Bounds for the dynamic modulus of unidirectional composites with bioinspired staggered distributions of platelets

Abstract Load-bearing biological materials like bone, nacre and tendon are bio-composites with superior mechanical properties to resist static and dynamic loadings and thus have been intensively studied not only for understanding the structure-property relationship but also for developing novel bioinspired materials. Here a theoretical framework was developed to establish the bounds for the storage and loss moduli of the bioinspired staggered composites. The bounds were first verified by the finite element analysis. Then, the framework was utilized to study how the storage and loss moduli of the bioinspired composites vary against a series of geometrical and constituent material parameters including the distribution, volume fraction, and aspect ratio of the mineral platelets, as well as the loading frequency. In a recursive way, the bounds were further extended for bioinspired composites with multiple levels of structural hierarchy, and the effect of structural hierarchy was investigated. The results showed that, in comparison with other structural architectures, stairwise staggering structure generally gives higher loss viscoelasticity. The bounds derived in the present paper not only add insights into the damping behaviors of load-bearing biological composites but also provide a useful tool to estimate and help design the dynamic moduli of bio-inspired composites.