Toughness and damage tolerance of fractal hierarchical metamaterials

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...

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...

A new type of elasticity of random (multifractal) structures is suggested. A closed system of constitutive equations is obtained on the basis of two proposed phenomenological laws of reversible deformations of multifractal structures. The results may be used for predictions of the mechanical behavior of materials with multifractal microstructure, as well as for the estimation of the metric, information, and correlation dimensions using experimental data on the elastic behavio...

Soft materials capable of large inelastic deformation play an essential role in high-performance nacre-inspired architectured materials with a combination of stiffness, strength and toughness. The rigid "building blocks" made from glass or ceramic in these architectured materials lack inelastic deformation capabilities and thus rely on the soft interface material that bonds together these building blocks to achieve large deformation and high toughness. Here, we demonstrate th...

Toughness describes the ability of a material to resist fracture or crack propagation. It is demonstrated here that fracture toughness of a material can be asymmetric, i.e., the resistance of a medium to a crack propagating from right to left can be significantly different from that to a crack propagating from left to right. Such asymmetry is unknown in natural materials, but we show that it can be built into artificial materials through the proper control of microstructure. ...