A characteristic length for stress transfer in the nanostructure of biological composites

Although it has been widely recognized that stress transfer in the nanostructure of biological composites follows a tension–shear chain, with mineral platelets primarily under tension and protein matrix primarily under shear, some of the critical assumptions of this model has not been thoroughly investigated. For example, an implicit assumption of the tension–shear chain model is that the shear stress in the protein layer between two neighboring platelets is uniformly distributed. Here we derive a characteristic length for stress transfer in a unit cell of biocomposites and show that the assumption of uniform shear stress in protein is valid only if the length of the mineral platelets is below a characteristic value. Numerical simulations have also been carried out to confirm that stress transfer in the staggered biocomposites is most efficient when the length of the mineral platelets is equal to the characteristic length.