Lossy Matrix Research Articles

Closed-cell hyperelastic elements with mechanical instabilities and structural negative stiffness

Metamaterials are subwavelength structures that generate enhanced or exotic properties that are unattainable with conventional materials. One such class of metamaterials utilizes inclusions with mechanical instabilities to generate a non-monotonic pressure versus strain response and thus regions of structural negative stiffness. By embedding these sub-wavelength structures in a lossy matrix material, it is possible to tune and enhance material properties of the mixture such as acoustic and elastic nonlinearity and energy dissipation. Previous theoretical work on this topic by the authors has focused on a dilute concentration of these types of hyperelastic inclusions within a fluid or nearly incompressible elastic matrix material to determine the overall response via both quasi-static and dynamic nonlinear homogenization methods. The present work focuses on numerical analysis using the finite element method for closed-cell elements that display non-monotonic pressure-strain behavior. The objective is to de...

Ultrasonic characterization of polymeric composites containing auxetic inclusions

Composite materials are often used as damping treatments or structural materials to mitigate the effects of unwanted vibration and sound. Recent work on materials displaying a negative Poisson’s ratio, known as auxetic materials, indicate that composite materials consisting of a lossy matrix containing auxetic inclusions may lead to improved vibro-acoustic absorption capacity compared to composites containing positive Poisson’s ratio inclusions. This work presents ultrasonic measurements of an epoxy matrix material (Epon E828/D400) containing volume fractions of α-cristobalite inclusions ranging from 5% to 25% by volume. The effective frequency dependent speed of sound and attenuation coefficient of each sample is measured from 1 to 10 MHz using ultrasonic immersion techniques. Ultrasonic test results are compared with Dynamic Mechanical Thermal Analysis and modal damping measurements of stiffness and loss behavior. This material is based upon work supported by the U. S. Army Research Office under grant number W911NF-11-1-0032.

Zn–Al-based metal–matrix composites with high stiffness and high viscoelastic damping

A maximal product of stiffness and viscoelastic damping ( E tan δ), a figure of merit for damping layers, is desirable for structural damping applications. Particulate-reinforced metal–matrix composites were prepared by ultrasonic agitation of the melt and composed of the zinc–aluminum (ZnAl) alloy Zn80Al20 (in wt%) as the lossy matrix and SiC or BaTiO3 as the particulate reinforcements. ZnAl–SiC composites were stiffer and exhibited higher damping at acoustic frequencies in comparison to the base alloy. ZnAl–SiC composites were superior to Sn–SiC composites and possessed an E tan δ in excess of 0.6 GPa, the maximum figure of merit provided by commercial polymer damping layers. Furthermore, ZnAl–SiC composites displayed a high figure of merit over a broad temperature range. ZnAl–BaTiO3 composites exhibited anomalies in modulus and damping associated with partial restraint of the phase transformation; one specimen was much stiffer than diamond over a narrow temperature range.

Acoustic scattering of metallic springs in elastic medium

In applications such as ultrasonic immersion testing, damping of flow noise in pipes and ducts and coating of acoustic control surfaces, it is very useful to reduce the reflection of acoustic waves from surfaces. Significant echo reduction can be achieved by addition of an anechoic coating. According to some general design guidelines for a single layer of homogenous coating, a single layer of 15 dB coating must be at least one wavelength thick. For absorbing acoustic waves of low frequencies, inhomogeneities such as metallic fillers, cavities and irregular metallic helices can be introduced into the lossy matrix to substantially enhance the acoustic absorption by acoustic scattering. In this presentation, the acoustic scattering of a single metallic spring embedded in an infinite elastic medium has been investigated using a boundary element formulation. The cross sections of the scattered longitudinal and shear waves have been calculated for various spring sizes, orientations and wave numbers. It will be shown that helical inclusions are more efficient in scattering longitudinal incident waves than spherical inclusions of equal volume. Steel helices are found to be more efficient in converting the incident longitudinal waves into shear waves than helical cavities of equal size.

Enhanced Absorption Due to Dependent Scattering

The role of multiple scattering on dependent scattering as well as on dependent absorption is investigated for heterogeneous media containing a high concentration of particles. The decrease of scattering and increase of absorption for lossy (with intrinsic absorption) particles in a lossless matrix is quantitatively described using a Rayleigh region solution derived from a multiple scattering formalism. For smaller wavelengths, dependent scattering and absorption can be obtained by solving the resulting dispersion equation numerically. Results are shown for lossless particles in a lossy matrix, which models an optical coating system.

The overall sink strength of an inhomogeneous lossy medium. Part II: variational estimates

Trial fields generated by trial polarizations are substituted into the classical variational principles for the model system introduced in Part I. The resulting expressions are simplified by discarding certain terms which vanish quadratically at the actual solution, to yield a ‘Hashin-Shtrikman’ variational principle for the system under consideration. Substitution of simple configuration-dependent trial polarizations yields expressions that are identical with those obtained from the QCA in Part I. This demonstrates that the self-consistent QCA has an interpretation in terms of a variational principle and, furthermore, that the self-consistent prescription of Willis (1983, 1984) in fact produces a bound. The opposite bound can also be obtained by choosing the sink parameter of the comparison medium to be that of the inclusions. Results are presented for two cases, both assuming Percus-Yevick statistics. The bounds are usefully close when k 1 2 k 2 2 = ;10 ; the self-consistent QCA lies between them but the simple Brailsford-Bullough estimate does not. The case k 1 2 k 2 2 = ;10 6 is also discussed, as a model for voids in a lossy matrix.