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Enthalpy under uniaxial compression of solid

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Hello,

I have found several references (I can send you the links if you want) that point to the fact that the enthalpy under uniaxial compression along z of a solid is simply given by:

H=U+PzV

This appears to make sense as during uniaxial compression the Pz pressure component is the only one doing work (zero transverse strain). If you do a second subsequent uniaxial compression (along y say), then by the same logic the enthalpy should be given by U+PyV. However at the starting point of this second uniaxial compression the enthalpy is then given simultaneously by U+PzV and U+PyV, which can't possibly be true for general non-hydrostatic stress conditions. Hence my question is: is this formulation of the enthalpy valid only starting from equilibrium and doing only one uniaxial compression, or is it valid for general non-hydrostatic conditions?

Many thanks,

Gabriel

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