We test the elasticity of granular aggregates using increments of shear and volume strain in a numerical simulation. We find that the increment in volume strain is almost reversible, but the increment in shear strain is not. The strength of this irreversibility increases as the average number of contacts per particle (the coordination number) decreases. For increments of volume strain, an elastic model that includes both average and fluctuating motions between contacting particles reproduces well the numerical results over the entire range of coordination numbers. For increments of shear strain, the theory and simulations agree quite well for high values of the coordination number.
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