Speaker
Description
The nonlinear behavior of consolidated granular materials includes three distinct phenomena: classical nonlinearity, hysteresis, and slow dynamics. Despite the occurrence of these phenomena simultaneously, they have been studied separately, resulting in the development of independent theoretical models.
In our recent work, we have proposed the concept of non-equilibrium strain, which we have introduced into the classical acoustoelastic theory. This theory states that the relative velocity variation is proportional to the sum of the applied strain and the non-equilibrium strain: $\delta v_{ij}=\beta_{ij} \left(\varepsilon+\varepsilon_\mathrm{neq}\right).$
The non-equilibrium strain builds up as the material is subjected to loading, and slowly relaxes to zero as the applied strain is removed. We demonstrate that the non-equilibrium strain can be used to describe both slow dynamics and hysteresis. In fact, hysteresis can be seen as a consequence of slow dynamics.
The non-equilibrium strain can be expressed as a superposition of components with different relaxation times, resulting in a multirelaxation process with a given distribution.
A viscoelastic model for non-equilibrium strain is proposed, and it is demonstrated that short relaxation times are responsible for the cubic nonlinearity, moderate relaxation times cause hysteresis, and long relaxation times allow for the accumulation of velocity variation.