Quasi-Static Compression of FDM-Printed Rotating-Square Auxetic Cores: Relative Density Dominates over Rotation Angle

Rotating-square cellular cores were produced by fused deposition modelling in a rigid matrix, polylactic acid, and an elastomeric matrix, thermoplastic polyurethane, and compressed quasi-statically at four initial rotation angles between 15 and 37.5 degrees. Ninety-six specimens were tested in total, and the relative density of every group was measured by two independent routes. Because a solid loading-face frame occupies a fixed 20% of the specimen envelope and takes no part in the cellular deformation, the scaling analysis is referred to the relative density of the lattice alone. On that basis a single power law describes the mean crush stress of all 48 specimens of each material, with exponents of 1.98 ± 0.06 for the rigid matrix and 2.27 ± 0.06 for the elastomeric one and coefficients of determination of 0.959 and 0.967; the corresponding fits for energy absorption reach 0.988 and 0.979. Referring the same data to the whole-specimen density instead returns exponents of 4.01 and 4.85, so a frame counted as cellular material inflates the fitted exponent by a factor of about two. Rotation angle is resolved but secondary: it raises the coefficient of determination by 0.009 and 0.006 respectively, and the largest fitted angle coefficient is worth 15 and 17 per cent against the factor of fourteen spanned by density. The strong angle dependence seen in the fixed-cell-size series is therefore largely a density effect, which that series on its own cannot show. A residual geometric effect, non-monotonic and reproducible across both density levels, is resolved for the rigid matrix only.