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Research on auxetic metamaterials is important due to their high performance against impact loadings and their usefulness in actuators, among other applications. These metamaterials offer a negative Poisson’s ratio at the macro level. However, usual auxetic metamaterials face challenges in (1) grading the effect, (2) coupling and combining auxetic metamaterials with non-auxetic materials due to boundary compatibility, (3) obtaining the same auxetic behavior in all directions in the transverse plane, and (4) adapting the regular geometry to the component design boundary and shape. The goal of this paper is to present a novel, recently patented tunable 3D metamaterial created to reproduce a wide spectrum of 3D auxetic and non-auxetic Poisson’s ratios and Young’s moduli. This wide range is obtained using the same basic unit cell geometry and boundary connections with neighboring cells, facilitating designs using functionally graded metamaterials as only the connectivity and position of the cell’s internal nodes are modified. Based on simple spatial triangularization, the metamaterial is easily scalable and better accommodates spatial curvatures or boundaries by changing the locations of nodes and lengths of bars.

The phenomenological linear theory of orthotropic compressible materials is employed systematically in the engineering and scientific analysis of a large scope of bulk and composite materials. However, at finite elastic strains, multiscale and fiber-based parametric models are typically employed, which material parameters are fitted to macroscopic experimental data using optimization procedures. Phenomenological extensions of the linear theory capable of effectively modelling such a large scope of materials are not available. What we present in this work is a simple extension of the linear theory to finite strains such that at every deformation level, the infinitesimal theory is fully recovered. The model is based in non-parametric spline complementary energies employing an energy decomposition compatible with the classical infinitesimal expression at all strain levels. No material parameter is explicitly involved because the spline-based stress energies are numerically computed (not fitted) directly from experimental data. We show the applicability of the model to capture (1) the behavior of orthotropic bimodulus materials consistent with hyperelasticity (a novel formulation also presented herein), (2) orthotropic auxetic foams, and (3) composites at finite strains.