Applied Mathematics and Mechanics >
The adhesive interlayer effect on the thermoelectric structure with multiple electrodes
Received date: 2025-11-24
Revised date: 2026-01-16
Online published: 2026-03-02
Supported by
Project supported by the National Natural Science Foundation of China (Nos. 12502117, 12272269, and 11972257), the Natural Science Foundation of Ningxia of China (No. 2024AAC03018), the Fundamental Research Funds for the Central Universities, and the Shanghai Gaofeng Project for University Academic Program Development
Copyright
Driven by the trend of device miniaturization and high-density integration, the interaction between adjacent electrodes has become a critical factor affecting the interfacial reliability of thermoelectric (TE) structures. This study investigates the influence of adjoining electrode interactions on the interfacial response of a multi-electrode/TE substrate structure, including interfacial stresses and stress intensity factors at the electrode ends. To solve the corresponding boundary-value problem, the Fourier transforms are adopted to derive a governing integro-differential equation for the interfacial shear stress in multi-electrode systems, incorporating the TE effects as generalized forces on the right-hand side. The results show that both the interfacial tension and transverse stress in the electrodes are significantly affected by the presence of adjacent electrodes. The interaction between neighboring electrodes diminishes as their spacing increases or when an adhesive interlayer is introduced. Furthermore, the softer and thinner electrodes, the softer and thicker adhesive interlayer, and the smaller TE loads are found to be beneficial for improving the interfacial performance. These findings may contribute to the accurate measurement in surface sensors and layout design of multi-point health monitoring systems for TE structures.
Xiaojuan TIAN , Yueting ZHOU . The adhesive interlayer effect on the thermoelectric structure with multiple electrodes[J]. Applied Mathematics and Mechanics, 2026 , 47(3) : 573 -598 . DOI: 10.1007/s10483-026-3363-9
| [1] | BELL, L. E. Cooling, heating, generating power, and recovering waste heat with thermoelectric systems. Science, 321, 1457–1461 (2008) |
| [2] | MAHFUZ, M. M. H., ARAI, S., MIYAKE, Y., MATSUKI, T., and WATANABE, T. Impact of metal/semiconductor contact layout on the performance of an integrated silicon cavity-free micro thermoelectric generator. Microelectronic Engineering, 300, 112365 (2025) |
| [3] | BUN, K., RAPAKA, S. S., PATHAK, S., DATE, A., and WANG, X. Additive manufacturing, topology optimization of thermoelectric generators, and beyond: a comprehensive review on pioneering thermoelectric conversion for a sustainable future. Applied Thermal Engineering, 278, 127437 (2025) |
| [4] | WANG, D., DING, J., MA, Y., ZHAO, L., and DI, C. Multi-heterojunctioned plastics with high thermoelectric figure of merit. nature, 632, 528–535 (2024) |
| [5] | SOLEIMANI, Z., ZORAS, S., CERANIC, B., SHAHZAD, S., and CUI, Y. A review on recent developments of thermoelectric materials for room-temperature applications. Sustainable Energy Technologies and Assessments, 37, 100604 (2020) |
| [6] | CHAMPIER, D. Thermoelectric generators: a review of applications. Energy Conversion and Management, 140, 167–181 (2017) |
| [7] | LIU, W., LU, Y., YANG, J., MAO, D., HUANG, Y., and WANG, F. Preparation of high-performance Ag2Se thermoelectric films and devices for wearable energy harvesting. Materials Research Bulletin, 193, 113650 (2026) |
| [8] | LI, H., WANG, Y. P., WU, X. Z., ZHU, K., WANG, S. H., YU, M., and LIU, W. S. A general route to design solar thermoelectric generators under the constant heat flux thermal boundary. Energy & Environmental Science, 18, 2861–2872 (2025) |
| [9] | HELT, A., DUPARCHY, A., COWLEY, A., MüLLER, E., and DE BOOR J. MgCuSb as a suitable electrode for contacting pre-compacted pellets of MgAgSb thermoelectric material. Science and Technology of Advanced Materials, 26, 2506982 (2025) |
| [10] | LING, Y., QIU, G., LIU, D., MIN, E., FENG, J., LI, J., ZHANG, P., SUN, R., and LIU, R. Impact of intrinsic properties and interface contacts on thermoelectric transient supercooling. Applied Thermal Engineering, 219, 119690 (2023) |
| [11] | BARAKO, M. T., PARK, W., MARCONNET, A. M., ASHEGHI, M., and GOODSON, K. E. Thermal cycling, mechanical degradation, and the effective figure of merit of a thermoelectric module. Journal of Electronic Materials, 42, 372–381 (2013) |
| [12] | KUMARI, N. and DASGUPTA, T. Developing contacting solutions for n-type Mg3Sb1.5Bi0.5 based thermoelectric materials. Journal of Alloys and Compounds, 944, 169220 (2023) |
| [13] | TIAN, X. J., ZHOU, Y. T., GUAN, X. F., WANG, L. H., and DING, S. H. The frictional contact problem of a rigid punch sliding over thermoelectric materials. International Journal of Solids and Structures, 200-201, 145–157 (2020) |
| [14] | ERDOGAN, F. and GUPTA, G. D. The problem of an elastic stiffener bonded to a half plane. Journal of Applied Mechanics?—?Transactions of ASME, 38, 937–941 (1971) |
| [15] | SHIELD, T. W. and KIM, K. S. Beam theory models for thin film segments cohesively bonded to an elastic half space. International Journal of Solids and Structures, 29, 1085–1103 (1992) |
| [16] | WANG, X. D. and MEGUID, S. A. On the electroelastic behaviour of a thin piezoelectric actuator attached to an infinite host structure. International Journal of Solids and Structures, 37, 3231–3251 (2000) |
| [17] | JIN, C. and WANG, X. Analytical modelling of the electromechanical behaviour of surface-bonded piezoelectric actuators including the adhesive layer. Engineering Fracture Mechanics, 78, 2547–2562 (2011) |
| [18] | CHEN, P. J., PENG, J., LIU, H., GAO, F., and GUO, W. The electromechanical behavior of a piezoelectric actuator bonded to a graded substrate including an adhesive layer. Mechanics of Materials, 123, 77–87 (2018) |
| [19] | CHEN, P. J., CHEN, S. H., and YAO, Y. Nonslipping contact between a mismatch film and a finite-thickness graded substrate. Journal of Applied Mechanics, 83, 021007 (2016) |
| [20] | CHEN, P. J., CHEN, S. H., GUO, W., and GAO, F. The interface behavior of a thin piezoelectric film bonded to a graded substrate. Mechanics of Materials, 127, 26–38 (2018) |
| [21] | KUMAR, D., MEENA, R. K., HIRSHIKESH, and GHADAI, R. K. Experimentally validated finite element model for mechanical and fracture characteristics of SiCN thin films under different loads. Scientific Reports, 15, 31759 (2025) |
| [22] | ALIZADEH, M. and WANG, X. A nonlinear electromechanical model for partially debonded thin-sheet piezoelectric actuators. Acta Mechanica, 235, 833–850 (2024) |
| [23] | ERDEM ALACA B., SAIF, M. T. A., and SEHITOGLU, H. On the interface debond at the edge of a thin film on a thick substrate. Acta Materialia, 50, 1197–1209 (2002) |
| [24] | CHEN, P. J., CHEN, S. H., PENG, J., GAO, F., and LIU, H. The interface behavior of a thin film bonded imperfectly to a finite thickness gradient substrate. Engineering Fracture Mechanics, 217, 106529 (2019) |
| [25] | GüLER, M., ALINIA, Y., and RADI, E. Couple-stress effects in a thin film bonded to a half-space. Mathematics and Mechanics of Solids, 29, 629–644 (2024) |
| [26] | ERDOGAN, F. and JOSEPH, P. F. Mechanical modeling of multilayered films on an elastic substrate?—?part I: analysis. Journal of Electronic Packaging, 112, 309–316 (1990) |
| [27] | CHEN, P. J., CHEN, S. H., LIU, H., PENG, J., and GAO, F. The interface behavior of multiple piezoelectric films attaching to a finite-thickness gradient substrate. Journal of Applied Mechanics?—?Transactions of ASME, 87, 011003 (2020) |
| [28] | ABBASZADEH-FATHABADI, S. A., ALINIA, Y., and GüLER, M. A. On the mechanics of a double thin film on a finite thickness substrate. International Journal of Solids and Structures, 279, 112349 (2023) |
| [29] | DANG, H., QI, D., FAN, C., LU, C., and ZHAO, M. On the interfacial behavior of two-dimensional decagonal quasicrystal films with an adhesive layer due to thermal misfit. Engineering Fracture Mechanics, 303, 110119 (2024) |
| [30] | ZHANG, W., LU, C. S., ZHAO, M., FAN, C., and DANG, H. On the interfacial behavior of a one-dimensional hexagonal piezoelectric quasicrystal film based on the beam theory. Applied Mathematics and Mechanics (English Edition), 46(2), 289–304 (2025) https://doi.org/10.1007/s10483-025-3214-9 |
| [31] | GüLER, M. A. and ALINIA, Y. An elastic-constant stress cohesive zone model for an orthotropic piezoelectric actuator adhesively bonded to a substrate. Engineering Fracture Mechanics, 309, 110391 (2024) |
| [32] | LV, S., LI, X., QI, L., HUA, J., XING, S., SHI, Y., SHIMADA, T., and GAO, C. Phase-field modeling of flexible piezoelectric composites incorporating interfacial failure. Engineering Fracture Mechanics, 328, 111512 (2025) |
| [33] | LIU, Y., WANG, B. L., and ZHANG, C. Mechanical model for a thermoelectric thin film bonded to an elastic infinite substrate. Mechanics of Materials, 114, 88–96 (2017) |
| [34] | LIU, Y., WANG, B. L., and ZHANG, C. Thermoelastic behavior of a thermoelectric thin-film attached to an infinite elastic substrate. Philosophical Magazine, 97, 43–57 (2017) |
| [35] | LIU, Y., WANG, K. F., and WANG, B. L. Instability-induced wrinkling in thermoelectric thin film/substrate structures for thermal protection systems in supersonic space shuttle applications. Mechanics of Advanced Materials and Structures, 27, 455–461 (2020) |
| [36] | LI, D., CHEN, P., HUANG, Z., LIU, H., and CHEN, S. The interfacial behavior of a thermoelectric thin-film bonded to an orthotropic substrate. International Journal of Solids and Structures, 267, 112160 (2023) |
| [37] | ZHOU, Y. T., TIAN, X. J., and DING, S. H. Microstructure size-dependent contact behavior of a thermoelectric film bonded to an elastic substrate with couple stress theory. International Journal of Solids and Structures, 256, 111982 (2022) |
| [38] | FARHADIAN, A. and ALINIA, Y. Thermal stress analysis in a graded thermoelectric film bonded to a homogeneous substrate. Mechanics of Materials, 203, 105256 (2025) |
| [39] | TIAN, X. J., ZHOU, Y. T., and DING, S. H. The effectiveness of the bonding layer to attain reliable thermoelectric structures. European Journal of Mechanics-A/Solids, 93, 104513 (2022) |
| [40] | TIAN, X. J., ZHOU, Y. T., and ZHANG, C. Z. The reliability of elastic electrode/graded thermoelectric substrate systems with the adhesive interlayer. Mechanics of Materials, 209, 105424 (2025) |
| [41] | TIAN, X. J., JIN, J. H., WANG, W. S., DING, S. H., and ZHOU, Y. T. The interface behavior of an electrode imperfectly bonded to a thermoelectric substrate. International Journal of Solids and Structures, 324, 113688 (2026) |
/
| 〈 |
|
〉 |
Email Alert
RSS