shear Buckling Analysis of Laminated Composite Plates Containing Matrix Cracks Using a Hybrid Approach of Higher-Order Shear Deformation Theory and Experimental Damage Model

Khodamorady, Keramat; Malakzadeh Fard, Keramat; Nabavi, Seid Mehdi; Sarhkosh, Reza

shear Buckling Analysis of Laminated Composite Plates Containing Matrix Cracks Using a Hybrid Approach of Higher-Order Shear Deformation Theory and Experimental Damage Model

Document Type : Original Article

Authors

keramat khodamorady ¹

Keramat Malakzadeh Fard ²

seid mehdi nabavi ³

reza sarhkosh ⁴

¹ Ph.D. Candidate, Faculty of Aerospace Engineering, Malek Ashtar University of Technology, Tehran, Iran

² Professor, Faculty of Aerospace Engineering, Malek Ashtar University of Technology, Tehran, Ira

³ Associate Professor, Faculty of Aerospace Engineering, Malek Ashtar University of Technology, Tehran, Iran

⁴ Assistant Professor, Department of Aerospace Engineering (Aircraft Structures), Shahid Sattari Aeronautical University, Tehran, Iran

Abstract

Introduction: Multilayered composite structures are widely used in aerospace and engineering applications due to their high strength-to-weight ratio. However, their structural performance is highly sensitive to manufacturing defects, particularly matrix cracks, which can significantly reduce the critical load-bearing capacity and accelerate buckling failure under shear loading. Therefore, developing accurate analytical models capable of accounting for damage-induced stiffness degradation is essential for reliable structural design.
Methods: An advanced analytical model was developed to predict the critical shear buckling load of thick laminated composite plates containing matrix cracks. The formulation is based on a higher-order shear deformation theory (HSDT) with 11 degrees of freedom, which accurately captures the parabolic distribution of transverse shear stresses and transverse normal strain effects without requiring shear correction factors. Stiffness degradation parameters resulting from matrix cracking were directly incorporated into the model using experimental tensile test data. The governing equations were derived through the principle of minimum potential energy and solved using the Galerkin method.
Findings: The effects of matrix crack density (0–1 crack/mm), plate thickness-to-length ratio (a/h = 5–100), and fiber orientation angle (θ = 0°–90°) on the normalized critical shear buckling load and its reduction percentage were investigated. The results demonstrated that matrix cracking substantially decreases the buckling resistance of composite plates. For the [±45]s laminate configuration, a crack density of 1 crack/mm resulted in a reduction of up to 64% in the critical shear buckling load. Furthermore, the proposed analytical predictions showed excellent agreement with three-dimensional elasticity solutions and finite element simulations.
Conclusion: The developed HSDT-based analytical model provides an accurate and efficient tool for evaluating the shear buckling behavior of damaged thick composite plates. The results highlight the significant influence of matrix crack density on structural stability and demonstrate the necessity of considering experimentally determined stiffness degradation in buckling analyses of composite structures.

Keywords

Shear buckling

Matrix crack

Galerkin method

20.1001.1.28211553.1405.5.1.3.8

Subjects

Structure/mechanics of solids/dynamics of solids/vibrations/aeroelasticity/...

[1] Reddy, J. N. (2004). Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. CRC Press.

[2] Jones, R. M. (1999). Mechanics of Composite Materials. Taylor & Francis

[3] Kashtalyan, M., & Soutis, C. (2000). Stiffness degradation in cross-ply laminates with matrix cracks in 90° and 0°

[4] Talreja, R., & Varna, J. (2015). Modeling Damage, Fatigue and Failure of Composite Materials. Woodhead Publishing.

[5] Sun, C. T., & Vaidya, R. S. (1996). Prediction of composite properties from a representative volume element. Composites Science and Technology, 56(2), 171-179.

[6] Shirinbayan, M., Nouira, S., Zghal, J., & Fitoussi, J. (2025). A hybrid approach for predicting fatigue life of fiber-reinforced polypropylene composite: integrating micromechanical modelling. Composites Part C: Open Access, 16, 100660.

[7] Ermis, M., Dorduncu, M., & Aydogan, G. (2025). Physics-based machine learning for modeling of laminated composite plates based on refined zigzag theory. Archive of Applied Mechanics, 95(5), 1-24.

[8] Deng, J., Zhao, J., Peng, A., & Zhou, G. (2025). Buckling and failure mechanisms of asymmetric composite sandwich panels subjected to shear loadings. Engineering Failure Analysis, 167, 109039.

[9] Reissner, E. (1945). The effect of transverse shear deformation on the bending of elastic plates. Journal of Applied Mechanics, 12, 69-77.

[10] Sayyad, A. S., Ghugal, Y. M., & Kant, T. (2025). Static and Vibration Analysis of Laminated Sandwich Hyperbolic and Elliptical Paraboloids. AIAA Journal, 63(1), 1-17.

[11] Thai, H. T., & Kim, S. E. (2015). A review of theories for the modeling and analysis of non-homogeneous microstructure-dependent structures. Composite Structures, 128, 134-154.

[12] Kant, T., & Swaminathan, K. (2001). Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order refined theory. Composite Structures, 53(1), 73-85.

[13] Carrera, E. (2003). Theories and finite elements for multilayered plates and shells. Progress in Aerospace Sciences, 39(2-3), 97-146.

[14] Tessler, A., Di Sciuva, M., & Gherlone, M. (2009). A refined zigzag theory for laminated composite and sandwich plates. NASA Technical Reports, TP-2009-215555.

[15] Murakami, H. (1986). Laminated composite plate theory with improved in-plane responses. Journal of Applied Mechanics, 53(3), 661-666.

[16] Highsmith, A. L., & Reifsnider, K. L. (1982). Stiffness-reduction mechanisms in composite laminates. ASTM Special Technical Publication, 775, 103-117.

[17] Talreja, R. (1986). Continuum damage mechanics for composite materials. Polymer Composites, 7(5), 348-354.

[18] Hashin, Z. (1985). Analysis of cracked laminates: a variational approach. Mechanics of Materials, 4(2), 121-136.

[19] Nairn, J. A. (2000). Matrix microcracking in composites. Comprehensive Composite Materials, 2, 403-432.

[20] Berthelot, J. M. (2003). Transverse cracking and delamination in cross-ply glass-fiber and carbon-fiber reinforced plastic laminates. Applied Mechanics Reviews, 56(1), 111-147.

[21] Kashtalyan, M. (2003). Three-dimensional elasticity solution for layered panels with stepped-wise varying properties. Composite Structures, 62(2), 135-144.

[22] Katerelos, D. T. G., Kashtalyan, M., & Galiotis, C. (2008). Matrix cracking in polymeric composites laminates: Modelling and experiments. Composites Science and Technology, 68(12), 2310-2317.

[23] Paris, F., Correa, E., & Mantic, V. (2007). Kinking of a transverse matrix crack at the interface in a fiber-reinforced composite. Journal of Applied Mechanics, 74(4), 703-716.

[24] Malekzadeh Fard, Analysis of Buckling of Sandwich Composite Panel with Symmetric Functionally Graded Core Using Improved Higher-Order Theory. Aerospace Mechanics Journal (Quarterly), 8(1), 1391 (In Persian).

[25] Mohammadi, B.; Asl Kamkar, S.; Farrokh Abadi, A. (2017). Analysis of Matrix Cracking and Delamination of Symmetric Composite Laminates Under Static Loading Using Multi-Scale Failure Method. Journal of Science and Technology of Composites, 4(1), pp. 9-24 (In Persian).

[26] Pourmoayed, A., Ranjbar, M. A., & Seyednejad, S. M. (2025). Buckling and post-buckling analysis of composite pipe reinforced with shape memory alloy under internal pressure. Science and Technology in Mechanical Engineering, 4(2). (In Persian)

[27] Thai, H. T., & Choi, D. H. (2012). A refined higher-order shear deformation theory for bending, vibration and buckling of laminated composite plates. European Journal of Mechanics-A/Solids, 34, 130-140.

[28] Taylor, R. L., & Sackman, J. L. (1967). Buckling of orthotropic rectangular plates. AIAA Journal, 5(3), 397-402.

[29] Librescu, L. (1975). Elastostatics and Kinetics of Anisotropic and Heterogeneous Shell-Type Structures. Noordhoff International.

[30] atra, R. C., & Vidoli, P. (2002). Higher-order piezoelectric plate theory derived from a three-dimensional variational principle. AIAA Journal, 40(11), 2359-2369.

[31] Singh, S. S., Singh, S. K., & Chakrabarti, A. (2013). Buckling analysis of laminated composite plates using an efficient higher-order theory. Journal of Reinforced Plastics and Composites, 32(14), 1017-1029.

[32] Muc, A. (2006). Buckling and post-buckling behavior of laminated composite plates. Key Engineering Materials, 326, 1335-1338.

[33] Zhou, G., Deng, J., & Zhao, J. (2022). Experimental investigation on shear buckling of composite panels with multiple matrix cracks. Composite Structures, 280, 114850.

[34] Zhao, J., & Wei, G. W. (2002). Galerkin method for the vibration and buckling of composite plates. Computer Methods in Applied Mechanics and Engineering, 191(41-42), 4561-4571.

[35] Wu, C. P., & Lin, C. Y. (2004). Three-dimensional buckling analysis of composite laminates with different boundary conditions. Composite Structures, 63(3-4), 317-333.

[36] Patel, A. (2024). Experimental and numerical buckling analysis of CNT reinforced polymer composite plates. Materials Science and Technology, 40(2), 112-125.

[37] Ghugal, Y. M., & Sayyad, A. S. (2008). A review of refined shear deformation theories for isotropic and anisotropic laminated plates. Journal of Reinforced Plastics and Composites, 27(6), 629-666.

[38] Oliveira Pedro, J. J., Nascimento, S., & Hendy, C. (2025). Shear buckling resistance models for steel plate girders – Numerical investigation. Engineering Structures, 322, 119054.

[39] Accelerated Aging of Materials and Structures: The Effects of Long-Term Elevated-Temperature Exposure. Washington, DC: The National Academies Press, 1996. doi: 10.17226/9251

[40] Khodamoradi, M.k., Malekzadeh Fard, K. (2026). Shear Buckling Analysis of Sandwich laminate with a Flexible Core Using a Higher-Order Theory and the Galerkin Method. Scientific-Research Journal of Aerospace Engineering, Air University, 28(2), Autumn and Winter (In Persian).