Wave propagation effects possible in solid composite materials by use of stabilized negative-stiffness components

Effects possible on wave propagation in solid composite materials by use of a stabilized negative stiffness phase are explored. One composite treated is an infinite periodic laminate comprised of two different homogeneous, isotropic linear elastic phases, for which uniaxial strain perpendicular to the laminae applies. Longitudinal plane wave propagation in this direction is analyzed, showing that the composite is stable provided both phases have merely strongly elliptic moduli. By tuning the negative bulk modulus thus permitted in one phase, the no-pass zones between dispersion curves can be substantially enlarged, the initiation frequency of the lowest no-pass zone can be made to approach zero, and the bands of permitted propagating frequencies can be substantially diminished, as can the phase and group velocities of long-wavelength waves. When material damping is added via linear viscoelasticity, a tuned negative bulk modulus dramatically enhances wave amplitude attenuation. The second composite considered is a matrix containing a random distribution of spherical inclusions, both materials being homogeneous, isotropic and linear elastic. Applying our recent demonstration for dilute distributions that such inclusions can have a negative bulk modulus while the overall composite remains stable, J. R. Willis’ variational approach is employed to analyze mean longitudinal plane waves. For low frequency/long wavelength waves, a dilute distribution of such inclusions can significantly reduce the wave speed. The next order correction in a regular perturbation analysis in frequency captures wave amplitude attenuation. It shows that at a mere 3.6% volume fraction of inclusions having a negative bulk modulus well within the stable range, the attenuation term (appearing in an exponential) has over twice the value attainable by a random distribution of rigid spherical particles of any volume fraction. These results suggest an effective and efficient means of attenuating waves in elastic solids via elastic wave scattering, even without use of material damping.