Anomalous elastic response of a 3D anti-tetrachiral metamaterial

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.Accepted versionTemasek Research FellowshipFunding for this project was partially provided by C.Q.L.’s Temasek Research Fellowship, for which he gives thanks. Samples for experimental testing were provided by SLM Solutions Singapore Pte Ltd