A unified treatment of nonclassical nonlinear effects in the propagation of ultrasound in heterogeneous media

Recent experiments on rocks and other materials, such as soil, cement, concrete and damaged elastic materials, have led to the discovery of nonlinear (NL) hysteretic effects in their elastic behaviour. These observations suggest the existence of a NL mesoscopic elasticity universality class, to which all the aforementioned materials belong. The purpose of the present contribution is to search for the basic mathematical roots for nonclassical nonlinearity, in order to explain its universality, classify it and correlate it with the underlying meso- or microscopic interaction mechanisms. In our discussions we explicitly consider two quite different kinds of specimens: a two-bonded-elements structure and a thin multigrained bar. It is remarkable that, although the former includes only one interface and the latter very many interstices, the same "interaction box" formalism can be applied to both. Another important result of the proposed formalism is that the spectral contents of an arbitrary system for any input amplitude may be predicted, under certain assumptions, from the result of a single experiment at a higher amplitude.     

Propagation of acoustic pulses in material with hysteretic nonlinearity

Evolution equations for propagation of both unipolar and bipolar acoustic pulses are derived by using hysteretic stress-strain relationships. Hysteretic stress-strain loops that incorporate quadratic nonlinearity are derived by applying the model of Preisach-Mayergoyz space for the characterization of structural elements in a micro-inhomogeneous material. Exact solutions of the nonlinear evolution equations predict broadening in time and reduction in amplitude of a unipolar finite-amplitude acoustic pulse. In contrast with some earlier theoretical predictions, the transformation of the pulse shape predicted here satisfies the law of "momentum" conservation (the "equality of areas" law in nonlinear acoustics of elastic materials). A bipolar pulse of nonzero momentum first transforms during its propagation into a unipolar pulse of the same duration. This process occurs in accordance with the "momentum" conservation law and without formation of shock fronts in the particle velocity profile.     

Cascade cross modulation due to the nonlinear interaction of elastic waves in samples with cracks

The phenomenon under study consists in that, in an inhomogeneous material with nonlinearity caused by the presence of soft defects (the so-called “nonclassical” nonlinearity), cascade nonlinear effects are fairly strong and may even become comparable to the first-order effects. Similar cascade effects in media with a common nonlinearity of the crystal lattice are much weaker. This difference can be used as an important diagnostic indicator in nondestructive testing. Experimental data obtained for samples with cracks, which exhibit both ordinary modulation and cross-modulation effects, as well as a cascade cross modulation, are presented. The origin of the enhanced level of cascade effects is explained by modeling with the use of a simple model of nonlinearity of an inhomogeneous material containing soft Hertzian contacts.     

High-accuracy acoustic detection of nonclassical component of material nonlinearity

The aim is to assess the nonclassical component of material nonlinearity in several classes of materials with weak, intermediate, and high nonlinear properties. In this contribution, an optimized nonlinear resonant ultrasound spectroscopy (NRUS) measuring and data processing protocol applied to small samples is described. The protocol is used to overcome the effects of environmental condition changes that take place during an experiment, and that may mask the intrinsic nonlinearity. External temperature fluctuation is identified as a primary source of measurement contamination. For instance, a variation of 0.1?°C produced a frequency variation of 0.01%, which is similar to the expected nonlinear frequency shift for weakly nonlinear materials. In order to overcome environmental effects, the reference frequency measurements are repeated before each excitation level and then used to compute nonlinear parameters. Using this approach, relative resonant frequency shifts of 10(-5) can be measured, which is below the limit of 10(-4) often considered as the limit of NRUS sensitivity under common experimental conditions. Due to enhanced sensitivity resulting from the correction procedure applied in this work, nonclassical nonlinearity in materials that before have been assumed to only be classically nonlinear in past work (steel, brass, and aluminum) is reported.     

声波在有裂纹的固体中的非经典非线性传播

固体材料的无损检测是一个非常重要的课题,带裂纹的固体材料显示非经典非线性声学现象,本文对此现象进行了实验和理论研究。从实验上一维观察到此现象,发现奇次谐波振幅与基波振幅呈平方关系,与理论预计基本吻合;理论上从二维的角度数值模拟了声波在有损耗的带裂纹的固体中的声传播,并讨论了经典非线性和非经典非线性对声传播的影响,发现裂纹的贡献主要体现在非经典非线性上。分析了样品中裂纹的宽度和位置与非线性声参数的关系,在靠近样品中心的两个对称区域以及距离声源较近点,非线性声参数对样品的破损较为敏感,而在中央和距声源最远端敏感性较低;随着裂纹宽度的扩大,非线性声参数也开始变大,但在破损区域蔓延到棒边缘之前,有下降的趋势。      

Modelling and dynamic properties of a novel solid and liquid mixture vibration isolator

Solid and Liquid Mixture (SALiM) vibration isolator is a new isolator which is designed for vibration isolation of heavy equipment with low frequency. The isolator contains liquid and elastic solid elements as working media. To get the stiffness property of the isolator, this paper establishes the mechanics model of elastic solid elements by introducing plate-shell model. Considering geometry nonlinearity, the stiffness of the element under outer liquid pressure and inner air pressure was obtained by perturbation method. Then the stiffness of isolator is derived. As a result, the stiffness is piecewise linear-nonlinear and determined by parameters of the elastic elements and elastic container. In addition, the equation of motion (EOM) of a single degree of freedom system supported by a SALiM isolator is given. The properties of the frequency response function (FRF) of the system are analysed using averaging method which is a classical approximation approach for estimating nonlinear system FRF. And it is found that the system with SALiM isolator shows softening stiffness behaviour. The jumping phenomenon clearly occurs under certain condition. Finally, the vibration isolation property is predicted based on energy transmissibility (ET) in different cases.     

岩石等非线性介观弹性固体材料的谐波特性的超声研究

岩石、混凝土等非线性介观弹性固体材料显示出与经典的非线性声学不同的非经典非线性声学现象，比如滞后现象、离散记忆等。本文实验研究了超声波在岩石材料中产生的基波、二次、三次谐波随声源幅度的依赖关系，研究了岩石的超声衰减，与金属材料的进行了对比；并且将浸水后的混凝土与浸水前的混凝土的超声谐波特性进行了对比，对此实验现象作出了定性的解释。此研究有利于岩石等非线性介观弹性固体材料的无损检测的研究。     

Modeling the propagation of ultrasonic waves in the interface region between two bonded elements

An important task in nondestructive materials evaluation is the development of techniques to characterize the bond quality of adherent joints. Binding forces are nonlinear and cause a nonlinear modulation of transmitted and reflected ultrasonic waves. As a consequence, the higher harmonics generated by an insonified monochromatic wave give information about the adhesive bonds. The local binding forces in thin bonded interfaces can be obtained by the amplitudes of the ultrasonic waves of the insonified frequency and its higher harmonics as transmitted through the interface. Additional phase measurements may enable one to obtain the evaluation of the full hysteretic cycle of the interaction force. In order to gain a deeper understanding of the interface region and to improve the technique, numerical simulations of the ultrasonic wave propagation through specimens of two bonded elements can be used. A simple model based on the local interaction simulation approach (LISA) is described in this contribution, and a comparison between the results of the simulations and the experimental data is presented. Besides its intrinsic relevance for NDE, the problem considered in this paper may be very useful to analyze and test models for the simulation of ultrasonic wave propagation in nonclassical nonlinear mesoscopic elastic materials.     

Structural and mechanical stability of rare-earth diborides

Structural and mechanical properties of several rare-earth diborides were systematically investigated by first principles calculations. Specifically, we studied XB2 , where X=Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, and Lu in the hexagonal AlB2 , ReB2 , and orthorhombic OsB2 -type structures. The lattice parameters, bulk modulus, bond distances, second order elastic constants, and related polycrystalline elastic moduli (e.g., shear modulus, Young’s modulus, Poisson’s ratio, Debye temperature, sound velocities) were calculated. Our results indicate that these compounds are mechanically stable in the considered structures, and according to "Chen’s method", the predicted Vickers hardness shows that they are hard materials in AlB2 - and OsB2 -type structures.     

Generation of higher acoustic harmonics at a flat rough interface between two solids

The results of experimental studies of the influence of a static pressure applied to a flat rough interface between two solids on its nonlinear elastic properties are presented. The studies were performed by the spectral method on the basis of an analysis of the efficiency of generation of higher acoustic harmonics, which arise upon the reflection of a longitudinal elastic wave of finite amplitude from the boundary and the passage through it. A nonmonotonic dependence of the amplitudes of acoustic harmonics on the value of the external reversible static pressure applied to the interface was revealed: pronounced amplitude maxima for the amplitudes of the second and third harmonics were observed with a decrease in the external static pressure. It was also found that the amplitudes of the second, third, and fourth acoustic harmonics increase with a decrease in the external static pressure (in comparison with their values at the same pressure values during its increase). The experimentally determined power dependence of the higher acoustic harmonics on the amplitude of the first acoustic harmonic significantly differed from the classical indices for these harmonics. The influence of the external pressure on the values of the nonlinear second- and third-order elastic parameters was analyzed. The experimental results were analyzed on the basis of nonclassical acoustic nonlinearity.     

Wave equations in linear viscoelastic materials

Conditions for writing wave equations in linear viscoelastic materials are investigated. The study is restricted to the infinitesimal theory and an application is suggested in modeling ultrasound propagation in soft biological tissues. First, a general wave equation is obtained for the displacement field in an inhomogeneous medium. Second, the propagation of "the mean principal stress" (i.e., minus the arithmetical mean of the principal stresses) is examined. That quantity is particularly relevant when the force per unit area is detected at the surface of a nondissipative coupling medium. If the material is homogeneous, a wave equation is always obtained for the mean principal stress. Otherwise, supplementary conditions have to be assumed on the material and possibly on the motion. Results are illustrated by examples which present linearly elastic perfect fluids and linearly elastic Newtonian viscous fluids as particular viscoelastic materials.     

Evaluation of two-photon nonlinearity by a semiclassical method

In order to discuss the two-photon nonlinearity theoretically, both photons and nonlinear materials should be treated quantum mechanically, which usually is a heavy theoretical task. Contrarily, nonlinear optics for classical light has been developed well and a detailed analysis is possible for realistic complex nonlinear systems. Here we show that the two-photon nonlinearity can be evaluated from the linear and third-order nonlinear output fields against a classical input pulse, which contains 2(-1/2) photons on average.     

Conditioning-induced elastic nonlinearity in hysteretic media

The definition and measurement of the nonlinear elastic properties of a sample is of great importance for a large number of applications, including characterization of material performances and damage detection. However, such measurements are often influenced by spurious effects due to a combination of nonlinearity and nonequilibrium phenomena. We will present experimental data to show how nonlinearity due to small cracks in concrete samples increases as a consequence of conditioning, i.e., after having perturbed them with a constant amplitude excitation. In addition, our experimental data highlight “memory effects,” i.e., they show that when the excitation is removed, the elastic modulus does not return instantaneously to the initial value.     

Nonlinear shear wave interaction in soft solids

This paper describes nonlinear shear wave experiments conducted in soft solids with transient elastography technique. The nonlinear solutions that theoretically account for plane and nonplane shear wave propagation are compared with experimental results. It is observed that the cubic nonlinearity implied in high amplitude transverse waves at f(0)=100 Hz results in the generation of odd harmonics 3f(0), 5f(0). In the case of the nonlinear interaction between two transverse waves at frequencies f(1) and f(2), the resulting harmonics are f(i)+/-2f(j)(i,j=1,2). Experimental data are compared to numerical solutions of the modified Burgers equation, allowing an estimation of the nonlinear parameter relative to shear waves. The definition of this combination of elastic moduli (up to fourth order) can be obtained using an energy development adapted to soft solid. In the more complex situation of nonplane shear waves, the quadratic nonlinearity gives rise to more usual harmonics, at sum and difference frequencies, f(i)+/-f(j). All components of the field have to be taken into account.     

Nonlinear acoustic effects in a resonator with saturation of hysteretic loss

Nonlinear wave processes in an acoustic rod resonator with hysteretic nonlinearity under harmonic excitation are studied. The characteristics of longitudinal nonlinear modes of the resonator with hard and soft boundaries (amplitude-dependent loss, shifts of resonance frequencies, and amplitudes of the second and third harmonics) are determined. The comparison of the theoretical and experimental dependences of nonlinear acoustic effects in a resonator that is made of annealed polycrystalline copper is used to determine the parameters of the hysteretic nonlinearity.     

Transport coefficients and mechanical response in hard-disk colloidal suspensions

We investigate the transport properties and mechanical response of glassy hard disks using nonlinear Langevin equation theory.We derive expressions for the elastic shear modulus and viscosity in two dimensions on the basis of thermalactivated barrier-hopping dynamics and mechanically accelerated motion.Dense hard disks exhibit phenomena such as softening elasticity,shear-thinning of viscosity,and yielding upon deformation,which are qualitatively similar to dense hard-sphere colloidal suspensions in three dimensions.These phenomena can be ascribed to stress-induced "landscape tilting".Quantitative comparisons of these phenomena between hard disks and hard spheres are presented.Interestingly,we find that the density dependence of yield stress in hard disks is much more significant than in hard spheres.Our work provides a foundation for further generalizing the nonlinear Langevin equation theory to address slow dynamics and rheological behavior in binary or polydisperse mixtures of hard or soft disks.     

Enhanced nucleation fields due to dipolar interactions in nanocomposite magnets

One approach to construct powerful permanent magnets while using less rare-earth elements is to combine a hard magnetic material having a high coercive field with a soft magnetic material having a high saturation magnetization at the nanometer scale and create so-called nanocomposite magnets. If both materials are strongly coupled, exchange forces will form a stable magnet. We use finite element micromagnetics simulations to investigate the changing hysteresis properties for varying arrays of soft magnetic spherical inclusions in a hard magnetic body. We show that the anisotropy arising from dipolar interactions between soft magnetic particles in a hard magnetic matrix can enhance the nucleation field by more than 10% and strongly depends on the arrangement of the inclusions.     

Nonlinear elastic imaging using reciprocal time reversal and third order symmetry analysis

This paper presents a nonlinear imaging method for the detection of the nonlinear signature due to impact damage in complex anisotropic solids with diffuse field conditions. The proposed technique, based on a combination of an inverse filtering approach with phase symmetry analysis and frequency modulated excitation signals, is applied to a number of waveforms containing the nonlinear impulse responses of the medium. Phase symmetry analysis was used to characterize the third order nonlinearity of the structure by exploiting its invariant properties with the phase angle of the input waveforms. Then, a "virtual" reciprocal time reversal imaging process, using only one broadcasting transducer and one receiving transducer, was used to insonify the defect taking advantage of multiple linear scattering as mode conversion and boundary reflections. The robustness of this technique was experimentally demonstrated on a damaged sandwich panel, and the nonlinear source, induced by low-velocity impact loading, was retrieved with a high level of accuracy. Its minimal processing requirements make this method a valid alternative to the traditional nonlinear elastic wave spectroscopy techniques for materials showing either classical or non-classical nonlinear behavior.     

In quest of a systematic framework for unifying and defining nanoscience

This article proposes a systematic framework for unifying and defining nanoscience based on historic first principles and step logic that led to a “central paradigm” (i.e., unifying framework) for traditional elemental/small-molecule chemistry. As such, a Nanomaterials classification roadmap is proposed, which divides all nanomatter into Category I: discrete, well-defined and Category II: statistical, undefined nanoparticles. We consider only Category I, well-defined nanoparticles which are >90% monodisperse as a function of Critical Nanoscale Design Parameters (CNDPs) defined according to: (a) size, (b) shape, (c) surface chemistry, (d) flexibility, and (e) elemental composition. Classified as either hard (H) (i.e., inorganic-based) or soft (S) (i.e., organic-based) categories, these nanoparticles were found to manifest pervasive atom mimicry features that included: (1) a dominance of zero-dimensional (0D) core–shell nanoarchitectures, (2) the ability to self-assemble or chemically bond as discrete, quantized nanounits, and (3) exhibited well-defined nanoscale valencies and stoichiometries reminiscent of atom-based elements. These discrete nanoparticle categories are referred to as hard or soft particle nanoelements. Many examples describing chemical bonding/assembly of these nanoelements have been reported in the literature. We refer to these hard:hard (H-n:H-n), soft:soft (S-n:S-n), or hard:soft (H-n:S-n) nanoelement combinations as nanocompounds. Due to their quantized features, many nanoelement and nanocompound categories are reported to exhibit well-defined nanoperiodic property patterns. These periodic property patterns are dependent on their quantized nanofeatures (CNDPs) and dramatically influence intrinsic physicochemical properties (i.e., melting points, reactivity/self-assembly, sterics, and nanoencapsulation), as well as important functional/performance properties (i.e., magnetic, photonic, electronic, and toxicologic properties). We propose this perspective as a modest first step toward more clearly defining synthetic nanochemistry as well as providing a systematic framework for unifying nanoscience. With further progress, one should anticipate the evolution of future nanoperiodic table(s) suitable for predicting important risk/benefit boundaries in the field of nanoscience. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.

Self-organized structures in soft confined thin films

We present a mini-review of our recent work on spontaneous, self-organized creation of mesostructures in soft materials like thin films of polymeric liquids and elastic solids. These very small scale, highly confined systems are inherently unstable and thus self-organize into ordered structures which can be exploited for MEMS, sensors, opto-electronic devices and a host of other nanotechnology applications. In particular, mesomechanics requires incorporation of intermolecular interactions and surface tension forces, which are usually inconsequential in classical macroscale mechanics. We point to some experiments and quasi-continuum simulations of self-organized structures in thin soft films which are germane not only to nanotechnology, but also to a spectrum of classical issues such as adhesion/debonding, wetting, coatings, tribology and membranes.