Anomalous elastic response of a 3D anti - tetrachiral metamaterial. (15th February 2021) - Lai, Chang Quan; Markandan, Kalaimani; Lu, Zhen
Highlights: Elastic response of an auxetic 3D Anti-Tetrachiral (3ATC) lattice was investigated and it was found to exhibit an uncommon nonlinear stress-strain response in the elastic regime at small strain. With a sufficiently large eccentricity between the positions of opposing trusses, joint rotation becomes the main contributor to elastic strain of the 3ATC lattices, indicating that there exists a third, 'rotation-dominated', topology in Ashby's framework for the mechanical behavior of cellular solids, in addition to the well-known stretch-dominated and bend-dominated topologies. The relative modulus vs. relative density relationship for rotation-dominated structures can be linear, similar to stretch-dominated lattices, or disjointed (does not follow the power law). As the number of unit cells in the lattice decreases, the 3ATC design loses its cubic symmetry. This symmetric-to-asymmetric transition is contingent on 4 features of the geometry (i) the sub-unit cell has rotational symmetry (ii) the sub-unit cell does not have plane symmetry (iii) the sub-unit cells are assembled according to the anti-chiral arrangement (iv) the resultant unit cell has cubic asymmetry. Smaller lattices are stiffer and exhibit a wider range of Poisson's ratio (-1.2 to 1) due to a greater influence of fixed boundary conditions on the lattice mechanics i.e. size effects originate from edge effects (boundary conditions). 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. Graphical abstract: Image, graphical abstract