Since 1963
ARTICLE
Physics-informed neural networks for inhomogeneous swelling analysis of dual-layer gels with chain entanglement effects
1
College of Information and Management Science, Henan Agricultural University, Zhengzhou, China
These authors had equal contribution to this work
Submission date: 2025-08-10
Final revision date: 2025-11-21
Acceptance date: 2025-12-09
Online publication date: 2026-02-26
Corresponding author
Jianjun Zhang
College of Information and Management Science, Henan Agricultural University, Zhengzhou, China
College of Information and Management Science, Henan Agricultural University, Zhengzhou, China
KEYWORDS
TOPICS
ABSTRACT
A field theory incorporating Edwards–Vilgis slip-link elasticity with Flory–Huggins mixing is developed for dual-layer gels containing rigid cores, capturing chain entanglement effects neglected by Neo–Hookean models. Physics-informed neural networks (PINNs) transform complexities of handling interfacial constraints into a neural network optimization problem, thereby reducing both algorithmic complexity and implementation requirements. Systematic parametric studies demonstrate that micromaterial parameters critically govern stress distributions, solvent concentration profiles, and swelling behavior. The framework enables precise control of target solvent concentrations and equilibrium configurations through optimal micromaterial parameter selection and thickness ratio design in dual-layer spherical gel systems.
REFERENCES (23)
1.
Abdolahi, J., Baghani, M., Arbabi, N., & Mazaheri, H. (2017). Finite bending of a temperature-sensitive hydrogel tri-layer: An analytical and finite element analysis. Composite Structures, 164, 219–228. https://doi.org/10.1016/j.comp....
2.
Ahmadi, M., Zholobko, O., & Wu, X.-f. (2020). Inhomogeneous swelling behavior of a bi-layered spherical hydrogel containing a hard core. Journal of Applied Physics, 128 (4), Article 044703. https://doi.org/10.1063/5.0016....
3.
Ballauff, M., & Lu, Y. (2007). “Smart” nanoparticles: Preparation, characterization and applications. Polymer, 48 (7), 1815–1823. https://doi.org/10.1016/j.poly....
4.
Chester, S.A., & Anand, L. (2010). A coupled theory of fluid permeation and large deformations for elastomeric materials. Journal of the Mechanics and Physics of Solids, 58 (11), 1879–1906. https://doi.org/10.1016/j.jmps....
5.
Diao, Y., Yang, J., Zhang, Y., Zhang, D., & Du, Y. (2023). Solving multi-material problems in solid mechanics using physics-informed neural networks based on domain decomposition technology. Computer Methods in Applied Mechanics and Engineering, 413, Article 116120. https://doi.org/10.1016/j.cma.....
6.
Edwards, S.F., & Vilgis, Th. (1986). The effect of entanglements in rubber elasticity. Polymer, 27 (4), 483–492. https://doi.org/10.1016/0032-3...
7.
Flory, P.J. (1942). Thermodynamics of high polymer solutions. The Journal of Chemical Physics, 10 (1), 51–61. https://doi.org/10.1063/1.1723....
8.
Flory, P.J., & Rehner, J. (1943). Statistical mechanics of cross-linked polymer networks II. Swelling. The Journal of Chemical Physics, 11 (11), 521–526. https://doi.org/10.1063/1.1723....
9.
Huggins, M.L. (1941). Solutions of long chain compounds. The Journal of Chemical Physics, 9 (5), 440. https://doi.org/10.1063/1.1750....
10.
Jin, L., Xu, J., Xue, Y., Zhang, X., Feng, M., Wang, C., Yao, W., Wang, J., & He, M. (2021). Research progress in the multilayer hydrogels. Gels, 7 (4), Article 172. https://doi.org/10.3390/gels70....
11.
Khan, M.U.A., Stojanović, G.M., Abdullah, M.F.B., Dolatshahi-Pirouz, A., Marei, H.E., Ashammakhi, N., & Hasan, A. (2024). Fundamental properties of smart hydrogels for tissue engineering applications: A review. International Journal of Biological Macromolecules, 254 (Part 3), Article 127882. https://doi.org/10.1016/j.ijbi....
12.
López-Díaz, A., Vázquez, A.S., & Vázquez, E. (2024). Hydrogels in soft robotics: Past, present, and future. ACS Nano, 18 (32), 20817–20826. https://doi.org/10.1021/acsnan....
13.
Morimoto, T., & Ashida, F. (2015). Temperature-responsive bending of a bilayer gel. International Journal of Solids and Structures, 56–57, 20–28. https://doi.org/10.1016/j.ijso....
14.
Raissi, M., Perdikaris, P., & Karniadakis, G.E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, 686–707. https://doi.org/10.1016/j.jcp.....
15.
Su, H., Yan, H., Zhang, X., & Zhong, Z. (2022). Multiphysics-informed deep learning for swelling of pH/temperature sensitive cationic hydrogels and its inverse problem. Mechanics of Materials, 175, Article 104498. https://doi.org/10.1016/j.mech....
16.
Su, H., Yan, H., & Zhong, Z. (2021). Deep neural networks for large deformation of photo-thermo-pH responsive cationic gels. Applied Mathematical Modelling, 100, 549–563. https://doi.org/10.1016/j.apm.....
17.
Urayama, K., Kawamura, T., & Kohjiya, S. (2003). Multiaxial deformations of end-linked poly(dimethylsiloxane) networks. 4. Further assessment of the slip-link model for chain-entanglement effect on rubber elasticity. The Journal of Chemical Physics, 118 (12), 5658–5664. https://doi.org/10.1063/1.1555....
18.
Wu, Z., & Zhong, Z. (2013). Inhomogeneous equilibrium swelling of core-shell-coating gels. Soft Materials, 11 (2), 215–220. https://doi.org/10.1080/153944....
19.
Yan, H., & Jin, B. (2012). Influence of microstructural parameters on mechanical behavior of polymer gels. International Journal of Solids and Structures, 49 (3–4), 436–444. https://doi.org/10.1016/j.ijso....
20.
Yan, K., Xu, F., Wei, W., Yang, C., Wang, D., & Shi, X. (2021). Electrochemical synthesis of chitosan/silver nanoparticles multilayer hydrogel coating with pH-dependent controlled release capability and antibacterial property. Colloids and Surfaces B: Biointerfaces, 202, Article 111711. https://doi.org/10.1016/j.cols....
21.
Yang, J., Bai, R., Chen, B., & Suo, Z. (2020). Hydrogel adhesion: A supramolecular synergy of chemistry, topology, and mechanics. Advanced Functional Materials, 30 (2), Article 1901693. https://doi.org/10.1002/adfm.2....
22.
Zhao, X., Hong, W., & Suo, Z. (2008). Inhomogeneous and anisotropic equilibrium state of a swollen hydrogel containing a hard core. Applied Physics Letters, 92 (5), Article 051904. https://doi.org/10.1063/1.2840....
23.
Zhao, Y.-D., Lai, J.-H., & Wang, M. (2021). 4D printing of self-folding hydrogel tubes for potential tissue engineering applications. Nano LIFE, 11 (04), Article 2141001. https://doi.org/10.1142/s17939....
| eISSN: | 2543-6309 |
| ISSN: | 1429-2955 |
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