Generalization and optimization of two hierarchical non-self-similar bio-inspired composites

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The matchless properties possessed by biological composites such as nacre, bone, turtle, armadillo, and spider silk are a great inspiration to humankind which lead to the mimicking of their geometric and material features to simulate synthetic so-called bio-inspired composites. Bio-inspired composites are often considered an ideal candidate in the field of light and innovative structures, which the world is in need of. In order to develop a bio-inspired composite with fine mechanical properties, it is required to study all the possible factors which are responsible for the superior mechanical properties of a biological composite. The hierarchical arrangement and the staggering pattern of the platelets inside the matrix are major factors affecting the final properties of such composite materials. The generalization of parameters in a hierarchical structure could be beneficial in finding out the optimum parameters responsible for the maximum desirable mechanical properties in a bio-inspired composite. In this paper, we formulate a novel generalized model for a stairwise staggered (which is regarded as one of the patterns mostly found in nature due to its optimized properties) two hierarchical bio-inspired composite, and we optimize the model for a tailored design according to the stiffness, strength, and toughness requirements. The developed model can evaluate self-similar as well as non-self-similar configurations, and the analytical results from the studies show a good agreement when compared with the models of specific known designs from the literature. Also, the ternary plots obtained from optimization show that the number of platelets in a period at the first and second levels of hierarchy are the key parameters other than the volume fractions and the critical aspect ratios, controlling the final properties of the two hierarchical composites.