what happens when a body is under hydrostatic stress with respect to its microstructure

Hydrostatic stress state is free from shear stresses which trigger dislocation plasticity mechanism in metals. In this case yield limit doesn`t depend on the value of hydrostatic pressure and the volume change is elastic.

However other mechanisms of inelastic deformation (like microcracking, void growth, etc...) may be sensitive to hydrostatic pressure.

Anyway, in continuum mechanics, assumptions about  material`s response are verified with proper experiments. I suggest reading "Studies in Large Plastic Flow and  Fracture: With Special Emphasis on the
Effects of Hydrostatic Pressure" (Bridgman, 1952).

whether the material yields or not under hydrostatic pressure really depends on the mechanical property of the material in question. For instance, rock may yield under hydrostatic compression. This yielding may be caused by grain crushing or other possible mechanisms. In plasticity theory, this plastic response is often modelled by adding a cap to the yield surface.

For instance,

E. Grueschow and J. W. Rudnicki, "Elliptic yield cap constitutive modeling for high porosity sandstone," International Journal of Solids and Structures, Vol. 42, pp. 4574-4587, 2005.