Multiscale approach to modeling intrinsic dissipation in solids

In this paper, we develop a multiscale approach to model intrinsic dissipation under high frequency of vibrations in solids. For vibrations with a timescale comparable to the phonon relaxation time, the local phonon distribution deviates from the equilibrium distribution. We extend the quasiharmonic (QHM) method to describe the dynamics under such a condition. The local deviation from the equilibrium state is characterized using a nonequilibrium stress tensor. A constitutive relation for the time evolution of the stress component is obtained. We then parametrize the evolution equation using the QHM method and a stochastic sampling approach. The stress relaxation dynamics is obtained using mode Langevin dynamics. Methods to obtain the input variables for the Langevin dynamics are discussed. The proposed methodology is used to obtain the dissipation rate Edissip for different cases. Frequency and size effect on Edissip are studied. The results are compared with those obtained using nonequilibrium molecular dynamics (MD).