Manufacturing Technology 2026, 26(3):258-270 | DOI: 10.21062/mft.2026.035

Gradient Stiffness Modelling of Thin Adhesive Bonds

Kamil Anasiewicz ORCID...
Faculty of Mechanical Engineering, Lublin University of Technology. Nadbystrzycka st. 36, 20-618 Lublin. Poland.

The objective of this study was to evaluate the influence of through-thickness variability of Young’s modulus on the numerical modelling of adhesive joint behaviour. The study combined experimental characterization with finite element simulations. Nanoindentation measurements were used to deter-mine the distribution of Young’s modulus across adhesive layers with thicknesses of 0.05 mm and 0.1 mm. Based on these measurements, two-dimensional finite element models of double-overlap joints were developed in Abaqus. Two modelling approaches were analysed: a conventional homogeneous model with constant material properties and a heterogeneous multi-zone model in which Young’s modu-lus varies across the adhesive thickness and is implemented using the USDFLD user subroutine. The results indicate that incorporating experimentally determined stiffness gradients significantly alters the predicted stress field, particularly in regions near the overlap ends where failure initiation is expected. The heterogeneous model provides improved agreement between numerical predictions and experimen-tally determined failure stresses. These findings demonstrate that accounting for stiffness heterogeneity improves the accuracy of numerical modelling of ultra-thin adhesive joints.

Keywords: Adhesive bonding, Apparent Young’s modulus, Heterogeneity of adhesive joints, FEM

Received: December 3, 2025; Revised: May 19, 2026; Accepted: June 7, 2026; Prepublished online: June 28, 2026; Published: June 29, 2026  Show citation

ACS AIP APA ASA Harvard Chicago Chicago Notes IEEE ISO690 MLA NLM Turabian Vancouver
Anasiewicz K. Gradient Stiffness Modelling of Thin Adhesive Bonds. Manufacturing Technology. 2026;26(3):258-270. doi: 10.21062/mft.2026.035.
Share...
Download citation
  • BibTeX (.bib)
  • Bookends (.ris)
  • EasyBib (.ris)
  • EndNote (.enw)
  • EndNote 8 (.xml)
  • ISI WoS (.isi)
  • Medlars (.medlars)
  • Mendeley (.ris)
  • MODS (.xml)
  • Papers (.ris)
  • RefWorks (.txt)
  • RefManager (.ris)
  • RIS (.ris)
  • MS Word (.xml)
  • Zotero (.ris)
    • Open full article

    References

    1. ADAMS, R.D., WAKE, W.C. (1984). Structural adhesive joints in engineering. Springer Netherlands, Dordrecht. Go to original source...
    2. PN-EN ISO 527-1:2020-01 (2024). Plastics - determination of tensile properties - Part 1: General principles. Polish Committee for Standardization.
    3. KINLOCH, A.J., KODOKIAN, G.A. (1987). The impact resistance of structural adhesive joints. In: The Journal of Adhesion, Vol. 24, pp. 109-126. Go to original source...
    4. KINLOCH, A.J., TAIG, C.M. (1987). The adhesive bonding of thermoplastic composites. In: The Journal of Adhesion, Vol. 21, pp. 291-302. Go to original source...
    5. KUCZMASZEWSKI, J., ANASIEWICZ, K. (2017). Influence of adhesive layer thickness on joint rigidity in metal-metal butt joints. In: Assembly Techniques and Technologies, Vol. 97.
    6. ANASIEWICZ, K., KUCZMASZEWSKI, J. (2019). Adhesive joint stiffness in the aspect of FEM modelling. In: Materials, Vol. 12(23), 3911. doi.org/10.3390/ma12233911 Go to original source...
    7. ANASIEWICZ, K., KUCZMASZEWSKI, J. (2021). Apparent Young's modulus of the adhesive in numerical modelling of adhesive joints. In: Materials, Vol. 14(2), 328. doi.org/10.3390/ma14020328 Go to original source...
    8. KEDWARD, K., ZHU, Y., KIEFER, S. (2005). Evaluation of composite bonded joint designs for space applications. In: 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. doi:10.2514/6.2005-2098 Go to original source...
    9. KUCZMASZEWSKI, J. (1995). Podstawy konstrukcyjne i technologiczne oceny wytrzymałości adhezyjnych połączeń metali, WUPL, Lublin.
    10. TAIB, A.A., BOUKHILI, R., ACHIOU, S., GORDON, S., BOUKEHILI, H. (2006). Bonded joints with composite adherends. Part I. In: International Journal of Adhesion and Adhesives, Vol. 26, pp. 226-236. doi: 10.1016/j.ijadhadh.2005.03.015 Go to original source...
    11. DAVIES, P., SOHIER, L., COGNARD, J.-Y., BOURMAUD, A., CHOQUEUSE, D., RINNERT, E., CRÉAC'HCADEC, R. (2009). Influence of adhesive bond line thickness on joint strength. In: International Journal of Adhesion and Adhesives, Vol. 29, pp. 724-736. doi: 10.1016/j.ijadhadh.2009.03.002 Go to original source...
    12. YAN, C., MAI, Y.-W., YE, L. (2001). Effect of bond thickness on fracture behavior in adhesive joints. In: The Journal of Adhesion, 75(1), pp. 27-44. doi: 10.1080/00218460108029592. Go to original source...
    13. PARK, J.-H., CHOI, J.-H., KWEON, J.-H. (2010). Evaluating the strengths of thick aluminum-to-aluminum joints with different adhesive lengths and thicknesses. In: Composite Structures, Vol. 92, pp. 2226-2235. doi: 10.1016/j.compstruct.2009.08.037 Go to original source...
    14. LEE, D.-B., IKEDA, T., MIYAZAKI, N., CHOI, N.-S. (2002). Damage zone and fracture toughness. In: Engineering Fracture Mechanics, Vol. 69, pp. 1363-1375. doi.org/10.1115/1.1417980 Go to original source...
    15. ADAMS, R.D., COPPENDALE, J. (1979). Stress-strain behaviour of axially-loaded butt joints. In: The Journal of Adhesion, Vol. 10, pp. 49-62. Go to original source...
    16. BYKOV, Y.A., KARPUKHIN, S.D., PANFILOV, Y.V., BOICHENKO, M.K., CHEPTSOV, V.O., OSIPOV, A.V. (2003). Measurement of hardness of thin films. In: Metal Science and Heat Treatment, Vol. 45, pp. 396-399. doi.org/10.1023/B:MSAT.0000009788.88059.14 Go to original source...
    17. ANASIEWICZ, K., KUCZMASZEWSKI, J. (2016). Pozorny moduł Younga w połączeniach adhezyjnych. In: Welding Technology Review, Vol. 88. Go to original source...
    18. BUDZIK, M.K., MASCARO, B., JUMEL, J., CASTAINGS, M., SHANAHAN, M. (2012). Monitoring crosslinking of a DGEBA-PAMAM adhesive in composite/aluminium bonded joint using mechanical and ultrasound techniques. In: International Journal of Adhesion and Adhesives, Vol. 35, pp. 120-128. doi:10.1016/j.ijadhadh.2012.02.009 Go to original source...
    19. CARRILLO, F. GUPTA, S., BALOOCH, M., et al. (2005). Nanoindentation of polydimethylsiloxane elastomers: Effect of crosslinking, work of adhesion, and fluid environment on elastic modulus. In: Journal of Materials Research, Vol. 20, pp. 2820-2830. doi.org/10.1557/JMR.2005.0354 Go to original source...
    20. MASCARO, B. BUDZIK, M. K., CASTAINGS, M., JUMEL, J., SHANAHAN, M. E. R., (2012). Evalua-tion of adhesive bond modulus. In: Journal of Physics Conference Series, Vol. 353, 12006. doi:10.1088/1742-6596/353/1/012006 Go to original source...
    21. CZUB, P., PENCZEK, P., BOŃCZA-TOMASZEWSKI, Z., PIELICHOWSKI, J. (2002). Chemia i technologia żywic epoksydowych, WNT, Warszawa.
    22. STAPLETON, S.E., WAAS, A.M., BEDNARCZYK, B.A. (2012). Modelling progressive failure of bond-ed joints using a single joint finite element. In: AIAA Journal, Vol. 49, pp. 1740-1749. doi:10.2514/1.J050889 Go to original source...
    23. MAGGIORE, S., BANEA, M.D., STAGNARO, P., LUCIANO, G. (2021). Review of structural adhesive joints in hybrid joining processes. In: Polymers, Vol. 13. doi.org/10.3390/polym13223961 Go to original source...
    24. GOLAND, M., REISSNER, E. (1944). The stresses in cemented joints. In: Journal of Applied Mechanics, Vol. 11, pp. A17-A27. Go to original source...
    25. VOLKERSEN, O. (1938). Die Nietkraftverteilung in zugbeanspruchten Nietverbindungen mit konstanten Laschenquerschnitten. In: Luftfahrtforschung, Vol. 15, pp. 41-47.
    26. HART-SMITH, L.J. (1973). Adhesive-bonded double-lap joints, Report/Monograph.
    27. KALINA, T., SEDLÁČEK, F. (2019). Design and determination of strength of adhesive bonded joints. In: Manufacturing Technology, Vol. 19(3), pp. 409-413, DOI: 10.21062/ujep/305.2019/a/1213-2489/MT/19/3/409. Go to original source...
    28. KOLAR, V., MULLER, M. (2018). Research on influence of polyurethane adhesive modified by polyurethane filler based on recyclate. In: Manufacturing Technology, Vol. 18(3), pp. 418-423. doi: 10.21062/ujep/115.2018/a/1213-2489/MT/18/3/418. Go to original source...
    29. MÜLLER, M. (2013). Research of renovation possibility of machine tools damage by adhesive bonding technology. In: Manufacturing Technology, Vol. 13(4), pp. 504-509. doi: 10.21062/ujep/x.2013/a/1213-2489/MT/13/4/504 Go to original source...
    30. ŠLEGER, V., MÜLLER, M. (2016). Low-cyclic fatigue of adhesive bonds. In: Manufacturing Technology, Vol. 16(5). pp. 1151-1157. doi: 10.21062/ujep/x.2016/a/1213-2489/MT/16/5/1151 Go to original source...
    31. CIDLINA, J., MULLER, M., VALASEK, P. (2014). Evaluation of adhesive bond strength depending on degradation type and time. In: Manufacturing Technology, Vol. 14(1), pp. 8-12. doi: 10.21062/ujep/x.2014/a/1213-2489/MT/14/1/8 Go to original source...
    32. CORRADO, A., POLINI, W. (2024). A unique numerical model to evaluate the influence of adherends' misalignment on adhesive joint strength. In: Manufacturing Technology, Vol. 24(2), pp. 183-191. doi: 10.21062/mft.2024.029 Go to original source...
    33. ANASIEWICZ, K. (2024). Studies of nanoscratching in the aspect of homogeneity of adhesive joints. In: Manufacturing Technology, Vol. 24(6), pp. 150-157. doi: 10.21062/mft.2024.102 Go to original source...
    34. ANASIEWICZ, K., KUCZMASZEWSKI, J. (2023). Heterogeneity of adhesive joint properties. In: Ma-terials, Vol. 16(23), 7303. doi.org/10.3390/ma16237303 Go to original source...
    35. CIECH-SARZYNA (2022). Safety Data Sheet - EPIDIAN® 57. Available at: https://www.polimal.com.pl/wp-content/uploads/2019/02/EPIDIAN_Ciech_Sarzyna.pdf (accessed 2 Dec 2025).
    36. CIECH-SARZYNA (2022). Safety Data Sheet - PAC Hardener. Available at: https://www.zywicesarzyna.pl/produkty/utwardzacz-pac/ (accessed 2 Dec 2025).
    37. CIECH-SARZYNA (2022). Safety Data Sheet - Z1 Hardener. Available at: https://www.zywicesarzyna.pl/produkty/utwardzacz-z1/ (accessed 2 Dec 2025).
    38. LAMBERTI, M., MAUREL-PANTEL, A., LEBON, F. (2023). Experimental characterization and modelling of adhesive bonded joints under static and non-monotonic fracture loading in the mode II regime. International Journal of Adhesion and Adhesives, 124, 103394. DOI: 10.1016/j.ijadhadh.2023.103394. Go to original source...
    39. RIES, M. (2024). Mechanical behavior of adhesive joints: A review on modeling techniques. Computer Methods in Materials Science, 24(4), pp. 5-35. DOI: 10.7494/cmms.2024.4.1010. Go to original source...
    40. DOBRZAŃSKI, P., OLEKSIAK, W. (2021). Design and analysis methods for composite bonded joints. Transactions on Aerospace Research, 2021(1), pp. 45-63. DOI: 10.2478/tar-2021-0004. Go to original source...

    This is an open access article distributed under the terms of the Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0), which permits non-comercial use, distribution, and reproduction in any medium, provided the original publication is properly cited. No use, distribution or reproduction is permitted which does not comply with these terms.


    Return to the content