Elastic metamaterials with local resonances: an overview

Metamaterials are artificial composite materials engineered to have properties that may not be found in nature. By exploring locally resonant effect of the building units, elastic metamaterials are able to possess negative values of effective mass, effective bulk or shear modulus. Mass-spring and continuum material versions of these elastic metamaterials are reported and the physical mechanisms of negative effective parameters are demonstrated. Applications of metamaterials to acoustic cloaking and superlensing are also discussed.     

Broadband elastic metamaterial with single negativity by mimicking lattice systems

The narrow bandwidth is a significant limitation of elastic metamaterials for practical engineering applications. In this paper, a broadband elastic metamaterial with single negativity (negative mass density or Young's modulus) is proposed by mimicking lattice systems. It has two stop bands and the bandwidth of the second one is infinite theoretically. The effect of the relevant parameters on band gaps is discussed. A continuum model is proposed and the selection of materials is discussed in detail. It shows that continuum metamaterials can be described accurately by using the lattice model, and the second stopband can be ultra-broad but not infinite. This discrepancy is investigated and a method is provided to calculate the upper limit of the second stopband for a continuum metamaterial. As a verification, the proposed metamaterial is used for wave mitigation over broadband frequency ranges. Moreover, the present method is extended to design 2D anisotropic elastic metamaterials, and a device to control the direction of elastic wave transmission is proposed as an example.     

Study of anomalous wave propagation and reflection in semi-infinite elastic metamaterials

Elastic metamaterials have been investigated to achieve negative effective properties, which cannot be found in the conventional elastic medium. In this paper, plane wave propagation and reflection in semi-infinite elastic metamaterials with doubly or triply negative material properties are studied analytically and numerically. The unique negative refractions for the longitudinal (P) wave and transverse (S) wave are captured by the proposed generalized Snell’s law. Attention is paid to quantitative characterization of the effects of different negative property combinations on the anomalous wave propagation. The effects of different angles of incidence are also investigated for both double-negative and triple-negative transmitted media and some unusual wave propagation phenomena such as complete wave mode conversion are numerically demonstrated. This study can serve as the theoretical foundation for engineering and designing general metamaterial-based elastic wave devices.     

声波超材料设计的力学原理与进展

声波超材料是一种特殊的人工复合材料,它基于连续介质力学理论描述,通过对微观结构的精心设计,在宏观上获得反常规的动态材料属性,如负动态质量,负动态模量,负折射率等.超材料的出现为实现波动控制提供了可能,相关研究在工程领域具有潜在的应用价值.本文着重阐述了弹性固体超材料、声波超材料、超表面、主动超材料的设计原理与相关研究进展, 所述原理对于波控结构的设计与制备实现具有指导意义.     

厚度梯度型箭形负泊松比蜂窝基座抗冲击性能

设计了一种箭形负泊松比的蜂窝基座结构,推导了其胞元结构的力学性能解析公式,并利用有限元方法研究了具有厚度梯度箭形负泊松比蜂窝材料的抗冲击性能。基于功能梯度材料,其基体呈连续梯度变化的概念,以胞元壁厚为自变量,设计了顺厚度梯度、逆厚度梯度型和均匀厚度的蜂窝层,并建立基座模型。在基座质量不变的前提下具体讨论了蜂窝胞元凹角及厚度梯度的不同设置情况对基座抗冲击性能的影响。结果表明,相同梯度设置情况下,胞角的变化会引起蜂窝结构等效弹性模量的变化,进而改变基座的抗冲击性能,而将胞壁厚度较小的蜂窝层放置于迎冲端时,基座整体的应力水平明显降低;将壁厚较大的蜂窝层放置于迎冲端时,基座面板的输出冲击环境能够有效地得到控制。     

Theoretical investigation of the behavior of an acoustic metamaterial with extreme Young's modulus

A mechanical model with local resonators is proposed as an acoustic metamaterial that exhibits an unusual frequency-dependent effective stiffness. If treated as an equivalent elastic solid, its effective Young's modulus can become unbounded or vanishingly small at two respective frequencies. Moreover, in a certain frequency range, the effective Young's modulus would become negative, resulting in a band gap that coincides with this frequency range. The wave attenuation behavior and mechanism are studied through numerical simulations on the acoustic metamaterial model. The capability of the metamaterial to selectively block or filter unwanted waves is demonstrated by a numerical simulation example.     

闭孔泡沫铝材料十四面体模型的改进

基于对闭孔泡沫铝发泡过程更为合理的假设,提出了描述胞体结构的改进的十四面体模型,使之可以反映密度增大时质量集中于支柱和顶点的情况。采用有限元方法及耦合边界条件,研究了闭孔泡沫铝的相对弹性模量、泊松比等弹性特征与胞体参数的关系,给出了拟合的弹性模量的计算公式,并对模型在弹性压缩变形下应力分布进行了分析。通过与已有模型的比较表明,改进模型可以较好地模拟闭孔泡沫铝材料的弹性性能。     

Designing orthotropic materials for negative or zero compressibility

There has been considerable interest in materials exhibiting negative or zero compressibility. Such materials are desirable for various applications. A number of models or mechanisms have been proposed to characterize the unusual phenomena of negative linear compressibility (NLC) and negative area compressibility (NAC) in natural or synthetic systems. In this paper we propose a general design technique for finding metamaterials with negative or zero compressibility by using a topology optimization approach. Based on the bi-directional evolutionary structural optimization (BESO) method, we establish a systematic computational procedure and present a series of designs of orthotropic materials with various magnitudes of negative compressibility, or with zero compressibility, in one or two directions. A physical prototype of one of such metamaterials is fabricated using a 3D printer and tested in the laboratory under either unidirectional loading or triaxial compression. The experimental results compare well with the numerical predictions. This research has demonstrated the feasibility of designing and fabricating metamaterials with negative or zero compressibility and paved the way towards their practical applications.     

两种五零能模式材料单胞构型及其性能分析

五零能模式材料是一种新型的人工超材料,虽属于弹性材料,但组成其单胞的特殊构型使其宏观静态表现为仅能承载一种受力状态,动态表现为仅能传播一种弹性波。本文首先构造了两种五零能模式材料的单胞构型,其具有不同的弹性特性,其中一种材料可传播弹性膨胀波,另一种可传播弹性剪切波。然后分别采用代表体元法和均匀化法分析这两种单胞的等效弹性模量。五零能模式材料的分析分为两步更直观,开始从单胞桁架模型入手,检验单胞构型是否满足五零能模式的定义,然后分析单胞实体模型,考察单胞构型的结构参数与其等效弹性模量的关系。研究表明对于这种低密度弹性材料的分析,代表体元法更适合。     

折纸超材料折展稳态特性研究

Origami metamaterials can regulate and control macroscopic deformation by continuous deformation of their internal microstructure. Hence, mechanical properties such as Poisson's ratio, stiffness, and modulus of the metamaterials can be adjusted and designed. This work theoretically studied the mechanical behavior of origami metamaterials under the synergy of complex internal configuration and folding motion, with the methods of torsion spring equivalent and energy principle. Here, we established a mechanical model to describe the folding deformation of the metamaterials, and analyzed the influence of geometric parameters on external loading. Through parameter analysis, it is found that the external loading exhibits monotonicity during the unfolding process and does not have stability. The external loading can show three situations such as monotonicity, mono-stability and bi-stability during the folding process, which are closely related to the parameters. This work provides important guidance to origami metamaterials for improving the design of the configuration and the regulation of their performance.      

压电超构材料及其波动控制研究:现状与展望

弹性波超构材料是一种人为设计的周期结构材料, 因其独特的力学性能而受到广泛的关注, 在军用和民用领域都展现出重要而独特的应用前景. 根据需求主动或被动地调控弹性波超构材料的力学特性, 能够赋予其更强的适用性能. 其调控的方式多种多样, 其中运用压电材料进行调控是一种方便、速度快、精度高、体积小且价格低的调控方式. 文章中首先简要地介绍弹性波超构材料、可调超构材料、压电材料和几种常用的分流电路的基本特性. 然后依据压电材料在弹性波超构材料中应用形式的不同, 将其分为两大类: 第一类中, 压电材料作为主体结构材料或主体结构的一部分组成材料; 第二类中, 压电材料主要以压电弹簧或压电片的形式贴附于主体结构的表面或内嵌在结构中, 作为激励器或/和传感器. 文章主要介绍两种类型弹性波超构材料的研究内容和发展历史, 涉及带隙调控、波导、负折射、超传输、拓扑态、隐身以及外接分流电路等. 最后总结压电弹性波超构材料研究的不足之处并给出相应的未来研究展望.      

Numerical analysis of effective elastic properties of geomaterials containing voids using 3D random fields and finite elements

The purpose of the study is to investigate the influence of porosity and void size on effective elastic geotechnical engineering properties with a 3D model of random fields and finite element. The random field theory is used to generate models of geomaterials containing spatially random voids with controlled porosity and void size. A “tied freedom” analysis is developed to evaluate the effective Young’s modulus and Poisson’s ratio in an ideal block material of finite elements. To deliver a mean and standard deviation of the elastic parameters, this approach uses Monte-Carlo simulations and finite elements, where each simulation leads to an effective value of the property under investigation. The results are extended to investigate an influence of representative volume element (RVE). A comparison of the effective elastic stiffness of 2D and 3D models is also discussed.     

Nonlinear elasticity modeling of biogels

A second-order nonlinear elastic model is developed for biogels, whereby the elastic constants are estimated from the free energy densities for polymer networks and polymer-water mixtures. For typical values of the constants, important physical insights are revealed: a biogel stiffens under tension, contracts longitudinally under torsion (inverse Poynting effect), and experiences a negative normal stress under simple shear. This approach of extracting nonlinear elastic constants works for any constitutive law, and has the advantage of exploring physical phenomena without recourse to computationally intensive simulations.     

系统锚杆对边坡岩体加固效果的数值模型试验研究

以大型的岩土工程数值分析软件AD INA为研究手段,对边坡岩体的分离块体经系统锚杆加固后,其抗压强度、弹性模量及c、φ值的提高,并计算和比较了锚固对不同强度岩体的参数影响大小,并对锚固岩体的各向异性进行了初步研究,垂直布锚对岩体的弹性模量影响较大,但是对于岩体的抗压强度的影响相对较小。     

岩体原位流变荷载试验的力学参数与模型反演

根据现场岩体原位测试的60m和70m处两试验点的流变变形曲线,首先通过曲线特征筛选出了能够描述其变形特性的流变模型(三参量固体模型,Burgers模型),基于粘弹性分析理论及两步反分析法思路,建立了荷载试验的三参量固体模型、Burgers模型的位移优化反演格式,利用分级加载所获得的瞬时弹性位移,反算出了两试验点处的岩体弹性体积模量K、剪切模量G0和变形模量E0,并由优化反演方法获得了两模型的所有流变参数G1,η1,η2和E1以及长期弹性模量E∞。利用所获得的粘弹性参数分别计算出了在不同载荷下两种模型的理论解析曲线,并与实测曲线进行了分析对比,最终获得了能够较真实地描述试验区域岩体流变变形特性的最佳模型,即三参量固体模型。通过对比分析验证了所用思路及方法的正确性和实用性,文中方法虽然应用于流变荷载实验情况,但其具有一定的普遍意义,可应用于不同状况的流变实验的参数确定和模型反演。     

Analysis of elastic and plastic deformation associated with indentation testing of thin films on substrates

A study has been made of the elastic and plastic deformation associated with submicrometer indentation of thin films on substrates using the finite element method. The effects of the elastic and plastic properties of both the film and substrate on the hardness of the film/substrate composite are studied by determining the average pressure under the indenter as a function of the indentation depth. Calculations have been made for film/substrate combinations for which the substrate is either harder or softer than the film and for combinations for which the substrate is either stiffer or more compliant than the film. It is found, as expected, that the hardness increases with indentation depth when either the yield strength or the elastic modulus of the substrate is higher than that of the film. Correspondingly, the hardness decreases with indentation depth when the yield strength or elastic modulus of the substrate is lower than that of the film. Functional equations have been developed to predict the hardness variation with depth under these different conditions. Finite element simulation of the unloading portion of the load displacement curve permits a determination of the elastic compliance of the film/substrate composite as a function of indentation depth. The elastic properties of the film can be separated from those of the substrate using this information. The results are in good agreement with King's analytical treatment of this problem.     

低频弹性波超材料的若干进展

超材料是一类新兴的具有超常物理性质的人造周期/拟周期材料, 能够改变电磁波、声波以及弹性波等在介质中的传播特性. 因在航天、国防以及民用科学等方面的巨大应用潜力, 超材料自被提出后便受到极大的关注并引发研究热潮. 弹性波超材料是超材料的一种, 能够基于弹性波与超材料结构的相互耦合作用实现对弹性波的操控. 带隙是评估弹性波超材料实现弹性波操控的重要工具, 其性质与超材料的材料参数、晶格常数以及局域振子的固有频率相关. 受制于超材料的承载能力、外观尺寸以及局域振子结构等因素, 利用传统超材料开启低频(约100 Hz)弹性波带隙依然存在较大困难. 文章首先简要介绍超材料开启弹性波带隙的基本原理, 然后从低频弹性波超材料基本结构与低频带隙实现方法、低频带隙优化与调控策略、低频带隙潜在应用等三个方面详细总结低频弹性波超材料的研究工作. 其中, 低频带隙超材料的基本结构主要包括布拉格散射型超材料、传统局域共振型超材料以及准零刚度局域共振超材料. 文章通过总结低频弹性波超材料的研究进展, 分析了目前研究中的不足并对未来低频弹性波的研究方向进行了展望.      

基于等效特征应变原理的复合材料有效模量细观力学分析

基于等效特征应变原理,提出了一种新的复合材料有效模量细观力学分析方法。首先,在等效特征应变原理基础上提出平均等效特征应变原理,它可用于解决有限体下任意形状(无论是凸或凹形)的单个夹杂或多个夹杂的弹性变形问题。其次,将平均等效特征应变原理与细观力学直接均匀法相结合,来分析确定复合材料的有效模量。最后利用复合材料纤维与基体的力学性能参数及纤维的体分比,借助MATLAB编程方法,预测其有效模量。通过将理论预测值与已有的的试验值、其它理论预测值进行对比,验证了新分析方法的合理性和分析精度。     

Active elastic metamaterials for subwavelength wave propagation control

Recent research activities in elastic metamaterials demonstrate a significant potential for subwavelength wave propagation control owing to their interior locally resonant mechanism. The growing technological developments in electro/magnetomechanical couplings of smart materials have introduced a controlling degree of freedom for passive elastic metamaterials. Active elastic metamaterials could allow for a fine control of material physical behavior and thereby induce new functional properties that cannot be produced by passive approaches. In this paper, two types of active elastic metamaterials with shunted piezoelectric materials and electrorheological elastomers are proposed.Theoretical analyses and numerical validations of the active elastic metamaterials with detailed microstructures are presented for designing adaptive applications in band gap structures and extraordinary waveguides. The active elastic metamaterial could provide a new design methodology for adaptive wave filters, high signal-to-noise sensors, and structural health monitoring applications.     

基于OTTOSEN准则的混凝土粘塑性力学模型

研究了混凝土的弹．粘塑性动态本构关系,提出一个应变率相关的非线性混凝土模型．模型改进Bicanic的混凝土塑性间断面变化规律和Ottosen的四参数屈服准则,建立冲击荷载下的混凝土本构方程,可以应用于地震和爆炸作用下混凝土材料响应的研究．根据混凝土动态实验结果对应变率和材料强度的关系提出合理假设,考虑以往被忽略的材料峰值应变和泊松比随应变率的变化．模型包含静水压力参数和动态塑性损伤因子,可以有效地反映混凝土的动态力学行为,为其动态问题的研究提供有益的思路和有效的工具．