基于多重多级子结构声子能带与传输特性分析

基于多重多级子结构方法提出一种快速的声子晶体能带与传输特性的计算策略. 主要思想是将声子晶体划分成多层级子结构有限元模型,在能带计算中采用静凝聚和子结构周游树技术将子结构的内部刚度阵凝聚到Bloch 边界上. 由于内部刚度阵并不随着简约波矢变化,所以这种计算策略可以大大降低求解规模并提高计算效率,并不对整体有限元模型引入近似. 在传输特性计算中同样采用该策略,由于声子晶体单胞具有周期性,所以各个单胞的系数矩阵是相同的,从而减少计算量,并且可以灵活地选择是否回代求解单胞内部自由度. 数值算例以三维局域共振型声子晶体和二维Bragg 散射型声子晶体为例,计算结果验证了这种求解策略的正确性和高效性,并适用于复杂声子晶体分析.      

BAND STRUCTURE AND TRANSMISSION CHARACTERISTICS CALCULATION OF PHONONIC CRYSTALS BASED ON MULTI-LEVEL SUBSTRUCTURE TECHNIQUE

基于多重多级子结构方法提出一种快速的声子晶体能带与传输特性的计算策略. 主要思想是将声子晶体划分成多层级子结构有限元模型,在能带计算中采用静凝聚和子结构周游树技术将子结构的内部刚度阵凝聚到Bloch 边界上. 由于内部刚度阵并不随着简约波矢变化,所以这种计算策略可以大大降低求解规模并提高计算效率,并不对整体有限元模型引入近似. 在传输特性计算中同样采用该策略,由于声子晶体单胞具有周期性,所以各个单胞的系数矩阵是相同的,从而减少计算量,并且可以灵活地选择是否回代求解单胞内部自由度. 数值算例以三维局域共振型声子晶体和二维Bragg 散射型声子晶体为例,计算结果验证了这种求解策略的正确性和高效性,并适用于复杂声子晶体分析.     

最优二维固/固声子晶体带隙特性研究

声子晶体是一种具有弹性波带隙特性的周期性复合材料,其带隙特性受单胞拓扑形状的影响。通过拓扑优化技术,能够突破传统设计方法的局限,实现对声子晶体的主动设计。本文基于遗传算法和改进的平面波展开法,通过两阶段的优化过程,得到具有最大相对带隙的二维铜/环氧树脂声子晶体结构,并进一步研究不同带隙最优声子晶体单胞拓扑形状及其带隙特性。结果表明,利用所开发的带隙优化程序,能够得到满足带隙要求的具有全局最优的声子晶体结构;声子晶体最低带隙所对应的单胞是简单晶格结构,其散射体形状简单,而且对应的带隙频率最低,相对带隙最大,对于隔音减振最有实用价值。     

一维声子晶体带隙的非局部辛分析

周期性弹性复合结构(声子晶体)中传播的弹性波存在特殊的色散关系:弹性波只能在某段频率范围内无损耗的传播,该频率范围称为通带.一维声子晶体的色散问题可以看作分层介质中弹性波的传播问题,利用二维弹性理论予以分析.为了研究非局部效应对声子晶体带隙特性的影响,将Eringen的二维非局部弹性理论引入到Hamilton体系下,利用精细积分与扩展的Wittrick Williams算法可获取任意频率范围内的本征解.通过对不同算例的数值计算,分析和对比了非局部理论方法与传统局部理论方法的差别.并进一步指出了该套算法的适用性和优势所在.     

局域共振型声子晶体板缺陷态带隙及其俘能特性研究

设计了一种由圆柱形散射体嵌入环氧树脂基体而组成的周期阵列局域共振型声子晶体板结构, 分析了其平直带区域以及缺陷态的能量集中特性, 并研究了其振动能量采集特性. 首先基于超元胞法结合有限元方法分析了5 $\times$ 5完美声子晶体结构和缺陷态声子晶体结构的能带曲线和能量传输特性; 考虑点缺陷局域共振声子晶体结构的能量集中特性, 利用压电材料代替超元胞中某点的散射体材料引入点缺陷, 分析其振动能量采集特性, 结果表明单个5 $\times$ 5点缺陷超胞结构共振频带较窄; 为提升俘能效率, 提出两种由3个具有不同缺陷态数量和构型的5 $\times$ 5超元胞结构并联而成的5 $\times$ 15声子晶体板结构, 机电耦合特性分析结果表明: 所提出的局域共振型声子晶体板结构克服了单个点缺陷超胞结构缺陷模过少、共振频带过窄的局限性, 拓宽了俘能器的工作频带, 提高了输出电压; 此外, 引入不同的缺陷态数量和构型, 可以进一步拓宽俘能带宽, 实现更好的俘能效果.      

石墨烯力学性能研究进展

石墨烯是近年来发现的由单层碳原子通过共价键结合而成的具有规则六方对称的理想二维晶体, 是继富勒烯和碳纳米管之后的又一种新型低维碳材料. 由于具有非凡的电学、热学和力学性能以及广阔的应用前景, 石墨烯被认为是具有战略意义的新材料, 近年来迅速成为材料科学和凝聚态物理等领域最为活跃的研究前沿. 本文简要介绍了研究石墨烯力学性能的实验测试、数值模拟和理论分析方法, 重点综述了石墨烯力学性能的最新研究进展, 主要包括二维石墨烯的不平整性和稳定性, 石墨烯的杨氏模量、强度等基本力学性能参数的预测, 石墨烯力学性能的温度相关性和应变率相关性、原子尺度缺陷和掺杂等对力学性能的影响以及石墨烯在纳米增强复合材料和微纳电子器件等领域的应用, 最后对石墨烯材料与结构的力学研究进行了展望.      

零维物质体和微态物质体

在这篇文章里,R.G Muncaster的零维弹性体被推广到一般的高阶零维物质体。从非极连续介质力学理论出发,我们推出了零维物质体的所有平衡方程和热力学不等式。再从这些方程和不等式推出微态物质体的相应平衡方程和热力学不等式。这样,我们在零维物质体理论和微态物质体理论之间建立了一个类似于刚性质点力学和古典非极连续介质力学之间关系的关系。     

一维声子晶体中声波能带的解析研究

为了对一维声子晶体的能带进行解析研究,采用一维声子晶体的色散法,推导出一维声子晶体禁带频率和通带频率的解析公式;并利用此式对一维声子晶体的能带结构进行了解析研究,得到了禁带和导带的频率中心、频率宽度分别随介质厚度和声阻抗两者的变化规律,并与转移矩阵方法的计算结果进行了比较.研究结果表明:两种方法得到的结论相同,但解析法能更准确、更深刻地反映出一维声子晶体的能带随介质厚度和声阻抗等因素的变化规律;并且解析法克服了转移矩阵法等其他方法不能对能带结构进行解析研究的不足,是一种研究一维声子晶体能带更有效的方法.     

基于人工神经网络的声子晶体逆向设计

声子晶体是一种人工周期性复合材料, 其带隙特性使其在减振、隔声、滤波和声学功能器件等领域具有潜在的应用价值. 如何准确操纵声波和机械波是声子晶体设计的主要挑战. 现有设计方法是基于对结构几何参数与材料参数的分析调整使其匹配特定的应用特性, 设计效率不高且无法达到最佳性能. 为此, 本文以一维层状声子晶体为例, 提出了一种基于Softmax逻辑回归和多任务学习的人工神经网络声子晶体逆向设计方法, 其中, Softmax逻辑回归实现分层结构各区域材料种类的选择, 通过多任务学习确定各区域材料的分布, 从而, 将声子晶体逆向设计问题转化为对单位胞元拓扑结构多组分材料的分类问题. 首先, 随机生成大量声子晶体拓扑结构样本; 然后, 采用有限元法进行并行计算得到所有样本的带隙分布; 接着, 通过神经网络建立带隙分布和拓扑结构之间的映射关系; 最后, 利用训练好的神经网络设计具有目标带隙特性的声子晶体, 即以目标带隙作为神经网络的输入, 网络将直接输出对应的声子晶体单元胞元拓扑结构. 算例表明本方法可根据应用需求快速高效地得到具有目标带隙的一维声子晶体. 该方法为声子晶体的逆向设计提供了一种新颖思路.      

二维类桁架材料结构弹塑性分析

类桁架材料所构成结构的弹塑性行为的精确建模分析保证非常耗时, 为了 在保证精度的前提下提高此类问题的求解效率, 本文利用类桁架材料基本构件长细比 较大的特点，将材料单胞简化为桁架模型. 考虑到微单胞空间分布的周期性，基于 数值均匀化理论提出了类桁架材料结构的宏微观两 级弹塑性求解格式. 原问题转化为宏观上一个非线性弹性连续体计算问题和微观上多个小规 模桁架系统的弹塑性计算问题. 两个数值算例分别考虑了简单加载，非单调加载，规则宏观 结构和具有非完整单胞的较复杂宏观结构等问题. 与实际结构计算结果在精度和时间等方面 的比较验证了求解格式的有效性. 最后还探讨了算法的适用范围.     

Force constants of BN,SiC, AlN and GaN sheets through discrete homogenization

The force constants related to the bond stretching and angular variation of boron nitride, silicon carbide, aluminium nitride and gallium nitride nanosheets are directly evaluated from ab-initio reference solutions of the Young’s modulus and the Poisson’s ratio. To this end, the analytical expressions of the elastic constants of a generic monolayer hexagonal diatomic sheet are derived, starting from its sticks-and-springs molecular mechanics model, through proper tools of the homogenization of periodic discrete media. Numerical benchmark assessments are given.     

六方氮化硼韧脆转变性能的理论研究

基于六方氮化硼原子间Tersoff势函数,本文建立了手性依赖的六方氮化硼“杆-簧”模型,得到了其在大变形下的非线性力学行为。结果表明六方氮化硼断裂模式从扶手椅型(Armchair,手性角为0o)到锯齿型(Zigzag,手性角为30o)由韧性断裂转变为脆性断裂。通过分析拉伸过程中键长键角变化情况,键角变化所起作用超过键长变化导致韧性断裂,而键长起主导作用时则为脆性断裂。探讨不同手性氮化硼非线性力学行为,获得两种断裂模式的分界点大约为手性角15o。相同条件下,石墨烯在拉伸过程中键长变化起支配作用,而氮化硼除了键长变化的影响之外,键角的变化对整个过程也有着至关重要的作用。最后,与分子动力学模拟结果对比显示本文的理论结果是可靠的。本研究对理解六方氮化硼优异的力学性能及其在微纳器件领域的应用提供了理论支撑。     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CON-TINUUM THEORIES (Ⅱ)—MICROMORPHIC CONTINUUM THEORY AND COUPLE STRESS THEORY

IntroductionThispaperisadirectcontinuationofRef.[1 ] .InitthecoupledconservationlawofenergypresentedinRef.[2 ]wasextendedandtherathercompletesystemsofbasicbalancelawsandequationsformicropolarcontinuumtheoryhavebeenconstitutedbycombiningtherenewedresultsandthetraditionalconservationlawsofmassandmicroinertiaandtheentropyinequality .Thepurposeofthispaperistorestablishthesystemsofbasicbalancelawsandequationsformicromorphiccontinuumtheoryandcouplestresstheoryviadirecttransitionsandreductionsfromth…     

Prediction of phonon properties of 1D polyatomic systems using concurrent atomistic–continuum simulation

In this work, we present the simulation results of phonon properties, including phonon dispersion relations, group velocities, phonon relaxation time and mode-specific thermal conductivity, of low-dimensional crystals using the newly developed concurrent atomistic–continuum (CAC) method. With significantly less number of degrees of freedoms than all-atom molecular dynamics, the CAC method predicts the phonon properties of one-dimensional (1D) polyatomic crystals at finite temperatures with the full anharmonicity of the atomic interactions being incorporated. Complete phonon branches of polyatomic crystals are obtained by CAC through the phonon spectral energy density analysis. It is shown that CAC allows medium to long-wavelength phonon transport from atomic to coarsely meshed finite element region without the need of special numerical treatment. The frequency-dependent phonon group velocities are explicitly measured in the simulation. Sub-THz phonon lifetimes in 100 -mm-long polyatomic chains containing 400 million of atoms are predicted. Analysis of the phonon mode-specific thermal conductivity shows that the medium to long-wavelength acoustic phonons are contributing to the majority of the heat transport in 1D crystal, suggesting that the long-wavelength phonons effectively act as thermal carriers in 1D system. This work provides a possible explanation for the anomalous heat transport observed in low-dimensional materials.     

On three-dimensional elastic problems of one-dimensional hexagonal quasicrystal bodies

Based on rigorous operator theory, a general solution of the three-dimensional elasticity equations of equilibrium for 1D hexagonal quasicrystals is obtained. The solution is expressed in terms of four quasiharmonic functions, which is very simple and useful. The point phonon (phason) force solution of an infinite 1D hexagonal quasicrystal body is derived, all in terms of elementary functions. They can play an important role in numerical simulations such as boundary element method.     

Atomistic simulation of free transverse vibration of graphene,hexagonal SiC,and BN nanosheets

Free transverse vibration of monolayer graphene, boron nitride (BN), and silicon carbide (SiC) sheets is inves-tigated by using molecular dynamics finite element method. Eigenfrequencies and eigenmodes of these three sheets in rectangular shape are studied with different aspect ratios with respect to various boundary conditions. It is found that aspect ratios and boundary conditions affect in a similar way on nat-ural frequencies of graphene, BN, and SiC sheets. Natural frequencies in all modes decrease with an increase of the sheet's size. Graphene exhibits the highest natural frequen-cies, and SiC sheet possesses the lowest ones. Missing atoms have minor effects on natural frequencies in this study.     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CON-TINUUM THEORIES (Ⅱ)—MICROMORPHIC CONTINUUM THEORY AND COUPLE STRESS THEORY

The purpose is to reestablish the balance laws of momentum, angular momentum and energy and to derive the corresponding local and nonlocal balance equations for micromorphic continuum mechanics and couple stress theory. The desired results for micromorphic continuum mechanics and couple stress theory are naturally obtained via direct transitions and reductions from the coupled conservation law of energy for micropolar continuum theory, respectively. The basic balance laws and equations for micromorphic continuum mechanics and couple stress theory are constituted by combining these results derived here and the traditional conservation laws and equations of mass and microinertia and the entropy inequality. The incomplete degrees of the former related continuum theories are clarified. Finally, some special cases are conveniently derived. Foundation items: the National Natural Science Foundation of China (10072024); the Research Foundation of Liaoning Education Committee (990111001) Biography: DAI Tian-min (1931≈)     

ANALYTICAL AND NUMERICAL INVESTIGATIONS OF TWO SPECIAL CLASSES OF GENERALIZED CONTINUUM MEDIA

In this paper,the micromorphic theory and the second gradient theory are proposedwhere the micromorphic model can be reduced to the second gradient model with the vanishing relative deformation between macrodeformation gradient and microdeformation.Analytical solutions for the simple shear problem in the case of a general small strain isotropic elasticity micromorphic model and the second gradient model are presented,respectively.Besides,uniaxial tension of a constrained layer with two different boundary conditions is also analytically solved.Finally,the micromorphic theory is implemented numerically within a two-dimensional plane strain finite element framework by developing two isoparametric elements.     

Vibration of two-dimensional hexagonal boron nitride

The dynamic behavior of two-dimensional nanostructures is important to the future application of nano devices. The vibrational behaviors of single-layered hexagonal boron nitride(h-BN) are studied by molecular dynamics simulation and continuum plate model. The bending stiffness and Poisson's ratios of h-BN along zigzag direction and armchair direction are calculated. H-BN is softer compared with graphene. The continuum plate model can predict the vibration of h-BN with four edge-clamped boundary conditions well. The electric fields in different directions have obvious influence on the vibration of h-BN. The natural frequency of h-BN changes linearly with the electric field intensity along the polarization direction. The natural frequency of h-BN decreases with the increase of electric field intensity along both positive and negative nonpolarization direction. While the natural frequency of h-BN increases with the increase of electric field intensity along both positive and negative transverse electric field.     

A MECHANICS MODEL OF A MONOLAYER GRAPHENE BASED ON THE LENOSKY INTERATOMIC POTENTIAL ENERGY

基于对Lenosky 碳-碳共价键作用势连续化得到的单层石墨烯的势能和Hamilton 原理,导出了单层石墨烯的动力学方程. 使用该数学模型及Galerkin 方法,研究了矩形单层石墨烯片的静力挠曲问题. 结果显示,石墨烯片的几何尺寸较小时,弯曲刚度对结构的受力影响较大,可用板理论来描述;随着结构尺寸的增大,弯曲刚度的影响迅速降低;当矩形石墨烯片的短边尺寸大于10 nm 时,可以忽略弯曲刚度对结构的影响,使用薄膜理论来描述单层石墨烯的力学性质.