Pantographic lattices with non-orthogonal fibres: Experiments and their numerical simulations

Current research in metamaterials design is pushing to fill the gap between mathematical modelling and technological applications. To meet these requirements predictive and computationally effective, numerical tools need to be conceived and applied. In this paper, we describe the performances of a discrete model based on the microstructure architecture [1] and those of a second gradient continuum model [2] for pantographic structures with non-orthogonal fibres comparing them with some experimental results. The interest in these structures resides in the exotic behaviour that they have already shown [3] and their study seems promising. The comparison which we present here shows that, depending on the length scale characterising the structural cell of pantographic sheets, either discrete or continuum model performance and/or behaviour may prevail. Some homogenization interesting problems are listed in the conclusions in the hope that they may be rigorously studied with the most advanced mathematical tools.