Design and modeling of the 2D auxetic metamaterials with hyperelastic properties using topology optimization approach

Abstract In this paper, the modified SIMP topology optimization (TO) method was used, to introduce diverse auxetic unit cells with different volume fractions, composing of the symmetric, chiral and re-entrant unit cells. The output results suggested that the geometry of the 2D auxetic structures were extremely dependent on the values of SIMP method parameters, including initial designs and volume fractions. The brilliant modes of deformation in the auxetic structures, whose unit cells are symmetric, are based on either buckling or bending. To validate the TO results, four structures containing symmetric unit cells were chosen, called structure 1, 2, 3 and 4. The auxetic structures were produced by using 3D printing, with TPU as a hyperelastic material as well. Under Compression, the dominating mode of deformation in structures 1 and 2 is based on bending, caused by the movement of the oblique struts between the unit cells. There is also a linear relationship between the vertical and horizontal displacements in structure 1, the structure with 50 % volume fraction and -0.55 Poisson’s ratio value. However, the deformation mechanisms in structures 3 and 4 are based on buckling, called shearing deformation, which is the result of the buckling of the vertical struts between the unit cells.