Integral over a volume of (mass density)$cdot$(magnitude of displacement field)?

Let $u = u(X,t) = varphi(X,t)-X$ be the displacement field. Define the quantity
$$psi = 1/2int_Omega rho u^Tu~mathrm dX$$
where $rho$ is the mass density.

So if it were velocity instead of displacement field, this would equal kinetic energy. I’m struggling to figure out what it is with displacement though, like what this would represent physically. Maybe nothing? If I’m being asked to define the quantity, maybe I can define it however I like? Displacement energy of some sort?