The Young's modulus of a solid can be expressed as
$$
E = \frac{F/A}{\Delta L/L\_0}
$$
where the force $F$ is exerted perpendicular to surface $A$ resulting in a change in length of $\Delta L$ from the initial length $L\_0$.

When the solid is submerged in a fluid (let's say water), an additional force due to the pressure of the water is felt. **Does this change the definition of Young's modulus?** In other words, if I performed a compression test (i.e. apply a known force and measure displacement) of the same object in air and in water, would I expect to get the same or different results? We can assume the vessel of water is quite large relative to the object.

I am having trouble wrapping my mind around this because one one hand I think the force of water pushing down from above might "pre-stress" the object to some degree, but on the other hand maybe the pressure coming in from the sides eliminates this effect? Furthermore, doe the fact that pressure increases with depth make this challenging?