Zeleke Migbar Assefa, Xin Lai, Lisheng Liu
Department of Mechanical Engineering, University of Botswana, Gaborone 0061, Botswana.
Department of Mechanical Engineering, Hawassa University, Hawassa 05, Ethiopia.
Materials (Basel). 2020 Jun 3;13(11):2546. doi: 10.3390/ma13112546.
Thermoelectric materials are materials that involve the coexistence of heat flux and electric current in the absence of magnetic field. In such materials, there is a coupling among electric potential and temperature gradients, causing the thermoelectric effects of Seebeck and Peltier. Those coupling effects make the design and analysis of thermoelectric materials complicated and sophisticated. The main aim of this work is dealing with thermoelectric materials with discontinuities. Since heat and electric fluxes are undefined at the crack tip and the temperature and electric fields across the crack surface are discontinuous, it is better to apply peridynamic (PD) theory to capture such details at the crack tips. Hence, we propose in this paper a PD theory which is suitable in tackling such discontinuities in thermal and electric fields. In this study, the continuum-based electrical potentials and temperature fields are written in the form of nonlocal integrals of the electrical potentials and temperature that are effective whether we have discontinuities or not. To illustrate the consistency of the peridynamic technique, a number of examples were presented and witnessed that PD results were in good agreement with those results from the literature, finite element solutions and analytical solutions.
热电材料是指在无磁场情况下热通量和电流共存的材料。在这类材料中，电势和温度梯度之间存在耦合，从而产生塞贝克效应和珀尔帖效应等热电效应。这些耦合效应使得热电材料的设计和分析变得复杂而精细。这项工作的主要目的是处理具有不连续性的热电材料。由于裂纹尖端处的热通量和电通量未定义，且裂纹表面的温度和电场是不连续的，因此应用近场动力学（PD）理论来捕捉裂纹尖端处的此类细节更为合适。因此，我们在本文中提出一种适用于解决热场和电场中此类不连续性的近场动力学理论。在本研究中，基于连续介质的电势和温度场以电势和温度的非局部积分形式表示，无论是否存在不连续性，这种形式都是有效的。为了说明近场动力学技术的一致性，给出了一些示例，结果表明近场动力学结果与文献结果、有限元解和解析解吻合良好。
