The Effectiveness of 2D Unit Cells in Creating χ-Spring Based Metamaterials

Abstract

Elastic metamaterials can be used in a variety of vibration and shock absorbing applications due to having mechanical properties that are not typically seen in nature. This work creates 2-dimensional metamaterial from a tessellation of unit cells composed of array Chi-springs. The Chi-springs exhibit a J shaped force displacement relationship or equivalently an effective stress strain relationship that is characterized by three regions: a linear stiffness/module, a quasi-zero stiffness/modulus region, and region of high tangent force/stress. The springs form the fundamental building block for a 2-dimensional unit cell and are created through a series of isometric transformations while meeting constraints on its effective constitutive behavior. The orientations of each unit cell are analyzed using Cayley diagrams, which are then used to determine various 2 × 2 tessellations of the structure. The resulting unit cells and their tessellations are manufactured through 3D printing. They exhibit a J shaped effective constitutive relationship in 2 material loading directions that resembles the force displacement relationship. Material testing indicates that the resulting structures are anisotropic. Furthermore, they have a dominant loading direction that displays larger values of linear modulus, plateau stress, and toughness. This work represents the first nascent steps toward the systematic design of metamaterial behavior in multiple load directions.