Anomalous elastic response of a 3D anti-tetrachiral metamaterial

Abstract

The elastic modulus and Poisson's ratio of a 3D anti-tetrachiral (3ATC) metamaterial design was investigated using an exact analytical model, finite element simulations and experiments on additively manufactured Ti6Al4V lattices. The 3ATC structure was found to undergo a unique symmetric-to-asymmetric transition as the number of unit cells in the lattice decreases, an observation that has not been reported to date. A reduced lattice size also increases the influence of shear forces introduced by the fixed boundary conditions, which can lead to a higher elastic modulus in certain orientations and reduce it in others. These shear forces also drive the joints in small lattices into an out-of-plane rotation that causes the Poisson's ratio of such structures to range from -1.2 to 1 for different relative densities, in contrast to a constant value of -0.5 for bulk 3ATC lattices that do not undergo this joint twisting. Our results strongly indicate that the 3ATC structure belongs to a new ‘rotation-dominated’ geometric class in the Ashby framework for cellular materials, in addition to the well-established bending- and stretch- dominated topologies. The main contributor of strain for this class of materials is rigid joint rotation, with novel, distinctive traits such as a nonlinear elastic stress-strain response and multiple relative modulus vs. relative density relationships. For the 3ATC structure, one of these relations is linear, similar to stretch-dominated structures, while the other is disjointed and does not follow the power law, which is atypical of a cellular material.