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I would expect the heating of an elastic material upon sudden elastic compression to be given simply by the first law of thermodynamics, i.e. Delta Q=Delta U + P Delta V where P is constant since the compression is applied suddenly as in a square-wave pressure pulse (this is equivalent to the change in enthalpy). This heat released by the material upon elastic compression should then be re-absorbed entirely by the material assuming periodic boundary conditions, and this is what gives rise to the rise in temperature of the material after the compression. If I'm not wrong then this heat released is basically converted entirely into thermal vibrational energy upon re-absorption (3NkbT in the classical limit). I tried calculating (using classical MD codes) the thermal energy of iron for example from static zero-temperature energy surface calculations and phonon vibrational calculations, however my predictions for the rise in temperature upon elastic compression from these static calculations according to the above reasoning is much higher than the one I observe in the actual dynamic simulations. Can you see anything wrong with my reasoning?

Many thanks,

Gabriele