Toughness and damage tolerance of fractal hierarchical metamaterials

Hierarchical structures with constituents over multiple length scales are found in various natural materials like bones, shells, spider silk and others, all of which display enhanced quasi-static mechanical properties, such as high specific strength, stiffness and toughness. At the same time, the role of hierarchy on the dynamic behaviour of metamaterials remains largely unexplored. This study assesses the effect of bio-inspired hierarchical organization as well as of viscoel...

In many scenarios -- when we bite food or during a crash -- fracture is inevitable. Finding solutions to steer fracture to mitigate its impact or turn it into a purposeful functionality, is therefore crucial. Strategies using composites, changes in chemical composition or crystal orientation, have proven to be very efficient, but the crack path control remains limited and has not been achieved in load-bearing structures. Here, we introduce fracture metamaterials consisting of...

Natural hard composites like human bone possess a combination of strength and toughness that exceeds that of their constituents and of many engineered composites. This augmentation is attributed to their complex hierarchical structure, spanning multiple length scales; in bone, characteristic dimensions range from nanoscale fibrils to microscale lamellae to mesoscale osteons and macroscale organs. The mechanical properties of bone have been studied, with the understanding that...

This paper introduces the chain lattice, a hierarchical truss structure comprising two interpenetrating lattices. One lattice toughens the material and prevents catastrophic localized failure while the other lattice serves as a porous matrix that densifies to absorb energy during tensile loading. Chain lattices are amenable to additive manufacturing and can transform 3D-printable materials that are normally brittle and flaw-sensitive into damage-tolerant materials. Calculatio...

Natural cellular materials, such as honeycombs, woods, foams, trabecular bones, plant parenchyma, and sponges, may benefit from the disorderliness within their internal microstructures to achieve damage tolerant behaviours. Inspired by this, we have created quasi-disordered truss metamaterials (QTMs) via introducing spatial coordinate perturbations or strut thickness variations to the perfect, periodic truss lattices. Numerical studies have suggested that the QTMs can exhibit...

We discuss the relevance of methods of graph theory for the study of damage in simple model materials described by the random fuse model. While such methods are not commonly used when dealing with regular random lattices, which mimic disordered but statistically homogeneous materials, they become relevant in materials with microstructures that exhibit complex multi-scale patterns. We specifically address the case of hierarchical materials, whose failure, due to an uncommon fr...

Architected materials achieve unique mechanical properties through precisely engineered microstructures that minimize material usage. However, a key challenge of low-density materials is balancing high stiffness with stable deformability up to large strains. Current microstructures, which employ slender elements such as thin beams and plates arranged in periodic patterns to optimize stiffness, are largely prone to instabilities, including buckling and brittle collapse at low ...

A solid slender beam of length $L$, made from a material of Young's modulus $Y$ and subject to a gentle compressive force $F$, requires a volume of material proportional to $L^{3}f^{1/2}$ [where $f\equiv F/(YL^{2})\ll 1$] in order to be stable against Euler buckling. By constructing a hierarchical space frame, we are able to systematically change the scaling of required material with $f$ so that it is proportional to $L^{3}f^{(G+1)/(G+2)}$, through changing the number of hier...

Catastrophic failure of materials and structures due to unstable crack growth could be prevented if facture toughness could be enhanced at will through structural design, but how can this be possible if fracture toughness is a material constant related to energy dissipation in the vicinity of a propagating crack tip. Here we draw inspiration from the deformation behavior of biomolecules in load bearing biological materials, which have been evolved with a large extensibility a...

Mechanical metamaterials are renowned for their ability to achieve high stiffness and strength at low densities, often at the expense of low ductility and stretchability-a persistent trade-off in materials. In contrast, materials such as double-network hydrogels feature interpenetrating compliant and stiff polymer networks, and exhibit unprecedented combinations of high stiffness and stretchability, resulting in exceptional toughness. Here, we present double-network-inspired ...