十次对称二维纳米准晶层状板的力学行为研究

Quasicrystal (QC) is a new solid structure between crystal and amorphous bodies. The atomic scale of QC can reach a few hundred nanometers. In general, the size of QC block produced by the common methods is at micro- or nano-scale. Nano-QC composites possess high strength, excellent ductility, stable microstructures and special mechanical properties. Furthermore, the two-dimensional (2D) quasicrystalline structures give more possibility to adjust structural parameters and to mold the spectrum of excitation than the one-dimensional quasicrystalline structures. Therefore, it is very meaningful to study the related mechanical behaviors of 2D nano-QC multilayered composite plates. In this project, the nonlocal theory of 2D decagonal nano-QCs is developed and the thick plate model of anisotropic nano-QC composites is established. By using the pseudo-Stroh formulism and new propagating matrix method, some mechanical problems of anisotropic and multilayered decagonal nano-QC plates are investigated, such as the bending deformation under the static surface loadings, free vibration, propagation of time-harmonic waves, refection and transmission of plane wave in multilayered nano-plates immersed in liquid, and buckling problem under normal biaxial compression along the boundary of plates. The exact solutions of these mechanical behaviors are derived, which help us to understand the deformation mechanism, size effect and dynamic response, etc., of 2D decagonal nano-QC multilayered plates. The results obtained in this project will provide an important theoretical basis for the QC applications such as surface coating of structures, solar selective absorber and reinforced composites in engineering.

准晶是一种介于晶体和非晶体之间新的固体结构，其原子关联尺度可以达到几百纳米，通常方法制备的准晶块体尺度一般在微米级和纳米级。纳米准晶复合材料具有很高的强度、优良的延展性、稳定的微结构和独特的力学性能。并且，二维准晶结构比一维准晶结构更可能调整结构参数和形成激发光谱。因此，研究二维纳米准晶复合材料层状板的相关力学行为具有重要的科学意义。本课题拟发展十次对称二维纳米准晶的非局部理论，建立各向异性纳米准晶的厚板模型。利用伪Stroh型公式和新的传递矩阵法，研究各向异性十次对称二维纳米准晶多层板受表面载荷作用下的静态弯曲变形、自由振动、时谐波传播、浸入液体中平面波传播的反射和透射以及板边界受法向双轴压缩时的屈曲问题，给出这些力学行为的精确解答，揭示十次对称二维纳米准晶层状板的变形机制、尺寸效应以及动力学响应等，为工程上准晶材料用做结构表面涂层、太阳能选择吸收器及增强复合材料提供重要的理论依据。

准晶作为一种新型固体结构，在微纳尺度下具有尺度依赖性。纳米准晶复合材料具有很高的强度、很好的韧性、稳定的微结构和独特的力学性能，在增强复合材料、涂层技术等领域有广阔的应用前景。本项目发展了十次对称二维纳米准晶和一维纳米准晶的非局部理论、修正偶应力理论和非局部应变梯度理论，建立了各向异性纳米准晶的厚板模型。采用伪Stroh型公式和传递矩阵法，系统地研究了各向异性十次对称二维纳米准晶和一维纳米准晶多层板结构的静态弯曲变形、自由振动、受迫振动、波的传播及屈曲等问题，获得准晶多层纳米板力学行为的精确解。通过数值算例，分析了准周期方向、尺度效应、周围弹性介质、几何尺寸、叠层顺序和波数等因素对准晶纳米板的弯曲变形、振动响应、频散曲线和临界屈曲载荷的影响规律。进一步，基于于Gurtin-Murdoch 表/界面模型，研究了纳米准晶板的缺陷如夹杂、椭圆孔和裂纹问题的尺度效应，获得缺陷附近的场强度因子和准晶纳米复合材料的有效力学性能。结果表明，准晶材料作为纳米板的外层时，频率明显升高，刚度增大，适合用作工程结构的涂层材料；十次对称二维准晶的准周期方向对弯曲变形、振动频率和临界屈曲载荷的影响与板的长宽比有关；声子场和相位子场位移随输入频率的增加而增加；周围的弹性介质可提高板的固有频率和临界屈曲载荷；非局部参数会降低功能梯度纳米板的刚度，而应变梯度参数会提高功能梯度纳米板的刚度；非理想界面对准晶板的力学行为有很大影响，声子场和相位子场位移随着非理想程度的增大而增大；准晶纳米层合板的前两阶频率随波数的增加而增大；软涂层会降低纳米裂纹尖端的场强度因子，而硬涂层会提高纳米裂纹尖端场强度因子，电可通边界下的纳米孔和纳米裂纹表现出与电不可通边界完全不同的力学行为。本项取得的研究成果可为新型复合材料的制备、结构优化设计和工程应用提供科学依据。