Theory of Thermo-polar Materials and Application to Actual Structures

具有微观内部结构的材料由于其潜在的上级综合性能而受到广泛的研究关注。这种材料的制定始于对单个内部结构的响应的分析。微模材料与普通微极性材料的区别在于引入了一个称为介观畴的中间材料点。在本研究中引入的介观域是由有限数量的介观单元构成的。这些单元可以表示有限数量的薄壁梁的折叠板或光纤的组成部分。双力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。本文介绍了热力学材料理论，并对热力学材料理论进行了扩展。定义了作为微模材料主要几何量的热-力模矢量，并利用绿色方法从熵不等式出发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，表明了本理论的有效性。

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.