A Hierarchical Lattice Spring Model to Simulate the Mechanics of 2-D Materials-Based Composites

Abstract

Citation:Brely L, Bosia F and Pugno NM (2015) 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 Hierarchical 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 predictions as well as to finite elements simulations, and then employed to study how hierarchical structural aspects influence composite material (mainly 2d, e.g., graphene based) 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.

Evolution of aerial spider webs coincided with repeated structural optimization of silk anchorages

“…A homogenization procedure was adopted, imposing the equivalence of the strain energy density of the lattice with that of a corresponding homogeneous membrane (Ostoja‐Starzewski ; Brely et al. ). We used a standardized anchor geometry with length l = 1 mm, width w = 1 mm, thickness t = 1 µm, and with the dragline fused with the membrane over a length of c l = 0.33 mm.…”

Designing tough isotropic structural composite using computation, 3D printing and testing

“…We underline that the word 'lattice' in lattice spring model means "bead-spring network", adopted for the material discretization ( Figure 2b), and is different from the lattice defining the arrangements of stiff and soft constituents in the previous section. Because of its computational efficiency and ease of implementation, LSM has been used to analyze the deformation and fracture mechanism of nature-inspired composites [24,[33][34][35][36][37][38][39][40]. However, most previous studies have employed triangular LSM (tLSM), where mechanical properties highly depend on the loading direction [24,[33][34][35][36][37][38][39].…”

Tuning friction with composite hierarchical surfaces

“…In general, the numerical simulation of static friction is similar to that in a fracture mechanics problem [38]. The static friction coefficient distribution, corresponding to the threshold forces for block motion, are analogous to the thresholds for breaking bonds in fiber bundle or lattice spring models [39] [40]. Hence, we expect the global friction coefficient to decrease with a wider static statistical distribution, since the presence of weaker elements can trigger avalanche ruptures leading to a macroscopic sliding event.…”