No abstract

The mechanics of fiber bundles has been widely studied in the literature, and fiber bundle models in particular have provided a wealth of useful analytical and numerical results for modeling ordinary materials. These models, however, are inadequate to treat bioinspired nanostructured materials, where hierarchy, multiscale, and complex properties play a decisive role in determining the overall mechanical characteristics. Here, we develop an ad hoc hierarchical theory designed to tackle these complex architectures, thus allowing the determination of the strength of macroscopic hierarchical materials from the properties of their constituents at the nanoscale. The roles of finite size, twisting angle, and friction are also included. Size effects on the statistical distribution of fiber strengths naturally emerge without invoking best-fit or unknown parameters. A comparison between the developed theory and various experimental results on synthetic and natural materials yields considerable agreement.

This is an author version of the contribution published on:Questa è la versione dell'autore dell'opera: [Nanoscale, 2012,4, 1200-1207, DOI: 10.1039 AbstractNatural materials are often organized in complex hierarchical architectures to optimize mechanical properties. Artificial bio-inspired materials, however, have thus far failed to successfully mimic how these architectures improve material characteristics, for example strength. Here, a method is proposed for evaluating the role of hierarchy on structural strength. To do this, we consider different hierarchical architectures of fiber bundles through analytical multiscale calculations based on a fiber bundle model at each hierarchical level. In general, we find that an increase in the number of hierarchy levels leads to a decrease in the strength of material. However, when a composite bundle with two different types of fibers is considered, an improvement in the mean strength is obtained for some specific hierarchical architectures, indicating that both hierarchy and material "mixing" are necessary ingredients to obtain improved mechanical properties. Results are promising for the improvement and "tuning" of the strength of bio-inspired materials.

We present a theoretical and numerical analysis of the mechanical behavior of self-healing materials using an analytical model and numerical calculations both based on a Hierarchical Fiber Bundle Model, and applying them to graphene-or carbon-nanotube-based materials. The self-healing process can be described essentially through a single parameter, that is, the healing rate, but numerical simulations also highlight the influence of the location of the healing process on the overall strengthening and toughening of the material. The role of hierarchy is discussed, showing that full-scale hierarchical structures can in fact acquire more favorable properties than smaller, nonhierarchical ones through interaction with the self-healing process, thus inverting the common notion in fracture mechanics that specimen strength increases with decreasing size. Further, the study demonstrates that the developed analytical and numerical tools can be useful to develop strategies for the optimization of strength and toughness of synthetic bioinspired materials.

Computational modelling has received increasing attention to investigate multi-scale coupled problems in micro-heterogeneous biological structures such as cells. In the current study, we investigated for a single cell the effects of (1) different cell-substrate attachment (2) and different substrate modulus [Formula: see text] on intracellular deformations. A fibroblast was geometrically reconstructed from confocal micrographs. Finite element models of the cell on a planar substrate were developed. Intracellular deformations due to substrate stretch of [Formula: see text], were assessed for: (1) cell-substrate attachment implemented as full basal contact (FC) and 124 focal adhesions (FA), respectively, and [Formula: see text]140 KPa and (2) [Formula: see text], 140, 1000, and 10,000 KPa, respectively, and FA attachment. The largest strains in cytosol, nucleus and cell membrane were higher for FC (1.35[Formula: see text], 0.235[Formula: see text] and 0.6[Formula: see text]) than for FA attachment (0.0952[Formula: see text], 0.0472[Formula: see text] and 0.05[Formula: see text]). For increasing [Formula: see text], the largest maximum principal strain was 4.4[Formula: see text], 5[Formula: see text], 5.3[Formula: see text] and 5.3[Formula: see text] in the membrane, 9.5[Formula: see text], 1.1[Formula: see text], 1.2[Formula: see text] and 1.2[Formula: see text] in the cytosol, and 4.5[Formula: see text], 5.3[Formula: see text], 5.7[Formula: see text] and 5.7[Formula: see text] in the nucleus. The results show (1) the importance of representing FA in cell models and (2) higher cellular mechanical sensitivity for substrate stiffness changes in the range of cell stiffness. The latter indicates that matching substrate stiffness to cell stiffness, and moderate variation of the former is very effective for controlled variation of cell deformation. The developed methodology is useful for parametric studies on cellular mechanics to obtain quantitative data of subcellular strains and stresses that cannot easily be measured experimentally.