AI 中文总结
本文推导了双材料域中任意取向多面体夹杂的闭式Eshelby张量，验证了解的正确性并分析了奇异性特性，突破了现有双材料夹杂解的形状与本征应变局限。
AI 中文摘要
本文给出了双材料域中任意取向多面体夹杂在一般本征应变下的闭式Eshelby张量。现有双材料解主要局限于特殊夹杂形状或膨胀本征应变，原因在于双材料格林函数除了Kelvin解中的调和与双调和势外，还包含两个Boussinesq位移势。本文通过将体积积分简化为面积分和初等线积分，推导了两个Boussinesq势缺失的域积分。所得公式提供了完整的弹性和热弹性双材料Eshelby张量，已通过平行于双材料界面的球形及立方体夹杂的解析解，以及倾斜立方体的有限元结果验证。奇异性分析表明，当夹杂与双材料界面分离时，与界面相关的贡献保持正则；而当边或顶点接触界面时，会出现额外的对数奇异性，但主奇异性阶数并未增加。
英文摘要
This paper presents the closed-form Eshelby's tensor for an arbitrarily oriented polyhedral inclusion in a bimaterial domain under general uniform eigenstrain. Existing bimaterial solutions are mainly restricted to special inclusion shapes or dilatational eigenstrains, because the bimaterial Green's function contains two Boussinesq's displacement potentials in addition to the harmonic and biharmonic potentials in Kelvin's solution. This paper derives the missing domain integrals of the two Boussinesq's potentials by reducing the volume integrals to surface and elementary line integrals. The formulae provide the complete elastic and thermoelastic bimaterial Eshelby's tensors, which are verified against analytical solutions for spherical and cuboidal inclusions parallel to the bimaterial interface, and finite element results of an inclined cuboid. Singularity analysis demonstrates that the interface-related contribution remains regular when the inclusion is separated from the bimaterial interface, while additional logarithmic singularities arise when an edge or vertex touches the interface without increasing the dominant singularity order.
CommentsUnder consideration in Journal of the Mechanics and Physics of Solids, 36 pages, 8 figures
