刚性圆形压头作用下热电材料半平面的无摩擦接触问题

热电材料可以将热能转化为电能,反之亦然，这一优良的性质将有助于研发更具成本效益的设备和器件。本文研究了刚性圆形压头作用在热电材料半平面的无摩擦接触问题。假定压头为电导体、热导体，且压头压入深度及与材料的接触区域宽度未知。首先求解电场和温度场，利用傅里叶变换得到了电势函数、温度、电流密度和能量通量的解析表达式。然后求解弹性场，利用积分变换和边界条件，将该热弹性接触问题转化为第一类奇异积分方程并数值求解。数值结果讨论了压头半径和热电载荷对法向接触应力、电流强度因子和能量通量强度因子的影响。结果表明，对于圆压头，热电材料的法向电流密度、法向能量通量在接触边缘表现出奇异性，而表面法向接触应力在接触边缘为零。本文建立的研究模型有助于更深层次的了解热电材料的接触行为。

Frictionless Contact of Thermoelectric Materials Under the Rigid Circular Punch

Thermoelectric materials can convert thermal energy into electricity, and vice versa. This excellent performance will contribute to the development of more cost-effective equipment and devices. The contact problem of thermoelectric materials has aroused widespread concern due to its possible application in various structures of practical significance. The frictionless contact problem of rigid conductive circular punch acting on half plane of thermoelectric materials is studied in this paper. Assume that the punch is an electric conductor and a thermal conductor, and the depth of the pressure and the width of the contact area are unknown. First, for the electric fields and temperature fields, starting from the constitutive equation of the thermal electric field, the analytical expressions of potential function, temperature, electric current density and energy flux are obtained by using Fourier transform. Then, for the elastic field, starting from the Duhamel-Neumann constitutive relations for plane thermoelasticity, the thermoelastic contact problem is transformed into the first kind of singular integral equation and solved numerically by using integral transformation and boundary conditions. The effects of the punch radius and thermoelectric load on the normal contact stress, electric current intensity factor and energy flux intensity factor are discussed. The results show that the normal electric current density and the normal energy flux of thermoelectric materials show high singularity in the vicinity of the contact edge, while the normal contact stress of the surface is zero at the contact edge. It is found that the research model established in this paper helps to understand the contact behavior of thermoelectric materials in a deeper level. It is a great significance to explore methods to suppress contact deformation and contact damage and to realize the optimal design of materials.