Pentamodes: Effect of unit cell topology on mechanical properties

Pentamodes (first conceived theoretically by Milton and Cherkaev) are a very interesting class of mechanical metamaterials that they are characterized by their decoupling the bulk and shear moduli. 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 (Figure Of Merit 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, α, 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 (the smaller diameter size of double-cone) value, but its dependence on the D (the greater diameter of double-cone) value is very weak. For d/h∝0.05 (h representing the linkage length), figures of merit in the range of 103 could be reached for all the studied topologies.