Computational homogenization of bio-inspired metamaterial with a random fiber network microstructure

Fast progress in additive manufacturing will allow artificial random materials to mimic biological media such as extracellular matrix (ECM). The elastic properties of ECM and its behavior under the external stretching essentially influence cells’ communication. Hence, proper tuning of the fiber properties and their arrangement is essential and can be achieved as a result of the numerous lab experiments and computational simulations. However, due to a rather complex microstructure, such experiments and simulations with random fiber metamaterials require a lot of resources. This work proposes a homogenization method of fibrous bio-inspired materials with a pre-defined structure to estimate their effective elastic properties. For this purpose, a two-dimensional representative volumetric element (RVE) containing many randomly distributed elements was considered. RVE was subjected to small uniaxial displacements for the subsequent stress calculation. The resulting stress-strain relations were used to determine the corresponding continuum hyperelastic model. Finally, the elastic moduli in the direction of stretching and a mutually orthogonal direction were estimated for both discrete and continuum models. A comparison of the moduli shows that the Ogden model well predicts the average elastic properties of the fiber network. However, it neglects jumps of the moduli values due to microscopic effects such as network reconfigurations.