压电准晶材料的宏细观力学研究

Quasicrystals as a new structure materials, are different from crystals as well as non-crystals. There is an essential difference between quasicrystals and common crystals from the mechanical, electrical, thermal and other physical property point of view. Therefore, it is of great importance to study the coupling effects of quasicrystal materials. On the basis of the fundamental equations of piezoelasticity of quasicrystal materials deduced by thermodynamic law, the linear piezoelasticity behavior of one-dimensional (1D) hexagonal quasicrystals is investigated by using the symmetry operations of point groups. Moreover, the piezoelaticity problem of 1D hexagonal quasicrystals is decomposed into two uncoupled problems by the principle of superposition, i.e., the classical plane elasticity problem of conventional hexagonal crystals and the phonon-phason-electric coupling elasticity problem of 1D hexagonal quasicrystals, which can provide a theoretical foundation for mechanical-electrical coupling behavior of quasicrystals. Further, regarding quasicrystals as reinforced particles, the mechanical property of composite materials with the matrix of piezoelectricity are considered by Stroh formalism, such as the effective property of matrix with circular inclusion, elliptical inclusion and so on. After that, the analytical methods for solving fracture mechanics of mechanical-electrical coupling problem of quasicrystal materials including semi-inverse method and complex variable method are proposed. Finally, the analytical methods are applied to solve the interaction on between dislocation and cracks/hole and the basic solutions of electro-elastic fields are derived. The research of this project will provide an important theoretical reference for preparing new-type composite materials.

准晶作为一种新的固体材料，既不同于晶体，又不同于非晶体，这导致准晶的力、电、磁、热及其相关物理性能与普通晶体有本质性的区别。因此，研究准晶材料的这些耦合效应具有重要的科学意义。本课题拟通过热力学定律导出的基本方程，利用晶体点群的对称性给出特殊准晶晶系的电弹性耦合基本方程，利用叠加原理，将基本方程化解为两个简单问题来处理，为准晶的力电耦合行为提供重要的理论基础。进一步，将准晶体作为增强颗粒，利用Stroh法研究在压电基体中的复合材料力学性能，包括基体中含有圆形夹杂、椭圆等夹杂的有效性能。提出准晶材料的力电耦合问题断裂力学的解析方法，即半逆解法和复变函数法。作为应用，利用该方法研究裂纹或孔洞与位错的相互作用，给出其电弹性场的基本解。本项目的研究为工程中制备新型复合材料提供重要的理论参考。

准晶是一种介于晶体和非晶体之间新的固体结构，其力、电、磁、热及相关物理性能与普通晶体有本着的区别。本项目通过热力学定律，导出一维准晶各种晶系的电弹性耦合控制方程和一般解。提出电电准晶材料断裂力学的半逆解法和复势法，解决了Griffith裂纹和椭圆孔口及裂纹与位错相互作用等。发展热弹性介质中Stroh 型公式，研究二维十次对称准晶中椭圆孔在远处受热流作用下的热弹性问题，得到可导椭圆孔边界上的环向应力的显式解。建立压电准晶复合材料的细观力学椭圆夹杂模型和三相圆柱模型，得到了远场受反平面荷载作用下夹杂和基体中复势和电弹性场。所得解析解可退化为均匀材料、软可通夹杂、不可通夹杂、线夹杂、刚性夹杂、中空柱模型和裂纹问题。利用广义自洽方法，预测了压电准晶复合材料有效电弹性模量，为新型复合材料制备和设计提供理论参考。基于Gurtin-Murdoch表界面理论，提出纳米复合材料细观力学方法，发现在纳米尺度下，有效模量具有尺度依赖性。并且导出了表界面效应对磁电弹性材料中纳米椭圆孔和纳米裂纹的断裂行为的影响规律。基于非局部和修正的偶应力理论，利用Stroh型公式和传递矩阵法研究了纳米准晶、磁电弹性层状复合材料板的静态变形、自由振动和波传播问题，得到了受表载作用的静态响应、自由振动的自然频率和模态、波传播在不同电磁边界下的反射和透射系数以及功能梯度材料的尺度依赖关系。研究发现，铺层方式和非局部参数对微纳米层状复合材料的力学行为具有极大的影响。所得解不仅可用来检验薄板的适用范围，而且可用于分析厚板，为设计微型电子器件提供重要的理论参考。研究结果为工程上准晶材料用做结构表面涂层、增强复合材料和太阳能选择吸收装置提供重要的理论依据。