Research perspective on multiphysics and multiscale materials: a paradigmatic case

Pantographic fabrics are presented as a paradigmatic example to discuss the research perspective on multiphysics and multiscale materials. Reduced-order modeling, obtained by introducing higher-gradient or microstructured continua, shows much smaller computational needs than those required by full-scale 3D modeling calculations and by equivalent discrete spring systems. Researches already available in the literature compare theoretical predictions with results obtained in real experiments, analyzing both in-plane and out-of-plane deformations possibly induced by local buckling phenomena. The goal is to achieve three major objectives: (1) formulate coarse-scale nonlinear higher-gradient continuum models describing a more general class of pantographic metamaterials, based on finer-scale descriptions, through homogenization techniques; (2) implement finite element analyses with shape functions possessing higher regularity or employing mixed formulations to perform simulations with the above-formulated models; and (3) validate and verify the derived models through the acquisition and analysis of experimental data. These goals would likely push toward the improvement of 3D printing protocols to enhance the quality of the pantographic prototypes and DIC as experiments measurement technique. It can be also conjectured that many macroscopic deformation energies can be synthesized by using as elementary elements, inside periodicity cells, some pantographic modules.