  For a perfect fluid, the quantity defined through mixed components of the
stress-energy tensor
$\widetilde{w}=(T_{i}^{\phantom{i}i}/3)/(-T_{0}^{\phantom{0}0})$ is independent
on the choice of coordinates only for two values of the pressure to energy
density ratio $w=p/\rho$: for radiation with $w=1/3$, and for dark energy with
$w=-1$. With other choices of $w$, the quantity $\widetilde{w}$ is coordinate
dependent, and $\widetilde{w}=w$ only in the local rest frame of the fluid. We
show that the same is true also for solid matter with shear stress Lam\'e
coefficient set to zero in a flat Friedmann--Lema\^itre--Robertson--Walker
universe with perturbed metric as well as stress-energy tensor. We call the two
different solids with coordinate independent $\widetilde{w}$ radiation-like
solid and dark energy-like solid, and we restrict ourselves to these two
special cases. By analysing second order perturbations we discover two one
parametric sets of such solid matter models containing special cases of
radiation and dark energy as perfect fluids. We also study equations for
perturbations up to the second order for both sets of models.
