A hierarchical lattice spring model to simulate the mechanics of 2-D materials-based composites

It is known that structural biological materials such as bone or dentin show unprecedented damage tolerance, toughness, and strength. The common feature of these materials is their hierarchical heterogeneous structure, which contributes to increased energy dissipation before failure occurring at different scale levels. These structural properties are the key to achieve superior nanocomposites. Here, we develop a numerical model in order to simulate the mechanisms involved in damage progression and energy dissipation at different size scales in composites, which depend both on the heterogeneity of the material (defects or reinforcements) and on the type of hierarchical structure. Both these aspects have been incorporated into a 2-D model based on a lattice spring model approach, accounting for geometrical non-linearities and including statistically based fracture phenomena. The model has been validated by comparing numerical results to linear elastic fracture mechanics results as well as to finite elements simulations, and then employed to study how hierarchical structural aspects impact on composite material properties, which is the main novel feature of the approach. Results obtained with the numerical code highlight the dependence of stress distributions (and therefore crack propagation) on matrix properties and reinforcement dispersion, geometry, and properties, and how the redistribution of stresses after the failure of sacrificial elements is directly involved in the damage tolerance of the material