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<p>Introducing holes is a common strategy to enhance the properties of thermoelectric (TE) materials. However, the stress concentration induced by multiple holes remains poorly understood. This study investigates the electric–thermal–mechanical behavior of TE materials containing multiple circular holes under coupled electrical and thermal loadings. A theoretical model based on complex variable methods is established to reveal the interaction influence of thermal stress around holes with different radii and spacing. Results show that enlarging the hole radius significantly intensifies local tensile and compressive stresses due to enhanced temperature and electric potential differences, whereas increasing the space among holes weakens stress coupling and gradually restores the single-hole response. The combined effects of electrical current and heat flux are also examined, indicating that thermal loading dominates the stress response, while electrical loading contributes only a secondary effect through Joule heating. The proposed model provides fundamental insight into the multi-physics coupling and mechanical reliability of advanced TE materials.</p>

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Thermal stress interactions around multiple holes in thermoelectric materials

  • 期刊论文

  • 发表日期：

    2026年2月26日

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  • Ruifeng Zhang,
  • Junhua Xie,
  • Jie Wang,
  • Luqiao Qi,
  • Lijie Zhang,
  • Yun Ma,
  • Shichao Xing,
  • Kun Song,
  • Cunfa Gao

摘要

Introducing holes is a common strategy to enhance the properties of thermoelectric (TE) materials. However, the stress concentration induced by multiple holes remains poorly understood. This study investigates the electric–thermal–mechanical behavior of TE materials containing multiple circular holes under coupled electrical and thermal loadings. A theoretical model based on complex variable methods is established to reveal the interaction influence of thermal stress around holes with different radii and spacing. Results show that enlarging the hole radius significantly intensifies local tensile and compressive stresses due to enhanced temperature and electric potential differences, whereas increasing the space among holes weakens stress coupling and gradually restores the single-hole response. The combined effects of electrical current and heat flux are also examined, indicating that thermal loading dominates the stress response, while electrical loading contributes only a secondary effect through Joule heating. The proposed model provides fundamental insight into the multi-physics coupling and mechanical reliability of advanced TE materials.