This study establishes a three-dimensional frictionless contact model for the rigid indenter and the thermoelectric thin film under multiple physical fields. By combining the Navier–Cauchy equations, the Fourier heat conduction equation, and the thermoelectric transport equation, the governing equations of thermoelectric thin film are established. The frequency response functions of thermoelectric thin film are derived by using the double Fourier transform to convert the space domain equations into the frequency-domain equations. The discrete convolution fast Fourier transform algorithm combined with the conjugate gradient method and local mesh refinement technique is used to further improve the efficiency and precision of the numerical solution. This study solved the stress field, temperature field, and electric field at the contact interface, elucidating the synergistic mechanism through which multiple parameters (thermoelectric load, film thickness, probe radius, and probe spacing) regulate contact responses in single-indenter and arrayed-indenter thermoelectric thin film contact systems.
JiaSMaHGaoS, et al. Thermoelectric materials and devices for advanced biomedical applications. Small2024; 20: 2405019.
4.
BhukeshSKGawreSKKumarA. Review on advancement in solar and waste heat based thermoelectric generator. Energ Sourc Part A: Recover Utiliz Environ2023; 45: 4982–5002.
5.
SunQDuCChenG. Thermoelectric materials and applications in buildings. Prog Mater Sci2025; 149: 101402.
6.
ZhangCShiXLLiuQ, et al. Hydrogel-based functional materials for thermoelectric applications: progress and perspectives. Adv Funct Mater2024; 34: 2410127.
7.
XiaoRZhouXZhangC, et al. Organic thermoelectric materials for wearable electronic devices. Sensors2024; 24: 4600.
8.
KhanFKimDHLeeJ. Functionalized materials and geometric designs of thermoelectric devices for smart wearable applications. Appl Energ2025; 379: 124940.
9.
VenkatasubramanianRSiivolaEColpittsT, et al. Thin-film thermoelectric devices with high room-temperature figures of merit. Nature2001; 413: 597–602.
10.
HuangM-JPo-KueiCLinMC. An investigation of the thermal stresses induced in a thin-film thermoelectric cooler. J Thermal Stresses2008; 31: 438–454.
11.
JinZH. Thermal stresses in a multilayered thin film thermoelectric structure. Microelectron Reliab2014; 54: 1363–1368.
12.
JinZH. Buckling of thin film thermoelectrics. Int J Fract2013; 180: 129–136.
13.
WuYMingTLiX, et al. Numerical simulations on the temperature gradient and thermal stress of a thermoelectric power generator. Energ Conver Manag2014; 88: 915–927.
14.
MingTYangWWuY, et al. Numerical analysis on the thermal behavior of a segmented thermoelectric generator. Int J Hydrogen Energ2017; 42: 3521–3535.
15.
LiJEWangBLZhangC. Thermal and electrical electrode/punch problem of thermoelectric materials. Int J Heat Mass Trans2019; 143: 118504.
16.
LiXTianXJZhouYT. Thickness size effect on contact behavior of a thermoelectric strip. Acta Mech2021; 232: 3305–3321.
17.
TianXJZhouYTLiFJ, et al. Joint finite size influence and frictional influence on the contact behavior of thermoelectric strip. Archiv Appl Mech2023; 93: 405–425.
18.
TianXZhouYZhangC. The influences of the punch geometry on the contact behaviors of a finite-thickness strip with thermoelectric effects. Acta Mech2024; 235: 3953–3971.
19.
ZhangYMaHYangJ, et al. Frictionless multi-field coupling contact problem for a thermoelectric layer loaded by two rigid punches. Acta Mech Solida Sinica2023; 36: 282–292.
20.
ZhangCZhangBZhouY, et al. Continuous contact problem of interaction between two arbitrarily positioned flat stamps on the thermoelectric material. Acta Mech2023; 234: 4719–4732.
21.
HuCShenHWangY, et al. On the time-dependent sliding contact behavior of three-phase polymer matrix smart composites. Smart Mater Struct2024; 33: 105007.
22.
WangYShenHLiJ, et al. Three-dimensional frictional contact within the framework of couple stress elasticity. Appl Math Model2024; 131: 288–305.
23.
WangYZhangXShenH, et al. Couple stress-based 3D contact of elastic films. Int J Solid Struct2020; 191-192: 449–463.
24.
LiYHShenFGülerMA, et al. Modeling multi-physics electrical contact on rough surfaces considering elastic-plastic deformation. Int J Mech Sci2024; 269: 109066.
25.
LiYHKeLLZhouK, et al. On the multi-physics elastoplastic electrical contact of rough surfaces. Tribol Int2025; 204: 110418.
26.
LiJShenHHuC, et al. Semi-analytical solutions of three-dimensional thermoelectromechanical coupling frictionless contact problem of thermoelectric materials. Acta Mech236: 2297–2314.
27.
WangYZhangXShenH, et al. Three-dimensional contact analysis with couple stress elasticity. Int J Mech Sci2019; 153-154: 369–379.
28.
TianXZhouYDingS, et al. Exploring the effects of finite size and indenter shape on the contact behavior of functionally graded thermoelectric materials. Int J Solid Struct2024; 305: 113089.
29.
ZhangXWangQJ. Thermoelastic contact of layered materials with interfacial imperfection. Int J Mech Sci2020; 186: 105904.
30.
YangWBaiPFangJ, et al. Contact responses of transversely isotropic layered material with imperfect interface. Int J Mech Sci2024; 272: 109145.
31.
WangYLiJWangL, et al. Semi-analytical solutions of the three-dimensional size-dependent thermoelastic contact of the microstructured materials under a hot indenter. Math Mech Solid2025. DOI: 10.1177/10812865251315955.
32.
LiuSWangQ. Studying contact stress fields caused by surface tractions with a discrete convolution and fast fourier transform algorithm. J Tribol2001; 124: 36–45.
33.
ZhangXWangZShenH, et al. An efficient model for the frictional contact between two multiferroic bodies. Int J Solid Struct2018; 130-131: 133–152.
34.
WangYShenHZhangX, et al. Semi-analytical study of microscopic two-dimensional partial slip contact problem within the framework of couple stress elasticity: Cylindrical indenter. Int J Solid Struct2018; 138: 76–86.
35.
GongTGaoLWuY, et al. Transient thermal stress analysis of a thermoelectric cooler under pulsed thermal loading. Appl Therm Eng2019; 162: 114240.
36.
ZhangGKongXMiC. Mechanically manipulated in-plane electric currents and thermal control in piezoelectric semiconductor films. Acta Mech2024; 235: 3463–3481.
