A Power-Equivalence-Based Computational Method for Homogenized Equivalent Conductivity of Laminated Composites

Document Type : Research Paper

Authors
1 Key Laboratory of Aero-engine Thermal Environment and Structure, Ministry of Industry and Information Technology, College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R. China
2 Taihang National Laboratory, Chengdu 610504, P.R. China
3 Harbin Engineering University, Harbin, 150001, P.R. China
Abstract
Electrical resistivity tomography (ERT) has been widely applied in recent years for damage monitoring in composite materials, particularly in laminated plates. The prevailing approach in ERT-based laminate monitoring simplifies the analysis by treating composites as orthotropic materials, which contain solely 0° and 90° oriented layers. However, this orthotropic assumption becomes invalid for actual composite layups with arbitrary ply orientations. To address this problem, this paper proposes a homogenized equivalent conductivity calculation method for laminated composites based on power equivalence. This method enables solving equivalent conductivity for laminates with arbitrary layup configurations, thereby allowing substitution of the original layered model with a homogenized plate model. Comparative FEM analyses of various laminate configurations confirm that the boundary voltage distributions obtained using the homogenized conductivity model match the actual layered structure results within 1.2% mean absolute error.
Keywords
Subjects

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[1] Blecherman, S.S., Stankunas, T.N., Composite Fan Exit Guide Vanes for High Bypass Ratio Gas Turbine Engines, Journal of Aircraft, 19(12), 1982, 1032-1034. 
[2] Etri, H.E., Korkmaz, M.E., Gupta, M.K., Gunay, M., Xu, J., A state-of-the-art review on mechanical characteristics of different fiber metal laminates for aerospace and structural applications, International Journal of Advanced Manufacturing Technology, 123, 2022, 2965-2991.
[3] Bui, V.P., Thitsartarn, W., Liu, E.X., Chuan, J.Y.C., Chua, E.K., EM Performance of Conductive Composite Laminate Made of Nanostructured Materials for Aerospace Application, IEEE Transactions on Electromagnetic Compatibility, 57(5), 2015, 1-10.
[4] Hebsur, M.G., Noebe, R.D., Revilock, D.M., Impact Resistance of Lightweight Hybrid Structures for Gas Turbine Engine Fan Containment Application, Journal of Materials Engineering and Performance, 12, 2003, 470-479.
[5] Li, X., He, X., Liang, J., Song, Y., Zhang, L., Wang, B., Ma, J., Kong, G., Research Status of 3D Braiding Technology, Applied Composite Materials, 29, 2022, 147-157.
[6] Liu, L.L., Xuan, H.J., Chen, G.T., Ye, D., Hong, W.R., Xing, J., Wang, J., Ballistic impact testing and analysis of triaxial braided composite fan case material, Advanced Materials Research, 535, 2012, 121-132.
[7] Tallman, T.N., Homa, L., Flores, M., Wertz, J., Damage mapping via electrical impedance tomography in complex AM shapes using mixed smoothness and Bayesian regularization, Computer Methods in Applied Mechanics and Engineering, 414, 2023, 116185.
[8] Thomas, A.J., Kim, J.J., Tallman, T.N., Bakis, C.E., Damage detection in self-sensing composite tubes via electrical impedance tomography, Composites Part B: Engineering, 177, 2019, 107276.
[9] Gao, X., Wei, T., Dong, H., Song, Y., Damage detection in 2.5 DC/SiC composites using electrical resistance tomography, Journal of the European Ceramic Society, 39(13), 2019, 3583-3593.
[10] Gibson, R.F., Principles of Composite Material Mechanics, CRC Press, 2016.
[11] Cheney, M., Isaacson, D., Newell, J.C., Simske, S., Goble, J., NOSER: An algorithm for solving the inverse conductivity problem, International Journal of Imaging Systems and Technology, 2(2), 1990, 66-75.
[12] Wang, Q., Wang, H., Zhang, R., Wang, J., Zheng, Y., Cui, Z., Yang, C., Image reconstruction based on L1 regularization and projection methods for electrical impedance tomography, Review of Scientific Instruments, 83(10), 2012, 104707.
[13] Vauhkonen, P.J., Vauhkonen, M., Savolainen, T., Kaipio, J.P., Three-dimensional electrical impedance tomography based on the complete electrode model, IEEE Transactions on Biomedical Engineering, 46(9), 2002, 1150-1160.
[14] Yang, X., Zhang, Y., Chen, H., Ma, G., Wang, X., A Two-Stage Imaging Framework Combining CNN and Physics-Informed Neural Networks for Full-Inverse Tomography: A Case Study in Electrical Impedance Tomography (EIT), IEEE Signal Processing Letters, 32, 2025, 1096-1100.
[15] Boo, C.J., Kim, H.C., Kang, M.J., Lee, K.Y., Stochastic optimization approaches to image reconstruction in electrical impedance tomography, International Conference on Computational Science and Its Applications, Berlin, Heidelberg: Springer Berlin Heidelberg, 2010.
[16] Goncalves, S., De Munck, J.C., Heethaar, R.M., Lopes da Silva, F.H., Van Dijk, B.W., The application of electrical impedance tomography to reduce systematic errors in the EEG inverse problem-a simulation study, Physiological Measurement, 21(3), 2000, 379-393.

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