The Micromechanics of Biological and Biomimetic Staggered Composites

Natural materials such as bone, tooth and nacre achieve attractive properties through the "staggered structure", which consists of stiff, parallel inclusions of large aspect ratio bonded together by a more ductile and tougher matrix. This seemingly simple structure displays sophisticated micromechanics which lead to unique combinations of stiffness, strength and toughness. In this article we modeled the staggered structure using finite elements and small Representative Volume Elements (RVEs) in order to explore microstructure-property relationships. Larger aspect ratio of inclusions results in greater stiffness and strength, and also significant amounts of energy dissipation provided the inclusions do not fracture in a brittle fashion. Interestingly the ends of the inclusions (the junctions) behave as crack-like features, generating theoretically infinite stresses in the adjacent inclusions. A fracture mechanics criterion was therefore used to predict the failure of the inclusions, which led to new insights into how the interfaces act as a "soft wrap" for the inclusions, completely shielding them from excessive stresses. The effect of statistics on the mechanics of the staggered structure was also assessed using larger scale RVEs. Variations in the microstructure did not change the modulus of the material, but slightly decreased the strength and significantly decreased the failure strain. This is explained by strain localization, which can in turn be delayed by incorporating waviness to the inclusions. In addition, we show that the columnar and random arrangements, displaying different deformation mechanisms, lead to similar overall properties. The guidelines presented in this study can be used to optimize the design of staggered synthetic composites to achieve mechanical performances comparable to natural materials.