Elastic wave velocities in finitely pre-stretched soft fibers

Elastic wave velocity in a soft fiber that varies depending on material constitution and axial stress level is an essential measure of mechanical signals in many technical applications. In this work, based on the small-on-large theory, we establish a model of linear elastic wave propagation in a finitely pre-stretched soft fiber. The formulas of longitudinal (L-) and transverse (T-) wave velocities are provided and validated by numerical simulations as well as by experimental data on spider silk. The influences of material constitution, compressibility, and prestress on the wave propagation are investigated. We found that with increasing pre-stress, the variation of Lwave velocity highly relies on the concavity of the stress-strain curve. In contrast, an increase of T-wave velocity exhibits regardless of any constitutive model. For both L- and T-waves, the variation of the velocities is more significant in a compressible fiber than that in a nearly-incompressible one. Moreover, for minuscule pre-stress, we propose a modified formula for T-wave velocity based on the Rayleigh beam theory, which reveals the competition mechanism between "string vibration" and "beam vibration." This may provide a reliable theoretical basis for precise mechanical characterization of soft fibers and open a route for lightweight, tunable wave manipulation devices.