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Shashikant Prasad,
Chetan Jadhav,
Digvijay Kanase,
Harshal Vidya,
Yogesh Ikhe,
- Assistant Professor, Department of Electrical Engineering Dr. D. Y. Patil Institute of Technology Pune, Dnyaan Prasad Global University (DPGU), School of Technology and Research, Dr. D. Y. Patil Unitech Society, Sant Tukaram Nagar, Pimpri, Pune, Maharashtra, India
- Assistant Professor, Department of Electrical Engineering, G. H. raisoni College of Engineering & Management, Wagholi, Pune, Maharashtra, India
- Assistant Professor, Department of Electrical Engineering Dr. D. Y. Patil Institute of Technology Pune, Dnyaan Prasad Global University (DPGU), School of Technology and Research, Dr. D. Y. Patil Unitech Society, Sant Tukaram Nagar, Pimpri, Pune, Maharashtra, India
- Assistant Professor, Department of Engineering Sciences, Marathwada Mitra Mandal’s Institute of Technology, Lohgaon, Pune, Maharashtra, India
- Assistant Professor, Department of Electrical Engineering, G. H. Raisoni College of Engineering & Management Nagpur, Maharashtra, India
Abstract
Strain-dependent percolation models are mostly built and tested for uniaxial tension, yet many flexible sensors and stretchable devices work mainly in bending, where the outer fibre is stretched, the inner fibre is compressed and the strain changes with thickness. This study extends an aggregate-breakage percolation model, originally formulated for uniaxial strain, to through-thickness bending of a multi-walled carbon nanotube/thermoplastic polyurethane (MWCNT/TPU) nanocomposite. The local strain is taken as ε(y) = y/R, where y is the distance from the neutral axis and R is the bend radius, and the local percolation state, breakage probability and tunnelling-limited conductivity are integrated across the thickness. Only the percolation threshold (0.34 vol%) is anchored to a value reported for an independently fabricated MWCNT/TPU system; every other output is a model prediction that has not yet been compared with bending experiments. The effective conductivity is predicted to rise from about 0.226 S/m at a 50 mm bend radius to a peak of about 0.318 S/m near 8 mm, then fall as curvature tightens. The gauge factor, referenced to the 50 mm radius, is non-monotonic: it peaks in magnitude at about −18.4 near 1.25% outer-fibre strain and relaxes to about −2.8 at 8.3% strain. An artificial neural network (ANN) trained on the model’s own noise-added output reproduces the analytical curve with a mean deviation of 0.69% (maximum 2.50%); this is a numerical consistency check, not a comparison with measurements. Further analyses show that conductivity rises strongly with MWCNT loading (0.50–1.20 vol%) while the peak gauge factor barely changes, that the conductivity range narrows in thicker samples (0.25–1.0 mm), and that a simulated bend–unbend cycle produces a double-peaked current signal. A Monte Carlo analysis quantifies the gauge-factor spread caused by parameter uncertainty. The main limitation is the absence of bending-mode experimental validation.
Keywords: MWCNT/TPU nanocomposites, bending-mode piezoresistivity, percolation theory, aggregate breakage, neutral-axis strain gradient, percolation-threshold anchoring, ANN surrogate verification, flexible strain sensors
References
1. Ghasemi F, Sharifzadeh E. An innovative analytical approach to define the dynamic electrical conductivity in polymer nanocomposites: the effect of nanoparticle network rearrangement. Comput Mater Sci. 2026;262:114384. Available from: https://www.sciencedirect.com/science/article/pii/S092702562500727X
2. Bharadwaj S, Gupta TK, Chauhan GS, et al. Long length MWCNT/TPU composite materials for stretchable and wearable strain sensors. Sens Actuators A Phys. 2023;357:114364. Available from: https://www.sciencedirect.com/science/article/pii/S0924424723002133
3. Zhou Z, Tang W, Xu T, Zhao W, Zhang J, Bai C. Flexible strain sensors based on thermoplastic polyurethane fabricated by electrospinning: a review. Sensors (Basel). 2024;24(15):4793. doi:10.3390/s24154793
4. Kim H, Tak W, Choi Y, Jeon J, Lee S, Cho J, et al. Development of TPU/MWCNT composite bending sensor. Int J Precis Eng Manuf. 2025. doi:10.1007/s12541-024-01171-9
5. Payandehpeyman J, Mazaheri M. Micromechanical modeling of electrical conductivity and percolation in CNT/polymer nanocomposites by considering morphology: homogeneous, agglomerated, and segregated structures. Polym Compos. 2025. doi:10.1002/pc.70042
6. Kirkpatrick S. Percolation and conduction. Rev Mod Phys. 1973;45(4):574-88. doi:10.1103/RevModPhys.45.574
7. Stauffer D, Aharony A. Introduction to percolation theory. 2nd ed. London: Taylor & Francis; 1994.
8. Xu X, Yuan Y, Zhang T, Li K, Wang S, Liang C, et al. A silanized MCNT/TPU-based flexible strain sensor with high stretchability for deformation monitoring of elastomeric isolators for bridges. Constr Build Mater. 2022;338:127664. Available from: https://www.sciencedirect.com/science/article/pii/S0950061822013393
9. Hu N, Karube Y, Yan C, Masuda Z, Fukunaga H. Tunneling effect in a polymer/carbon nanotube nanocomposite strain sensor. Acta Mater. 2008;56(13):2929-36.
10. Hu N, Karube Y, Arai M, Watanabe T, Yan C, Li Y, et al. Investigation on sensitivity of a polymer/carbon nanotube composite strain sensor. Carbon N Y. 2010;48(3):680-7.
11. Kim SU, Kim JY. Characterizing six percolation cases in flexible electronic composites: a Monte Carlo-based 3D compressive percolation model for wearable pressure sensors. Materials (Basel). 2025;18(3):685.
12. Kim SU, Kim JY. Dynamic statistical mechanics modeling of percolation networks in conductive polymer composites for smart sensor applications. Materials (Basel). 2025;18(13):3097.
Journal of Polymer & Composites
| Volume | 14 | |
| 05 | ||
| Received | 07/09/2026 | |
| Accepted | 22/09/2026 | |
| Published | 29/09/2026 | |
| Publication Time | 22 Days |