Abstract
In this Letter, the tensorial nature of the nonequilibrium dynamics in nonlinear mesoscopic elastic materials is evidenced via multimode resonance experiments. In these experiments the dynamic response, including the spatial variations of velocities and strains, is carefully monitored while the sample is vibrated in a purely longitudinal or a purely torsional mode. By analogy with the fact that such experiments can decouple the elements of the linear elastic tensor, we demonstrate that the parameters quantifying the nonequilibrium dynamics of the material differ substantially for a compressional wave and for a shear wave. This result could lead to further understanding of the nonlinear mechanical phenomena that arise in natural systems as well as to the design and engineering of nonlinear acoustic metamaterials.
Highlights
In this Letter, the tensorial nature of the nonequilibrium dynamics in nonlinear mesoscopic elastic materials is evidenced via multimode resonance experiments
By analogy with the fact that such experiments can decouple the elements of the linear elastic tensor, we demonstrate that the parameters quantifying the nonequilibrium dynamics of the material differ substantially for a compressional wave and for a shear wave
Nonlinear mesoscopic elastic materials [1] exhibit unique and interesting properties related to nonlinear and nonequilibrium dynamics that are relevant to various natural and industrial processes ranging in scales and applications, e.g., the onset of earthquakes and avalanches in geophysics [2,3,4], the aging of infrastructures in civil engineering [5,6], the failure of mechanical parts in industrial settings [7,8,9], bone fragility in the medical field [10,11,12], or the design of novel materials, including nonlinear metamaterials, for shock absorption, acoustic focusing, and energy-harversting systems [13]
Summary
In this Letter, the tensorial nature of the nonequilibrium dynamics in nonlinear mesoscopic elastic materials is evidenced via multimode resonance experiments. Nonlinear mesoscopic elastic materials [1] exhibit unique and interesting properties related to nonlinear and nonequilibrium dynamics that are relevant to various natural and industrial processes ranging in scales and applications, e.g., the onset of earthquakes and avalanches in geophysics [2,3,4], the aging of infrastructures in civil engineering [5,6], the failure of mechanical parts in industrial settings [7,8,9], bone fragility in the medical field [10,11,12], or the design of novel materials, including nonlinear metamaterials, for shock absorption, acoustic focusing, and energy-harversting systems [13] These properties include the dependence of wave speed and damping parameters on strain amplitude [5,14,15], slow relaxation [16,17], and hysteresis with end-point memory [18,19,20]. In a 1D system made of an isotropic material, the longitudinal mode of vibration is related to the Young modulus E and so may be used to quantify the parameters of nonequilibrium
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