This manuscript has more than 150 papers as a reference about energy absorption of auxetic structures and shows how several authors have approached the subject and how research in this field has progressed. It can be noted from the present paper that additive manufacturing has been an ally of researchers in the samples manufacturing and numerical analysis has also been widely used by the authors. In addition, this manuscript will provide a context for auxetic structures, discussing some cell models. The results obtained here serve as additional guidelines to assist engineers and designers in the development of auxetic structures.

The demands for a high-performance prosthesis include high strength and low weight. This study addresses the optimization of a new tube concept, made of composite material, which makes use of an isogrid and internal layer. For the methodological procedure, a response surface methodology (RSM) was used to define in what quantity, under what conditions and which data should be collected during a given experiment, seeking to satisfy the highest statistical precision and the lowest cost in the response. After RSM analysis, the finite element method was used for structural calculations for each condition of the experiment. The numerical results allowed the creation of a meta-model capable of translating the global structural behaviour. Thus, it was possible to optimize the parameters that were translated as responses applied to a lattice structure by particle swarm optimization and the Lichtenberg algorithm (LA). Comparison of the results demonstrated the good performance of the LA.