Semianalytical Geometry-Property Relationships for Some Generalized Classes of Pentamodelike Additively Manufactured Mechanical Metamaterials

The microarchitecture of mechanical metamaterials is often based on lattice structures made of beamlike elements (struts). Analytical geometry-property relationships could greatly facilitate the rational design of such metamaterials, but are generally only available for struts of uniform cross section. Here the authors present geometry-property relationships for structures of beamlike components of v00exa00exr00exi00exa00exb00exl00exe cross section. This is of particular interest for pentamode metamaterials, a special class of extremal materials exhibiting unusually high resistance to deformation in certain directions. This work promotes $e.g.$ the design of artificial bone for medical implants.