Interpretable Symbolic Regression Modelling of Stacking Sequence Effects in Jute/Ramie and Jute/Flax Hybrid Composites

Abstract

In this study, a symbolic regression-based framework was developed to investigate the tensile and flexural behavior of natural fiber-reinforced hybrid composites with different stacking sequences. Experimental data from eleven six-layer laminates, including jute, ramie, flax, jute/ramie, and jute/flax configurations, were reanalyzed. Due to the limited dataset size, the proposed approach was considered an exploratory and interpretable modelling framework rather than a universal predictive model. Fifteen descriptors related to fiber position, interlayer contacts, fiber weight fractions, and density were defined to analytically represent laminate architectures. Pearson and Spearman correlation analyses were first performed, followed by symbolic regression modelling using HeuristicLab to derive interpretable expressions for tensile and flexural strength. The results indicated that ramie-related parameters generally showed positive relationships with mechanical performance, while the symbolic regression models highlighted the potential importance of flax fibers in the outer layers, jute fibers in the core region, and ramie–ramie contact density. The obtained models showed satisfactory agreement with the available experimental data; however, their interpretation should be limited to the investigated laminate configurations. Therefore, the obtained expressions are not intended as universal predictive equations, but as data-driven analytical representations that may help interpret the influence of stacking sequence on the mechanical behavior of hybrid composite laminates. The proposed framework may serve as an example for future studies aiming to establish interpretable relationships between laminate architecture and mechanical performance using larger and more diverse datasets.

Keywords

• Natural fiber composites
• hybrid laminates
• mechanical properties
• stacking sequence
• symbolic regression.

Ethical Statement

I declare that this study is original; that I have adhered to scientific ethical principles and rules in all stages of the study, including preparation, data collection, analysis, and presentation of information; that I have cited all sources for data and information not obtained within the scope of this study and included these sources in the bibliography; that I have not made any changes to the data used; and that I have complied with all ethical duties and responsibilities by accepting all the terms and conditions of the Committee on Publication Ethics (COPE). I also declare that I am willing to accept all moral and legal consequences should any situation contrary to this declaration I have made regarding the study be detected at any time.

Jüt/Rami ve Jüt/Keten Hibrit Kompozitlerde İstif Dizilimi Etkilerinin Yorumlanabilir Sembolik Regresyon Tabanlı Modellenmesi

Abstract

Bu çalışmada, farklı katman dizilimlerine sahip doğal fiber takviyeli hibrit kompozitlerin çekme ve eğilme davranışlarını incelemek amacıyla sembolik regresyon tabanlı bir yaklaşım geliştirilmiştir. Jüt, rami, keten, jüt/rami ve jüt/keten konfigürasyonlarını içeren on bir adet altı katmanlı laminattan elde edilen deneysel veriler yeniden analiz edilmiştir. Laminat mimarilerinin analitik olarak temsil edilebilmesi amacıyla fiber konumu, katmanlar arası temaslar, fiber ağırlık oranları ve yoğunluk ile ilişkili toplam on beş tanımlayıcı parametre oluşturulmuştur. İlk olarak tanımlanan parametreler ile mekanik özellikler arasındaki ilişkileri belirlemek amacıyla Pearson ve Spearman korelasyon analizleri gerçekleştirilmiştir. Daha sonra, çekme ve eğilme mukavemetleri için yorumlanabilir analitik ifadeler elde etmek amacıyla HeuristicLab yazılımı kullanılarak sembolik regresyon modelleri geliştirilmiştir. Korelasyon analizleri, rami fiberi ile ilişkili parametrelerin hem çekme hem de eğilme performansı ile genel olarak en güçlü pozitif ilişkilere sahip olduğunu göstermiştir. Sembolik regresyon modelleri ise dış tabakalarda keten fiberlerin, çekirdek bölgede jüt fiberlerin ve rami–rami temas yoğunluğunun önemini tutarlı bir şekilde ortaya koymuştur. Geliştirilen modeller, nispeten basit matematiksel yapıları korurken 0.99'a kadar belirleme katsayısı (R²) değerlerine ulaşmıştır. Elde edilen sonuçlar, laminat mimarilerinin fiziksel olarak anlamlı ve sınırlı sayıda parametre ile temsil edilebileceğini ve sembolik regresyonun katman diziliminin hibrit kompozit laminatların mekanik davranışı üzerindeki etkisini yorumlamak için etkili bir yaklaşım sunduğunu göstermiştir. Önerilen yaklaşım, laminat mimarisi ile mekanik performans arasında yorumlanabilir analitik ilişkiler kurmayı amaçlayan gelecekteki çalışmalar için örnek bir çerçeve sunabilir.

Keywords

• Doğal elyaf kompozitler
• hibrit laminatlar
• mekanik özellikler
• katman dizilimi
• sembolik regresyon.

Ethical Statement

Bu çalışmanın, özgün bir çalışma olduğunu; çalışmanın hazırlık, veri toplama, analiz ve bilgilerin sunumu olmak üzere tüm aşamalarından bilimsel etik ilke ve kurallarına uygun davrandığımı; bu çalışma kapsamında elde edilmeyen tüm veri ve bilgiler için kaynak gösterdiğimi ve bu kaynaklara kaynakçada yer verdiğimi; kullanılan verilerde herhangi bir değişiklik yapmadığımı, çalışmanın Committee on Publication Ethics (COPE)' in tüm şartlarını ve koşullarını kabul ederek etik görev ve sorumluluklara riayet ettiğimi beyan ederim. Herhangi bir zamanda, çalışmayla ilgili yaptığım bu beyana aykırı bir durumun saptanması durumunda, ortaya çıkacak tüm ahlaki ve hukuki sonuçlara razı olduğumu bildiririm.

References

1. [1] C.K. Sahoo, G.S. Bhatia, A. Arockiarajan, "Effect of patch-parent stacking sequence and patch stiffness on the tensile behaviour of the patch repaired carbon-glass hybrid composite", Thin-Walled Structures, vol.·179, pp.·109551, 2022. DOI: 10.1016/j.tws.2022.109551
2. [2] E. Kilickap, "Determination of optimum parameters on delamination in drilling of GFRP composites by Taguchi method", Indian Journal of Engineering & Materials Sciences, vol.·17, no.·4, pp.·265-274, 2010.
3. [3] E. Kilickap, "Analysis and modeling of delamination factor in drilling glass fiber reinforced plastic using response surface methodology", Journal of composite materials, vol.·45, no.·6, pp.·727-736, 2011.
4. [4] Ö. Keleş, S. Bati, Y.H. Çelik, "Hybrid effect on tensile, flexural, and quasi-static punch shear behavior of jute/ramie and jute/flax reinforced hybrid composites", Materials Testing, vol.·66, no.·6, pp.·802-816, 2024. DOI: 10.1515/mt-2023-0383
5. [5] A. Vinod, J. Tengsuthiwat, Y. Gowda, R. Vijay, M. Sanjay, S. Siengchin, H.N. Dhakal, "Jute/Hemp bio-epoxy hybrid bio-composites: Influence of stacking sequence on adhesion of fiber-matrix", International Journal of Adhesion and Adhesives, vol.·113, pp.·103050, 2022. DOI: 10.1016/j.ijadhadh.2021.103050
6. [6] B. Özdemir, A. Yardimeden, E. Bahce, E. Kilickap, E. Emir, "Analysis of Drilling Behaviour in Jute Fibres Reinforced Natural Composites", Journal of Natural Fibers, vol.·20, no.·1, pp.·2159608, 2023. 10.1080/15440478.2022.2159608
7. [7] F. Pinto, L. Boccarusso, D. De Fazio, S. Cuomo, M. Durante, M. Meo, "Carbon/hemp bio-hybrid composites: Effects of the stacking sequence on flexural, damping and impact properties", Composite Structures, vol.·242, pp.·112148, 2020. DOI: 10.1016/j.compstruct.2020.112148
8. [8] S. Acharya, T. Bera, V. Prakash, S. Pradhan, "Effect of stacking sequence on the tribological behaviour of jute-glass hybrid epoxy composite", Materials Today: Proceedings, vol.·28, pp.·936-939, 2020. DOI: 10.1016/j.matpr.2019.12.328

9. [9] A. Shahzad, S. Nasir, Mechanical properties of natural fiber/synthetic fiber reinforced polymer hybrid composites. in ‘Green biocomposites’(eds.: Jawaid M., Sapuan S., Alothman O.) Springer, 355–396 (2017).
10. [10] S. Dash, B. Chandra Routara, M. Prasad Satpathy, "Fibre stacking sequence and mechanical characterization of polymer hybrid composites: An experimental study", Materials Today: Proceedings, 2023. DOI: 10.1016/j.matpr.2023.10.137
11. [11] Y. Huang, M.T.H. Sultan, F.S. Shahar, S.Y. Nayak, "Influence of Stacking Sequence and Seawater Aging on Mechanical, Thermal, and Viscoelastic Properties of Hybrid kenaf/Flax/Glass Fiber-Reinforced Sustainable Composites", Journal of Natural Fibers, vol.·23, no.·1, pp.·2600508, 2026. DOI: 10.1080/15440478.2025.2600508
12. [12] K. Karthik, J.U. Prakash, J.S. Binoj, B.B. Mansingh, "Effect of stacking sequence and silicon carbide nanoparticles on properties of carbon/glass/Kevlar fiber reinforced hybrid polymer composites", Polymer Composites, vol.·43, no.·9, pp.·6096-6105, 2022. DOI: 10.1002/pc.26912
13. [13] R. Yahaya, S.M. Sapuan, M. Jawaid, Z. Leman, E.S. Zainudin, "Quasi-static penetration and ballistic properties of kenaf–aramid hybrid composites", Materials & Design, vol.·63, pp.·775-782, 2014. DOI: 10.1016/j.matdes.2014.07.010
14. [14] H. Ding, H. Yang, H. Jiang, Y. Ren, "Crashworthiness of Steeple-Triggered Hat-Shaped Composite Structure Under the Axial and Oblique Compression: Stacking Sequence Design", Applied Composite Materials, vol.·33, no.·1, pp.·19, 2025. DOI: 10.1007/s10443-025-10389-3
15. [15] F.E. Yakin, C.O. Senol, N. Birgün, H. Ulus, M. Yildiz, H.S. Sas, "Influence of stacking sequence and compaction force during the AFP process on mechanical performance and damage mechanisms elucidated by acoustic emission insights", Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, vol.·240, no.·1, pp.·19-34, 2025. DOI: 10.1177/14644207241309548
16. [16] K. Oine, K. Ryuzono, Y. Kawagoe, Y. Hoshikawa, K. Shirasu, Y. Takayama, T. Okabe, "Comparative study of thermosetting CF/epoxy and thermoplastic CF/PAEK composite laminates: Effects of stacking sequences on open-hole strength", Journal of Thermoplastic Composite Materials, vol.·39, no.·1, pp.·259-291, 2025. DOI: 10.1177/08927057251344271
17. [17] A.I. Ra’eis, M.A.M. Rizal, A.P. Md Saad, M.S.R.M. Saufi, A. Syamsir, "Influence of Stacking Sequence on the Structural Performance and Failure Behaviour of Pultruded Glass Fibre-Reinforced Polymer Composites", Fibers and Polymers, 2026. DOI: 10.1007/s12221-026-01333-8
18. [18] D. Gai, S. Yu, Z. Yao, L. Zhao, L. Huo, J. Zhang, C. Wang, "Mechanisms of interlaminar strength enhancement in CFRP bending beams via Double-Double laminate optimization: Effects of ply sequence and orientation", Composites Part B: Engineering, vol.·314, pp.·113439, 2026. DOI: 10.1016/j.compositesb.2026.113439
19. [19] L. Liu, G. Peng, Z. Wang, Q. Wang, R. Chen, "Tailored cross-helicoidal architectures for enhanced low-velocity impact resistance in hybrid composites", Composites Part B: Engineering, vol.·313, pp.·113407, 2026. DOI: 10.1016/j.compositesb.2026.113407
20. [20] S. Gopinath, V. Arumugam, V. Dinesh Babu, I. Elango, "Optimization of damage parameters in glass fiber-reinforced composites: numerical and experimental insights into structural integrity enhancement", Journal of Adhesion Science and Technology, vol.·40, no.·1, pp.·94-118, 2026. DOI: 10.1080/01694243.2025.2563904
21. [21] X. Liang, S. Yang, Q. Zhang, Z. Wang, Z. Cheng, H. Pu, J. Cai, "A hierarchical multi-objective optimization approach for hybrid variables design of deployable composite tubular structures", Structural and Multidisciplinary Optimization, vol.·69, no.·1, pp.·1, 2025. DOI: 10.1007/s00158-025-04187-5
22. [22] C. Vyas, R. Jhala, "Experimental Investigation of Low-Velocity Impact on Glass-Basalt Hybrid Laminates: Effect of Ply Sequence and Energy Levels", Polymer Composites, vol.·47, no.·1, pp.·336-351, 2026. DOI: 10.1002/pc.70148
23. [23] I. Isik, S. Bati, M.E. Demir, S. Fidan, Y.H. Celik, "Symbolic regression analysis of cutting force and delamination in drilling and punching of GFRP composites", Journal of Reinforced Plastics and Composites, vol.·45, no.·7-8, pp.·1656-1680, 2026.
24. [24] B. Özdemir, E. Emir, E. Bahçe, A. Yardımeden, E. Kılıçkap, "Estimation of Forces in Longitudinal and Multi-Pass Milling of GFRP and ABACA Composites Utilizing Machine LearningTechniques", Journal of Intelligent & Fuzzy Systems, pp.·18758967251401794, 2025.
25. [25] K. Scott, S. Miller, Inverse Design of Composite Laminates Using Neural Networks and Material Informatics, AIAA SCITECH 2026 Forum, American Institute of Aeronautics and Astronautics, 2026.
26. [26] S.J. Arunachalam, R. Saravanan, T. Sathish, "Tailoring mechanical behavior of Jute–Kenaf–glass hybrid composites with SiC nanoparticles: experimental and AI-based predictive analysis", Chemical Papers, 2026. DOI: 10.1007/s11696-026-04654-3
27. [27] M.M. Rahman, A.E. Ismail, M.F. Ramli, A.H.A. Rashid, "Predicting flexural properties of fiber reinforced composites: An experimental dataset analysis using machine learning models", Next Materials, vol.·11, pp.·101720, 2026. DOI: 10.1016/j.nxmate.2026.101720
28. [28] H. Ghasempoor, A. Keshavarzi, H. Saeidi Googarchin, "Machine learning-enhanced prediction of energy absorption in AL/CFRP hybrid tubes under oblique compression", Mechanics of Advanced Materials and Structures, vol.·33, no.·1, pp.·2627539, 2026. DOI: 10.1080/15376494.2026.2627539
29. [29] Y.H. Çelik, Ş. Fidan, "Analysis of cutting parameters on tool wear in turning of Ti-6Al-4V alloy by multiple linear regression and genetic expression programming methods", Measurement, vol.·200, pp.·111638, 2022.
30. [30] A. Erkliğ, B.H. Sulaiman, Ö.Y. Bozkurt, M. Bulut, "Synergistic effects of stacking sequence and graphene nanoplatelets on the mechanical and impact behavior of Kevlar/Carbon hybrid composites", Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol.·48, no.·6, pp.·444, 2026. DOI: 10.1007/s40430-026-06391-w
31. [31] K.C. Nagaraja, S. Rajanna, G.S. Prakash, G. Rajeshkumar, "The Role of Stacking Order on Mechanical Properties of Glass/Carbon Reinforced Epoxy Hybrid Composites Prepared by Resin Infusion Technique", Materials Today: Proceedings, vol.·22, pp.·2446-2451, 2020. DOI: 10.1016/j.matpr.2020.03.371
32. [32] M.J. Ms, C. Santulli, M. Yazid, N. Hussein, H. Ahmad, "Effect of stacking sequence on the tensile and flexural properties of glass fibre epoxy composites hybridized with basalt, flax or jute fibres", Material Science and Engineering with Advanced Research, vol.·1, no.·4, pp.·19-25, 2016. DOI: 10.24218/msear.2015.19
33. [33] E. Selver, N. Ucar, T. Gulmez, "Effect of stacking sequence on tensile, flexural and thermomechanical properties of hybrid flax/glass and jute/glass thermoset composites", Journal of Industrial Textiles, vol.·48, no.·2, pp.·494-520, 2018. DOI: 10.1177/1528083717736102
34. [34] J. Hauke, T. Kossowski, "Comparison of Values of Pearson's and Spearman's Correlation Coefficients on the Same Sets of Data", Quaestiones Geographicae, vol.·30, no.·2, pp.·87-93, 2011. DOI: 10.2478/v10117-011-0021-1
35. [35] Y. Karaduman, L. Onal, A. Rawal, "Effect of stacking sequence on mechanical properties of hybrid flax/jute fibers reinforced thermoplastic composites", Polymer Composites, vol.·36, no.·12, pp.·2167-2173, 2015. DOI: 10.1002/pc.23127
36. [36] I.D.G. Ary Subagia, Y. Kim, L.D. Tijing, C.S. Kim, H.K. Shon, "Effect of stacking sequence on the flexural properties of hybrid composites reinforced with carbon and basalt fibers", Composites Part B: Engineering, vol.·58, pp.·251-258, 2014. DOI: 10.1016/j.compositesb.2013.10.027