Propagation of elastic waves in a flexomagnetic solid

Abstract

Flexomagnetism is the coupling between magnetism and strain gradients and is a technologically relevant phenomenon. We present a theory of elastic wave propagation in a linear elastic flexomagnetic material with microstructure and strain gradient elastic interactions. The expressions of frequency, phase velocity, and group velocity of longitudinal and transverse waves are derived and are shown to depend on the flexomagnetic coefficient and microstructure. We also show that the effect of flexomagnetism and microstructure can lead to some interesting phenomena in wave propagation, which are not observed in classical linear elasticity theory of waves. Specifically, in contrast to classical linear elastic materials, where wave propagation is non-dispersive, flexomagnetic materials with microstructure can exhibit both normal and abnormal dispersion. It is also noteworthy that, in flexomagnetic materials with gradient elasticity, the phase velocities of transverse waves can exceed those of longitudinal waves, which is atypical in classical elasticity. Furthermore, waves can also attenuate for a certain range of wavenumbers that depend on the flexomagnetic coefficient and microstructural parameters. Finally, we explore the possibility of waves exhibiting zero group velocity modes, where waves are non-propagating but have strong local energy confinement, negative group velocity modes, where the wave packet moves in the opposite direction to that of wave propagation, and the phenomenon of wave freezing, where a propagating wave stops in space without diffusing or spreading.

Figures (9)

• Figure 1: A semi-infinite elastic solid with microstructure and non-local elastic interaction. The lengthscale of the microstructure is $\lambda$, and the non-local elastic interactions are restricted to a spherical region of radius $l$. The solid exhibits flexomagnetism. The wave is assumed to propagate in the $x$-direction.
• Figure 2: The effect of the length parameters $\lambda$ and $l$ on the wave frequency is shown for different values of wave number $k$. (a) shows the longitudinal case, and (b) shows the transverse case. The wave frequencies are normalized by the classical phase velocities of the longitudinal and transverse cases, respectively.
• Figure 3: The effect of length parameters $\lambda$ and $l$ on the phase velocities of (a)-(b) longitudinal and (c)-(d) transverse waves is shown for different values of wave number $k$. The phase velocities are normalized by the classical phase velocities. (b) and (d) shows an inset of (a) and (c), respectively, from wave numbers 0 to 1 Angstrom$^{-1}$, denoted by the black box in (a) and (c).
• Figure 4: The effect of magnetism on the phase velocities of (a) longitudinal and (b) transverse waves is shown for different values of wave number $k$. The phase velocities are normalized by the classical phase velocities.
• Figure 5: The effect of the length parameters $\lambda$ and $l$ on the group velocities of (a)-(b) longitudinal and (c)-(d) transverse waves is shown for different values of wave number $k$. The group velocities are normalized by the classical phase velocities. (b) and (d) shows an inset of (a) and (c), respectively, from wave numbers 0 to 1 Angstrom$^{-1}$, denoted by the black box in (a) and (c).