An improved failure criterion for biological and engineered staggered composites.

High-performance biological materials such as nacre, spider silk or bone have evolved a staggered microstructure consisting of stiff and strong elongated inclusions aligned with the direction of loading. This structure leads to useful combinations of stiffness, strength and toughness, and it is therefore increasingly mimicked in bio-inspired composites. The performance of staggered composites can be tuned; for example, their mechanical properties increase when the overlap between the inclusions is increased. However, larger overlaps may lead to excessive tensile stress and fracture of the inclusions themselves, a highly detrimental failure mode. Fracture of the inclusions has so far only been predicted using highly simplified models, which hinder our ability to properly design and optimize engineered staggered composites. In this work, we develop a new failure criterion that takes into account the complex stress field within the inclusions as well as initial defects. The model leads to an 'optimum criterion' for cases where the shear tractions on the inclusions is uniform, and a 'conservative' criterion for which the tractions are modelled as point forces at the ends of the overlap regions. The criterion can therefore be applied for a wide array of material behaviour at the interface, even if the details of the shear load transfer is not known. The new criterion is validated with experiments on staggered structures made of millimetre-thick alumina tablets, and by comparison with data on nacre. Formulated in a non-dimensional form, our new criterion can be applied on a wide variety of engineered staggered composites at any length scale. It also reveals new design guidelines, for example high aspect ratio inclusions with weak interfaces are preferable over inclusions with low aspect ratio and stronger interfaces. Together with existing models, this new criterion will lead to optimal designs that harness the full potential of bio-inspired staggered composites.