Dissipation in solids under oscillatory shear: Role of damping scheme and sample thickness

We study dissipation as a function of sample thickness in solids under global oscillatory shear applied to the top layer of the sample. Two types of damping mechanism are considered: Langevin and Dissipative Particle Dynamics (DPD). In the regime of low driving frequency, and under strain-controlled conditions, we observe that for Langevin damping, dissipation increases with sample thickness, while for DPD damping, it decreases. Under force-controlled conditions, dissipation increases with sample thickness for both damping schemes. These results can be physically understood by treating the solid as a one-dimensional harmonic chain in the quasi-static limit, for which explicit equations (scaling relations) describing dissipation as a function of chain length (sample thickness) are provided. The consequences of these results, in particular regarding the choice of damping scheme in computer simulations, are discussed.