Pentamodes: the role of unit cell base topology on mechanical properties

Abstract

Pentamodes (first conceived theoretically by Milton and Cherkaev) are a very interesting class of mechanical metamaterials where the bulk and shear moduli are decoupled. The pentamodes usually are composed of double cone-shaped struts with the middle diameter being large and the end diameters being tiny (ideally approaching zero). The cubic diamond geometry was proposed by Milton and Cherkaev as a suitable geometry for the unit cell and has since been used in the majority of the works on pentamodes. In this work, we aim to evaluate the degree to which the main unit cell design is contributing to high bulk to shear modulus ratio (known as FOM). In addition to the diamond unit cell, three other well-known unit cell designs are considered, and the effect of small diameter radius and the ratio of large-to-small diameter ratio, {\alpha}, on the FOM is evaluated. The results showed that regardless of the primitive unit cell shape, the FOM value is highly dependent on the d value, but its dependence on the D value is very weak. For d/h around 0.05 (h representing the linkage length), figures of merit in the range of 10^3 could be reached for all the studied topologies.