In the present paper we investigate macroscopic two-fluid effects in systems composed of two elastic media. Using two strain tensors as macroscopic variables, we present a nonlinear analysis in the regime of long wavelengths and low frequencies. We also discuss the description in terms of relative strains and total strains. Generalizing earlier work on relative rotations for systems such as nematic elastomers or uniaxial magnetic gels, we investigate how this concept can be applied to the case of two elastic media in the linear domain. For the two strain fields and relative rotations between the two elastic media, we find a number of reversible and dissipative cross-coupling terms that couple velocity differences, mean velocities, strain fields, and relative rotations to each other as well as to temperature and concentration gradients. The question of relative translations is also analyzed. A linearized description using relative translations is physically meaningful as well as technically consistent with using strain fields and relative rotations. Finally, we apply this description to the swinging of two coupled homogeneous elastic media relative to each other, and to the oscillating actuation or active stress introduced through one of the elastic compounds.

• Received 11 January 2021
• Revised 2 May 2021
• Accepted 6 May 2021

DOI:https://doi.org/10.1103/PhysRevB.103.174304

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

Published by the American Physical Society