Propagation of deformation waves in wool felt

The natural wool felt is becoming increasingly popular and important as a resource material in various applications. In this study, a constitutive equation that describes the deformation wave propagation in the felt material is derived using a hysteretic piano hammer model. A nonlinear partial differential equation with third-order terms that takes into account the elastic and hereditary properties of a microstructured felt is used to study a pulse propagation in the one-dimensional case. The boundary value problem is considered, and the numerical solution describing the strain wave propagation is provided. It is shown that the speed of a deformation wave increases with the growth of its amplitude. Also, the nonlinearity makes the front slope of a pulse steeper, which causes the eventual breaking of a pulse. The solution of the linear problem is analyzed, and the rate of the wave attenuation in the felt material is estimated.