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How to calculate a deformed mesh volume during calculation iteration

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I am doing a vertical compression of a filled bottle in a non linear calculation.
During the test, internal pressure will change due to the deformation of the bottle.
As internal volume contain 1L water and a small among of air, if we can know the
volume of the deformed mesh at every iteration, it will be possible to know the
pressure evolution, and to apply it at the next iteration.
Do you know if it has already been done?
If not, is it possible?
Best regards