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Characterizing Dissipative Elastic Metamaterials Produced by Additive Manufacturing

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Faraday waves in soft elastic solids.

Giulia Bevilacqua¹, Xingchen Shao², John R Saylor²

¹MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, Milano, Italy.

Proceedings. Mathematical, Physical, and Engineering Sciences

|October 19, 2020

Summary

Faraday instability in soft solids exhibits harmonic resonance, unlike the subharmonic resonance in fluids. This finding offers a new method to distinguish solid-like from fluid-like soft matter responses.

Keywords:

Faraday waves Floquet theory nonlinear elasticity soft solid

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Area of Science:

Soft matter physics
Continuum mechanics
Nonlinear dynamics

Background:

Faraday waves are well-understood in viscous fluids but lack theoretical explanation in soft solids.
Previous studies focused on fluid dynamics, leaving the solid-state phenomenon unexplained.

Purpose of the Study:

To theoretically characterize Faraday waves in soft incompressible slabs.
To investigate the onset of harmonic and subharmonic resonance eigenmodes in elastic solids.

Main Methods:

Utilized Floquet theory to analyze the incremental boundary value problem.
Transformed the problem into an algebraic eigenvalue problem.
Identified three dimensionless parameters governing gravity, capillary, and elastic waves.

Main Results:

Discovered that Faraday instability in soft solids is characterized by harmonic resonance.
This contrasts with the subharmonic resonance typically observed in viscous fluids.
The findings are valid within the physical range of material parameters.

Conclusions:

The study provides the first theoretical explanation for Faraday waves in soft solids.
Harmonic resonance in solids offers a distinct signature compared to fluid systems.
This opens avenues for using Faraday waves as a precise method to differentiate solid-like and fluid-like behaviors in soft matter.