Keywords: auxetic structures, direct three-dimenaional printing, voxel model, beam model, finite element, structural optimization.

This paper deals with finite element modelling of auxetic cellular structures and numerical optimization of their effective mechanical properties. Three different auxetic structures (two-dimensional cut missing-rib, two-dimensional inverted (re-entrant) honeycomb and three-dimensional inverted honeycomb) were designed and produced by additive manufacturing. Fully parametric representations of the structures are developed based on their geometric design and tested in a virtual finite element experiment to uncover the relationship between the overall properties and design parameters.

Deformation behaviour of the selected auxetics assessed numerically is verified against experiments in which deformation is measured precisely in a large area using digital image correlation up to large strain values. Then the strain-stress curves are compared to the numerically obtained values.

In the finite element analyses the geometries of the structures have been discretised either with three-dimensional solid elements (eight-node hexahedral elements) and with beam elements. The numerical model was equipped with the elasto-plastic material model with a von Mises yield criteria and bilinear isotropic work hardening. To inversely calculate the stress-strain relationship of the structures for large strain values both geometric and material nonlinearities were taken into account.

The effects of selected structural parameters (both geometric given e.g. by relative density, rod thickness, internal angles, etc. and material given by elastic properties of the base material) are studied using parametric finite element modelling to obtain their effects on overall mechanical properties (stiffness and strength). Auxetic structures are then optimized using design parameter driven finite element models which are able to predict various effective mechanical properties such as elastic modulus, strength and Poisson's ratio.

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