Modelling impact behavior of auxetic meta-materials using geometrically nonlinear lattices

High velocity impacts often occur in military or space context such as bullet and fragment impact on personal protective equipment or satellites in orbit being endangered by micro-meteorites or space debris. In the quest for better mitigation of such impact events Negative Poission's Ratio (NPR) materials, also called auxetic materials, offer beneficial properties, such as higher indentation resistance, shear resistance, fracture toughness and energy adsorption [1]. Auxetic materials are hardly found in nature, but they can be constructed artificially, e.g. by careful design of lattice structures. This approach of designing materials is well understood in the static and linear regime and a myriad of different types of materials have been investigated. However, the understanding of the corresponding properties in the dynamic regime is still not complete and the topic of ongoing research.
In this research the computational modelling of meta-materials in the dynamic regime is studied. The development of proper computational modelling techniques will allow the guided design and optimization of such meta-materials by means of understanding the effects at play as well as determining feasibility ranges. These computational techniques aim not only at a proper representation of the mesoscopic materials, but are directed towards the development of homogenized macroscopic models, that will help engineers to address design challenges quickly and reliably. However, in a first step a reliable numerical representation of the lattice structure of the metamaterials needs to be derived. The assembly of two- and three-dimensional auxetic lattices using geometrically nonlinear beams as well as the extension to a dynamical framework will be discussed. In the context of this numerical framework different architectures and their resulting properties for impact mitigation will be compared. First, the effect of nonlinearity on the macroscopic properties of the lattices is investigated using static analyses. Then the dynamic effects prevalent in aforementioned impact events are shown and compared for different lattice architectures, and their effects on the performance of materials in impact mitigation are discussed. For two-dimensional auxetics a comparison with experimental results is shown. Differences in auxetic architectures between two-dimensional and three-dimensional lattices as well as the resulting effects on the applicability for impact mitigation will be sketched together with different methods to create a three-dimensional structure from existing two-dimensional structures. Numerical examples will be presented to demonstrate the performance of the nonlinear computational model for the auxetic lattice structures. [1] Kolken, H.M.A. and Zadpoor, A.A., Auxetic mechanical metamaterials. RSC Advances, 2017. 7(9): p. 5111-5129.