What severe conditions make the rock of the asthenosphere to behave like a fluid?

The pressure builds down from the lithosphere onto the asthenosphere causing it to act like a viscous fluid, or soft plastic.

Is this a complete answer?

The answer you provided is partial and needs further explanation. While pressure is indeed one of the factors that contribute to the rock of the asthenosphere behaving like a fluid, there are other severe conditions involved as well.

One crucial factor is the extremely high temperature in the asthenosphere. The rock in this layer of the Earth's mantle is heated due to the heat flow from the Earth's core and the radioactive decay of elements in the mantle. These high temperatures cause the rock to melt partially and become more ductile, meaning it can deform and flow.

Additionally, the asthenosphere experiences shear stress due to the movement of tectonic plates on the lithosphere above it. This stress, combined with the elevated temperature, allows the rock to undergo plastic deformation. Plastic deformation is a process in which rock can change shape without breaking, similar to how a plastic material can be molded or deformed.

Moreover, the composition of the rock in the asthenosphere also plays a role. It contains a higher proportion of silica and other minerals that are less rigid compared to those found in the lithosphere. This composition contributes to the asthenosphere's ability to flow under extreme conditions.

Therefore, a complete answer to your question would incorporate all these factors: the high temperature, shear stress from plate movement, pressure, and the composition of the rock in the asthenosphere.