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We study dissipation as a function of sample thickness in solids under globaloscillatory shear applied to the top layer of the sample. Two types of dampingmechanism are considered: Langevin and Dissipative Particle Dynamics (DPD). Inthe regime of low driving frequency, and under strain-controlled conditions, weobserve 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. Theseresults can be physically understood by treating the solid as a one-dimensionalharmonic chain in the quasi-static limit, for which explicit equations (scalingrelations) describing dissipation as a function of chain length (samplethickness) are provided. The consequences of these results, in particularregarding the choice of damping scheme in computer simulations, are discussed.

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