Plastic analysis of the crack problem in two-dimensional decagonal Al-Ni-Co quasicrystalline materials of point group 10,10

The fundamental plastic nature of the quasicrystalline materials remains an open problem due to its essential complicacy. By developing the proposed generalized cohesive force model, the plastic deformation of crack in point group 10, 10 decagonal quasicrystals is analysed strictly and systematically. The crack tip opening displacement （CTOD） and the size of the plastic zone around the crack tip are determined exactly. The quantity of the crack tip opening displacement can be used as a parameter of nonlinear fracture mechanics of quasicrystalline material. In addition, the present work may provide a way for the plastic analysis of quasicrystals.     

Influence of disorders on the focusing property of photonic quasicrystal slab

The influence of disorders in the fabrication process on the focusing performance of two-dimensional optical quasicrystal slab is investigated. Two types of disorders are considered: positional randomness and radius randomness. The change in field distribution for E polarization and H polarization is examined by using the finite-difference time-domain method. We find that for both polarizations disorder has a detrimental effect on the focusing performance of quasicrystal lens. The tolerance of the focusing function to structural disorders is examined in detail. We show that the focusing quality is much more sensitive to the fluctuation of radius than to the randomness of position. These results will be helpful in devising photonic imaging devices based on quasiperiod photonic crystals.     

Decagonal quasicrystal plate with elliptic holes subjected to out-of-plane bending moments

In the present paper, we consider only the ideal elastic behavior, neglecting the dissipation associated with the atomic rearrangements. Under these conditions, the decagonal quasicrystal plate bending problems have been discussed. The Stroh-like formalism for the bending theory of decagonal quasicrystal plate is developed. The analytical solutions for problems of decagonal quasicrystal plate with elliptic hole subjected to out-of-plane bending moments are obtained directly by using the forms. The resultant bending moments around the hole boundaries are also given explicitly. When the phonon–phason coupling is absent, the results reduce to the corresponding solutions for the isotropic elastic plates.     

Fundamental solutions of critical wedge angles for one-dimensional piezoelectric quasicrystal wedge

Two problems of a one-dimensional (1D) piezoelectric quasicrystal (QC) wedge are investigated, i. e., the two sides of the wedge subject to uniform tractions and the wedge apex subject to the concentrated force. By virtue of the Stroh formalism and Barnett-Lothe matrices, the analytical expressions of the displacements and stresses are derived, and the generalized solutions for the critical wedge angles are discussed. Numerical examples are given to present the mechanical behaviors of the wedge in each field. The results indicate that the effects of the uniform tractions and the concentrated force on the phonon field displacement are larger than those on the phason field.     

软物质准晶广义流体动力学方程组

建立了软物质准晶广义流体动力学方程组,其基础为广义Langevin方程,推导方法为Poisson括号,它参考了固体准晶的广义流体动力学方程组,但是两者存在原则的不同.固体准晶的广义流体动力学方程组考虑了固体粘性与声子弹性和相位子弹性的相互作用,没有状态方程问题;软物质准晶广义流体动力学方程组考虑的是软物质流体声子与声子弹性和相位子弹性的相互作用,按物理学术语多出了一种元激发,而且必须考虑状态方程问题,这是一个新课题,又增加了难点.实际应用的结果发现,软物质准晶广义流体动力学方程组大大激活了广义流体动力学的效能,为软物质准晶学科的发展提供了一个数学模型,为探讨有关物理问题的时间-空间演化提供了可操作的实际可行的求解体系和分析工具,求解的结果令人满意.     

一维六方准晶的两类周期接触问题

利用复变函数方法讨论了一维六方准晶非周期平面的两类周期接触问题,即无摩擦周期接触以及半平面粘结周期接触问题.利用Hilbert核积分公式,得到了两类周期接触问题封闭形式的解.对于无摩擦周期接触问题,给出了3种常见压头(周期直水平基底、周期直倾斜基底、周期圆基底)作用下接触应力的显式表达式;对于半平面粘结周期接触问题,给出了实际工程中常见的边界上有尖劈形周期位移情况下应力的解析表达式.当忽略相位子场的贡献时,结果与正交各向异性材料周期接触问题的相应结果一致.     

Collinear periodic cracks and/or rigid line inclusions ofantiplane sliding mode in one-dimensional hexagonal quasicrystal

For a one-dimensional (1D) hexagonal quasicrystal (QC), there is the periodic (x₁,x₂)-plane of atomic structures with the quasiperiodic direction x₃-axis along which there exists a phason displacement. The macroscopically collinear periodic cracks and/or rigid line inclusions are placed on the periodic (x₁,x₂)-plane for finding out the influence of phason displacement on the related physical quantities. These two models are reduced to the Riemann–Hilbert problem of periodic analytic functions to obtain the closed-form solutions for the antiplane sliding mode. It is found that the phonon and phason stress intensity factors of cracks as well as the phonon and phason stress field intensity factors of rigid line inclusions are not related to the coupling of phonon and phason fields. These mean that there is not the influence of phason displacement on both the phonon stress intensity factor (usual stress intensity factor) of cracks and the phonon stress field intensity factor of rigid line inclusions. However, the energy release rates of periodic cracks and/or rigid line inclusions are obtained and affected not only by the periodicity of cracks and/or rigid line inclusions but also by the phason displacement.     

一维短沟槽复合准晶结构减阻效应及模拟分析

本文测试了人工构建的一维短沟槽复合准晶结构对流体的减阻性能,并与一维短沟槽复合周期结构和一维沟槽周期结构的流阻进行了对比.实验结果表明,一维短沟槽复合准晶结构的减阻效果优于一维短沟槽复合周期结构,其中一维短沟槽十二重复合准晶结构的减阻效果最佳,同时与一维沟槽周期结构具有同样的减阻效果.在机理分析方面,建立了二维光栅的夫琅禾费衍射波模型,对通过一维短沟槽复合准晶结构的波谱特征进行模拟分析. 频谱分析表明,经过二维准周期光栅的相干波强度谱具有谱带结构特征,抑制了大角度方向上的强峰形成.这一结果与流体流过一维短沟槽复合准晶结构相对应,展向上的准周期结构在激活边界层微扰动的同时,也使得二次涡分布比较均匀,从而抑制了展向强扰动的形成,所以能够有效减小流阻.