Journal of Space Science and Technology

Journal of Space Science and Technology

Prediction of Mechanical Behavior in Hyperelastic Materials Reinforced with Continuous Unidirectional Fibers under Large Deformations Using Neural Networks

Document Type : Original Research Paper

Author
Associate Professor, Aerospace Research Institute, Ministry of Science, Research and Technology, Tehran, Iran
Abstract
This paper introduces an efficient Neural Network (NN) model designed to predict the nonlinear mechanical behavior of fiber-reinforced elastomeric composites under large deformations. The foundation of this modeling approach is a scaler strain energy function derived from two tensoral values depending on material's deformation field and fiber orientation. The necessary training data for the NN is generated using a high-fidelity micromechanical homogenization method applied to a Representative Volume Element (RVE) that accurately captures the composite material's microstructure. By subjecting the RVE to large strain loading conditons, the complex micromechanical response is determined, yielding the equivalent macroscopic constitutive behavior for composite material. The developed NN model successfully predicts the complex outcomes of the micromechanical analysis, thus validating its efficacy for modeling anisotropic hyperelastic materials. The primary advantage of this methodology is its potential for a dramatic reduction in computational time during macroscopic Finite Element Analysis (FEM). By operating as a surrogate constitutive model, the NN eliminates the requirement for repeated, direct microstructure analysis at every computational increment, enabling faster and more feasible simulations of composite components.
Keywords
Subjects

Article Title Persian

پیش‌بینی رفتار مکانیکی مواد هایپرالاستیک تقویت‌شده با الیاف پیوسته تک‌جهته در تغییر شکل‌های بزرگ با استفاده از شبکه‌های عصبی

Author Persian

محمد طاهای ابدی
دانشیار، پژوهشگاه هوافضا، وزارت علوم، تحقیقات و فناوری، تهران، ایران
Abstract Persian

این مقاله یک مدل شبکه عصبی برای پیش‌بینی رفتار مکانیکی مواد الاستومری تقویت‌شده با الیاف پیوسته را در تغییر شکل‌های بزرگ معرفی می‌کند. مدل‌سازی بر اساس انرژی کرنش ماده انجام می‌شود که تابع اسکالر از مقادیر تانسوری مربوط به میدان تغییر شکل و جهت‌گیری الیاف است. داده‌های مورد نیاز برای آموزش شبکه عصبی، با استفاده از روش همگن‌سازی میکرومکانیکی بر روی یک عنصر حجمی نماینده که نشان‌دهنده ریزساختار ماده است، به دست آمده است. با اعمال تغییر شکل‌های بزرگ به این عنصر حجمی، پاسخ میکرومکانیکی ماده هایپرالاستیک ارزیابی شده و رفتار مکانیکی معادل برای کل ماده مرکب تعیین می‌شود. مدل نهایی توسعه‌یافته با استفاده از شبکه عصبی و نتایج میکرومکانیکی، می‌تواند به‌عنوان یک مدل رفتاری برای تحلیل اجزای محدود مورد استفاده قرار گیرد. یافته‌های این تحقیق به‌وضوح نشان می‌دهند مدل شبکه عصبی قادر به پیش‌بینی نتایج پیچیده تحلیل میکرومکانیکی است. این امر تأییدی بر کارایی روش ارائه‌شده در مدل‌سازی رفتار مواد هایپرالاستیک ناهمسانگرد است. مزیت اصلی این رویکرد، در توانایی آن برای کاهش چشمگیر زمان محاسبات در شبیه‌سازی‌های ماکروسکوپیک نهفته است، زیرا مدل شبکه‌ی عصبی به‌عنوان یک مدل رفتاری جایگزین، نیاز به تحلیل مستقیم ریزساختار در هر گام محاسباتی را مرتفع می‌سازد. این مدل به محققان امکان می‌دهد تا رفتار کلی مواد هایپرالاستیک ناهمسانگرد را بر اساس ویژگی‌های مواد تشکیل‌دهنده و ساختار داخلی آنها، با دقت بالا پیش‌بینی کنند.

Keywords Persian

شبکه عصبی
رفتار مکانیکی در کرنش‌های بزرگ
ماده هایپرالاستیک
الیاف پیوسته تک جهته
مدل‌سازی میکرومکانیک
[1] C. O. Horgan and G. Saccomandi, "A new constitutive theory for fiber-reinforced incompressible nonlinearly elastic solids," Journal of the Mechanics and Physics of Solids, vol. 53, no. 9, pp. 1985–2015, 2005, https://doi.org/10.1016/j.jmps.2005.04.004.
[2]N. Lahellec, F. Mazerolle, and J.-C. Michel, "Second-order estimate of the macroscopic behavior of periodic hyperelastic composites: theory and experimental validation,” Journal of the Mechanics and Physics of Solids, vol. 52, no. 1, pp. 27–49, 2004, https://doi.org/10.1016/S0022-5096(03)00104-2.
[3] A. J. M. Spencer, Continuum Theory of the Mechanics of Fibre-Reinforced Composites, Vienna: Springer, 2014, https://doi.org/10.1007/978-3-7091-4336-0.
[4]G. Y. Qiu and T. Pence, "Remarks on the behavior of simple directionally reinforced incompressible nonlinearly elastic solids," Journal of Elasticity, vol. 49, pp. 1–30, 1997, https://doi.org/10.1023/A:1007410321319.
[5] J. Merodio and R. W. Ogden, "Mechanical response of fiber-reinforced incompressible non-linearly elastic solids," International Journal of Non-Linear Mechanics, vol. 40, no. 2–3, pp. 213–227, 2005, https://doi.org/10.1016/j.ijnonlinmec.2004.05.003.
[6]Z. Y. Guo, X. Q. Peng, and B. Moran, "A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus," Journal of the Mechanics and Physics of Solids, vol. 54, no. 9, pp. 1952–1971, 2006, https://doi.org/10.1016/j.jmps.2006.02.006.
[7]G. DeBotton, I. Hariton, and E. A. Socolsky, "Neo-Hookean fiber-reinforced composites in finite elasticity,” Journal of the Mechanics and Physics of Solids, vol. 54, no. 3, pp. 533–559, 2006, https://doi.org/10.1016/j.jmps.2005.10.001.
[8]P. P. Castañeda, "Second-order theory for nonlinear dielectric composites incorporating field fluctuations," Physical Review B, vol. 64, no. 21, 2001, Art. no. 214205, https://doi.org/10.1103/PhysRevB.64.214205.
[9] P. P. Castaneda, "Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I-theory," Journal of the Mechanics and Physics of Solids, vol. 50, no. 4, pp. 737–757, 2002, https://doi.org/10.1016/S0022-5096(01)00099-0 .
[10] M. Brun, O. Lopez Pamies, and P. P. Castaneda, "Homogenization estimates for fiber-reinforced elastomers with periodic microstructures," International Journal of Solids and Structures, vol. 44, no. 18–19, pp. 5953–5979, 2007, https://doi.org/10.1016/j.ijsolstr.2007.02.003.
[11] J. Moraleda, J. Segurado, and J. Llorca, "Finite deformation of porous elastomers: a computational micromechanics approach," Philosophical Magazine, vol. 87, no. 35, pp. 5607–5627, 2007, https://doi.org/10.1080/14786430701678930.
[12] J. E. Bischoff, E. A. Arruda, and K. Grosh, "A microstructurally based orthotropic hyperelastic constitutive law," Journal of Applied Mechanics, vol. 69, no. 5, pp. 570–579, 2002, https://doi.org/10.1115/1.1485754.
[13] M. T. Abadi, "Rheological characterization of continuous fiber-reinforced viscous fluid," Journal of Non-Newtonian Fluid Mechanics, vol. 165, no. 15–16, pp. 914–922, 2010, https://doi.org/10.1016/j.jnnfm.2010.05.001.
[14] M. T. Abadi, "Mechanical behavior of continuous fiber-reinforced elastomeric materials at finite strain," Mechanics of Advanced Materials and Structures, vol. 19, no. 5, pp. 360–366, 2012, https://doi.org/10.1080/15376494.2010.528164.
[15] M. Fernández, M. Jamshidian, T. Böhlke, K. Kersting, and O. Weeger, "Anisotropic hyperelastic constitutive models for finite deformations combining material theory and data-driven approaches with application to cubic lattice metamaterials," Computational Mechanics, vol. 67, pp. 653–677, 2021, https://doi.org/10.1007/s00466-020-01954-7.
[16] X. Liu, S. Tian, F. Tao, and W. Yu, "A review of artificial neural networks in the constitutive modeling of composite materials," Composites Part B: Engineering, vol. 224, 2021, Art. no. 109152, https://doi.org/10.1016/j.compositesb.2021.109152.
[17] A. Hussain, A. H. Sakhaei, and M. Shafiee, "Machine learning-based constitutive modelling for material non-linearity: A review," Mechanics of Advanced Materials and Structures, 2024, https://doi.org/10.1080/15376494.2024.2439557.
[18] J. Ghaboussi, D. A. Pecknold, M. Zhang, and R. Haj Ali, "Autoprogressive training of neural network constitutive models," International Journal for Numerical Methods in Engineering, vol. 42, no. 1, pp. 105-126, 1998, https://doi.org/10.1002/(SICI)1097-0207(19980515)42:1<105::AID-NME356>3.0.CO;2-V.
[19] R. Haj Ali, D. Pecknold, J. Ghaboussi, and G. Voyiadjis, "Simulated micromechanical models using artificial neural networks," Journal of Engineering Mechanics, vol. 127, no. 7, pp. 730–738, 2001, https://doi.org/10.1061/(ASCE)0733-9399(2001)127:7(730).
[20] R. M. Haj Ali, D. A. Pecknold, and J. Ghaboussi, "Micromechanics-based constitutive damage models for composite materials using artificial neural-networks," Modeling and simulation based engineering, pp. 551–557, 1998.
[21] C. Yang, Y. Kim, S. Ryu, G. X. Gu, "Using convolutional neural networks to predict composite properties beyond the elastic limit," MRS Communications, vol. 9, no. 2, pp. 609-617, 2019, https://doi.org/10.1557/mrc.2019.49.
[22] M. Al Assadi, H. A. El Kadi, and I. M. Deiab, "Using artificial neural networks to predict the fatigue life of different composite materials including the stress ratio effect," Applied Composite Materials, vol. 18, no. 4, pp. 297–309, 2011, https://doi.org/10.1007/s10443-010-9158-7.
[23] P. Pratim Das, M. Elenchezhian, V. Vadlamudi, and R. Raihan, "Artificial intelligence assisted residual strength and life prediction of fiber reinforced polymer composites," in AIAA SCITECH 2023 Forum, National Harbor, MD & Online, 2023, https://doi.org/10.2514/6.2023-0773.
[24] A. H. Mirzaei, P. Haghi, M. M. Shokrieh, "Prediction of fatigue life of laminated composites by integrating artificial neural network model and non-dominated sorting genetic algorithm," International Journal of Fatigue, vol. 188, 2024, Art. no. 108528, https://doi.org/10.1016/j.ijfatigue.2024.108528.
[25] C. T. Chen and G. X. Gu, "Generative deep neural networks for inverse materials design using backpropagation and active learning," Advanced Science, vol. 7, no. 5, 2020, https://doi.org/10.1002/advs.201902607.
[26] M. K. Taher, S. Khudhair, G. Kovacs, S. Szaval, and M. M. Sahib, "Using artificial neural network in reverse design of fiber reinforced plastic composite materials," International Journal of Multiphysics, vol. 18, no. 3, pp. 1430-1445, 2024.
[27] X. Liu et al., "Design optimization of laminated composite structures using artificial neural network and genetic algorithm," Composite Structures, vol. 305, 2023, Art. no. 116500, https://doi.org/10.1016/j.compstruct.2022.116500.
[28] X. Liu, C. A. Featherston, and D. Keccedy, "A novel parallel method for layup optimization of composite structures with ply drop-offs," Composite Structures, vol. 312, 2023, Art. no. 116853, https://doi.org/10.1016/j.compstruct.2023.116853.
[29] B. Miller and L. Ziemianski, "Accelerating multi-objective optimization of composite structures using multi-fidelity surrogate models and curriculum learning," Materials, vol. 18, no. 7, 2025, Art. no. 1469. https://doi.org/10.3390/ma18071469.
[30]M. T. Abadi, "Characterization of heterogeneous materials under shear loading at finite strain," Composite Structures, vol. 92, no. 2, pp. 578–584, 2010, https://doi.org/10.1016/j.compstruct.2009.09.002.
[31]M. T. Abadi, "Micromechanical modeling of heterogeneous materials at finite strain," in Wiley Encyclopedia of Composites, L. Nicolais, Ed. John Wiley & Sons, Inc. 2011, pp. 1-13, https://doi.org/10.1002/9781118097298.weoc155.

Articles in Press, Accepted Manuscript
Available Online from 03 November 2025

  • Receive Date 16 August 2025
  • Revise Date 08 October 2025
  • Accept Date 23 October 2025
  • First Publish Date 03 November 2025