  We develop a theory of anomalous elasticity in disordered two-dimensional
flexible materials with orthorhombic crystal symmetry. Similar to the clean
case, we predict existence of infinitely many flat phases with anisotropic
bending rigidity and Young's modulus showing power-law scaling with momentum
controlled by a single universal exponent the very same as in the clean
isotropic case. With increase of temperature or disorder these flat phases
undergo crumpling transition. Remarkably, in contrast to the isotropic
materials where crumpling occurs in all spatial directions simultaneously, the
anisotropic materials crumple into tubular phase. In distinction to clean case
in which crumpling transition happens at unphysically high temperatures, a
disorder-induced tubular crumpled phase can exist even at room-temperature
conditions. Our results are applied to anisotropic atomic single layers doped
by adatoms or disordered by heavy ions bombarding.
