  This study examines the mechanical behavior of a novel class of mechanical
metamaterials alternating pentamode lattices and stiffening plates. The unit
cell of such lattices consists of a sub-lattice of the face cubic-centered unit
cell typically analyzed in the current literature on pentamode materials. The
studied systems exhibit only three soft deformation modes in the infinitesimal
stretch-dominated regime, as opposed to the five zero-energy modes of
unconfined pentamode lattices. We develop analytical formulae for the vertical
and bending stiffness properties and study the dependence of such quantities on
the main design parameters: the lattice constant, the solid volume fraction,
the cross-section area of the rods, and the layer thickness. A noteworthy
result is that the effective compression modulus of the analyzed structures is
equal to two thirds of the Young modulus of the stiffest isotropic elastic
networks currently available in the literature, being accompanied by
zero-rigidity against infinitesimal shear and twisting mechanisms. The use of
the proposed metamaterials as novel seismic-isolation devices and
impact-protection equipment is discussed by drawing comparisons with the
response of alternative devices already available or under development.
