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Auxetic metamaterials based on the Cassini oval aperture have been recently proposed. Owing to the resemblance of this aperture to a peanut, these structures are also referred to as Peanut Aperture Auxetic Metamaterials (PAMMs), which have garnered significant attention due to their superior mechanical properties. To objectively evaluate their performance, we conducted stress analyses on PAMMs and compared the results with those of conventional Elliptical Aperture Auxetic Lattices (EALs). It was demonstrated that stress invariants decreased in PAMMs compared to EALs under identical biaxial loading conditions for critical cases. This reduction was consistent across three configurations: a single aperture in an infinite medium, a unit cell, and a finite lattice. Subsequently, we implemented optimisation algorithms based on Artificial Neural Networks (ANNs) in conjunction with a curve fitting tool to geometrically refine the PAMM design under specified constraints and objective functions. The objective functions concerned von Mises stress (or equivalently J 2 ), maximum principal stress, Tresca shear stress, and negative Poisson's ratio. The optimised PAMM geometry was benchmarked against an EAL of equivalent aperture aspect ratio and areal density. With the constraints on these two parameters, it was discerned that the stress invariants and the Poisson's ratio increase exponentially with the increase of the scaling ratio, however, these parameters converge to constant values as the scaling ratio exceeds 25. Thus, the geometry of the lattice is optimised by maintaining the scaling ratio as 1, satisfying the lowest stress invariants while keeping the highest magnitude of the negative Poisson's ratio.
Fallah et al. (Thu,) studied this question.