  The ability to control Poisson's ratio of functional materials has been one
of the main objectives of researchers attempting to develop structures
efficient from the perspective of protective, biomedical and soundproofing
devices. This task becomes even more challenging at small scales, such as the
microscale, where the possibility to control mechanical properties of
functional materials is very significant, like in the case of flexible
electronics. In this work, we propose novel microscopic 2D and 3D
functionally-graded mechanical metamaterials capable of exhibiting a broad
range of Poisson's ratio depending on their composition. More specifically, we
show that upon adjusting the number of structural elements corresponding to one
type of the substructure at the expense of another, it is possible to change
the resultant Poisson's ratio of the entire system from highly positive to
highly negative values as well as to achieve arbitrary intermediate values.
Finally, in addition to static properties, we also analyze the dynamic
properties of these structures. Namely, we show how the variation in the
composition of the considered mechanical metamaterials affects the velocity of
a wave propagating through the system. This, in turn, could be essential in the
case of applications utilizing localized wave attenuation or sensors.
