  In this paper, we bring to the awareness of the scientific community and
civil engineers, an important fact: the possible lack of wave protection of
transformational elastic cloaks. To do so, we propose spherical cloaks
described by a non-singular asymmetric elasticity tensor depending upon a small
parameter $\eta,$ that defines the softness of a region one would like to
conceal from elastodynamic waves. By varying $\eta$, we generate a class of
soft spheres dressed by elastodynamic cloaks, which are shown to considerably
reduce the soft spheres' scattering. Importantly, such cloaks also provide some
wave protection except for a countable set of frequencies, for which some large
elastic field enhancement (resonance peaks) can be observed within the cloaked
soft spheres, hence entailing a possible lack of wave protection. We further
present an investigation of trapped modes in elasticity via which we supply a
good approximation of such Mie-type resonances by some transcendental equation.
Next, after a detailed presentation of spherical elastodynamic PML of Cosserat
type, we introduce a novel generation of cloaks, the mixed cloaks, as a
solution to the lack of wave protection in elastodynamic cloaking. Indeed,
mixed cloaks achieve both invisibility cloaking and protection throughout a
large range of frequencies. We think, mixed cloaks will soon be generalized to
other areas of physics and engineering and will in particular foster studies in
experiments.
