersion curve of the fundamental symmetric wave mode is essential for improving accuracy in predicting experimental data. Additionally, by removing thickness from the target parameters and applying it as an input in the proposed inverse method, the accuracy of the network improved sixfold when only the fundamental antisymmetric wave mode was used, and the accuracy improved times when both symmetric and antisymmetric wave modes were utilized. In the Mooney-Rivlin model, due to the higher complexity of this strain energy function and the non-uniqueness between the dispersion curve and the plate properties, challenges arose in the modeling process. This issue was due to the identical influence of certain parameters of the strain energy function on the dispersion curves. However, by changing the approach and using Cauchy stress, stretch, and plate thickness as the neural network outputs, the model was able to predict these parameters with higher accuracy. The MSE obtained was , indicating the network's ability to learn the relationships between input data and target outputs
  9. Keywords:
  10. Wave Propagation ; Neural Network ; Elastography ; Inverse Method ; Dispersion Curve ; Convolutional Neural Network ; Nondestructive Test

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