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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 design and manufacturing of high value industrial components is suffering a change of paradigm with 3D printing. In this change of paradigm, metamaterials have an important role because when a component is 3D-printed, it is performed from the micro level, where custom structures may be designed to endow the material and the component of special of customized mechanical properties. Topology optimization techniques facilitate the design of both the microstructures and the overall component topology, and today the component topology may be designed assuming a continuous spectrum of mechanical properties facilitated by different locally designed microstructures. However, current topology optimization techniques do not operate directly with the mechanical properties of the material, but through density intermediates, using density-based limits like a minimum or maximum density, assuming an homogeneous base material. We propose here a novel topology optimization algorithm which operates directly on the mechanical properties and energies, without employing density intermediates. The proposed approach reduces the algorithmic complexity since the optimization is performed by the direct iterative update of the mechanical properties, through information taken from its finite element analysis. We show that the proposed methodology can reach similar results as the current techniques based on a gradient descent optimization, eliminating the need for external parameters and, hence, increasing the easy of use and its robustness. The proposed technique is specially suitable for two-level concurrent material-component design using functionally graded metamaterials.

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.