Lateral response of a layered material with interlayer friction

ABSTRACT

We investigate the mechanical properties of a layered material with interlayer friction. We propose a model that contains lateral elasticity and interlayer friction to obtain the response function both in the Fourier and real spaces. By investigating how the internal deformation is laterally induced due to the applied surface displacement, we find that it is transmitted into the material with an apparent phase difference. We also obtain the effective complex modulus of the layered material and show that it exhibits an intermediate power-law behavior in the low-frequency regime. Our results can be used to estimate the internal deformation of layered materials that exists on various different scales.

KEYWORDS:

• Layer
• lamellar
• smectic
• viscoelastic
• rheology

Acknowledgments

K.Y. acknowledges the support by a Grant-in-Aid for JSPS Fellows (Grant No. 21J00096) from the Japan Society for the Promotion of Science. K.Y. was supported by the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University. S.K. acknowledges the supported by the startup fund of Wenzhou Institute, University of Chinese Academy of Sciences (No. WIUCASQD2021041).

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Wenzhou Institute [WIUCASQD2021041]; Grant-in-Aid for JSPS Fellows [21J00096].