Novel metamaterials with negative moduli under compressive, tensile, and shear loadings

Abstract

Although mechanical metamaterials are rationally designed structures with micro-architectures that, in theory, can lead to any desirable mechanical properties, great interest has especially raised towards those with negative mechanical properties. In this paper, we propose structures that can show negative stiffness under shear, tensile, and hydrostatic loads. The principal working mechanism of the proposed structures is embedded pre-buckled and pre-twisted elements that can behave bistably. The structures demonstrated negative stiffness in a wide range of displacements under tensile and compressive loading types.  Among the three model types, i.e. constant thickness, variable thickness, and variable column cases, in two cases (constant thickness and variable column), the structure demonstrated negative stiffness in a consecutive range of displacements over a large range of displacement values. The structure with variable thickness, on the other hand, demonstrated negative stiffness only in one displacement domain, and the structure behaved normally (i.e. with positive stiffness) in other displacement values. One can adjust the design parameters of lattice structure in order to get the negative and positive stiffness values in the desirable displacement values.