Computational modeling of the mechanics of hierarchical materials

Structural hierarchy coupled with material heterogeneity is often identified in natural materials, from the nano- to the macroscale. It combines disparate mechanical properties, such as strength and toughness, and multifunctionality, such as smart adhesion, water repellence, self-cleaning, and self-healing. Hierarchical architectures can be employed in synthetic bioinspired structured materials, also adopting constituents with superior mechanical properties, such as carbon nanotubes or graphene. Advanced computational modeling is essential to understand the complex mechanisms that couple material, structural, and topological hierarchy, merging phenomena of different nature, size, and time scales. Numerical modeling also allows extensive parametric studies for the optimization of material properties and arrangement, avoiding time-consuming and complex experimental trials, and providing guidance in the fabrication of novel advanced materials. Here, we review some of the most promising approaches, with a focus on the methods developed by our group