Fish Cells, a new zero Poisson’s ratio metamaterial - part II: Elastic properties

Fish Cells as a new metamaterial with zero Poisson’s ratio in two planar directions is introduced with application in morphing aircraft skin. In order to tailor the design of this metamaterial for arbitrary loadings, equivalent elastic properties of the Fish Cells metamaterial are derived and analyzed using analytical and numerical methods. The admissible range of geometric parameters is presented and variation of elastic properties with parameters is studied. The effective elastic modulus of the metamaterial is derived analytically and verified with finite element models. The in-plane and transverse shear modulus of the metamaterial are evaluated using finite element analysis where accurate periodic boundary conditions for in-plane shear loading are investigated. The lower and upper bounds of the transverse shear modulus are derived based on strain and complementary energy relations which are verified with finite element results. As zero Poisson’s ratio behavior of the Fish Cells topology is proved, derivative geometries from this topology with zero Poisson’s ratio behavior are also presented.