Theory of Thermo-polar Materials and Application to Actual Structures

具有微观内部结构的材料因其潜在的优异的综合性能而受到人们的广泛关注。这种材料的配制从分析单个内部结构的响应开始。微模材料与普通微极性材料的不同之处在于引入了一个中间材料点，称为介观区域。在本研究中引入的介观单元是由有限个的介观单元构成的。这些元件可以表示有限数量的薄壁光束折叠板或光纤成分。二阶矩的概念是本理论引入的典型力学量，微模材料的力学理论可以推广到材料的热力学理论。作者介绍了热力材料理论，并在本研究中作了推广。重新定义了微模材料的主要几何量--热力模矢，并用格林方法用熵不等式讨论了微模材料的本构方程。得到了场方程，并将解析解与数值解的结果进行了比较。这些结果符合得很好，说明了本文理论的有效性。

Materials with microscopic internal structures are receiving much research attention due to their potentially superior overall properties. The formulation of such materials begins with an analysis of the response of individual internal structures. The difference between the micro-mode materials and the ordinary micro-polar materials exists in the introduction of an intermediate material point that is called a meso-domain. In the meso-domain introduced in this study is constructed by the finite number mesoscopic elements. These elements can represent a finite number of folded plates of thin-walled beams or constituents of optical fibers. The concept of bimoment is the typical mechanical quantities introduced by the present theory.The mechanical theory of micro-mode materials can be extended to the thermo-mechanical theory of materials. The theory of thermo-mechanical materials is introduced by the author and is extended in the present study. Thermo-mechanical mode-vectors that are the principal geometrical quantities of micro-mode materials are newly defined.Constitutive equations of the micro-mode materials are also discussed by the entropy inequality using Green method. Field equations are obtained and the analytical solutions are compared with the results of numerical solutions. These results correspond well and show the validity of the present theory.