Hierarchical geometries and adhesion: Bio-inspired designs for stiff interfaces

Filamentous bio-materials such as fibrin or collagen networks exhibit an enormous stiffening of their elastic moduli upon large deformations. This pronounced nonlinear behavior stems from a significant separation between the stiffnesses scales associated with bending vs. stretching the material's constituent elements. Here we study a simple model of such materials - floppy networks of hinged rigid bars embedded in an elastic matrix - in which the effective ratio of bending to...

Hierarchically structured materials, which possess distinct features on different length scales, are ubiquitous in nature and engineering. In many cases, one structural level may be ordered while another structural level may be disordered. Here, we investigate the impact of structural disorder on the mechanical properties of hierarchical filamentous structures. Through simulations of networks with two hierarchical levels, we show that disorder does not change how stiffness sc...

Reinforced elastic sheets surround us in daily life, from concrete shell buildings to biological structures such as the arthropod exoskeleton or the venation network of dicotyledonous plant leaves. Natural structures are often highly optimized through evolution and natural selection, leading to the biologically and practically relevant problem of understanding and applying the principles of their design. Inspired by the hierarchically organized scaffolding networks found in p...

We introduce a numerical scheme to evolve functional materials that can accomplish a specified mechanical task. In this scheme, the number of solutions, their spatial architectures and the correlations among them can be computed. As an example, we consider an "allosteric" task, which requires the material to respond specifically to a stimulus at a distant active site. We find that functioning materials evolve a less-constrained trumpet-shaped region connecting the stimulus an...

Hierarchy seems to pervade complexity in both living and artificial systems. Despite its relevance, no general theory that captures all features of hierarchy and its origins has been proposed yet. Here we present a formal approach resulting from the convergence of theoretical morphology and network theory that allows constructing a 3D morphospace of hierarchies and hence comparing the hierarchical organization of ecological, cellular, technological and social networks. Embedd...

Unlike most synthetic materials, biological materials often stiffen as they are deformed. This nonlinear elastic response, critical for the physiological function of some tissues, has been documented since at least the 19th century, but the molecular structure and the design principles responsible for it are unknown. Current models for this response require geometrically complex ordered structures unique to each material. In this Article we show that a much simpler molecular ...

Vertebrate animals benefit from a combination of rigidity for structural support and softness for adaptation. Similarly, integrating rigidity and softness can enhance the versatility of soft robotics. However, the challenges associated with creating durable bonding interfaces between soft and rigid materials have limited the development of hybrid robots. Existing solutions require specialized machinery, such as polyjet 3D printers, which are not commonly available. In respons...

In this paper, the asymptotic first order analysis, both mathematical and numerical, of two structures bonded together is presented. Two cases are considered, the gluing of an elastic structure with a rigid body and the gluing of two elastic structures. The glue is supposed to be elastic and to have its stiffness of the same order than those of the elastic structures. An original numerical method is developed to solve the mechanical problem of stiff interface at order 1, base...

Architected materials derive their properties from the geometric arrangement of their internal structural elements, rather than solely from their chemical composition. They can display remarkable behaviors such as high strength while being lightweight, negative Poisson's ratios, and shear-normal coupling. However, architected materials so far have either exhibited solid-like or fluid-like behavior, but not both. Here, we introduce a class of materials that consist of linked p...

Bone is a stiff and though, hierarchical and continuously evolving material that optimizes its structure to respond to mechanical stimuli, which also govern growth and remodeling processes. However, a full understanding of the underlying mechanisms responsible for the cooperation of bone toughness and biological functions, with important implications in bone ageing, osteoporosis and tissue repair, has yet to be achieved. In particular, how micro-damage nucleation, needed for ...