Modeling of a biological material nacre: Waviness stiffness model.
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Nacre is a tough yet stiff natural composite composed of microscopic mineral polygonal tablets bonded by a tough biopolymer. The high stiffness of nacre is known to be due to its high mineral content. However, the remarkable toughness of nacre is explained by its ability to deform past a yield point and develop large inelastic strain over a large volume around defects and cracks. The high strain is mainly due to sliding and waviness of the tablets. Mimicking nacre's remarkable properties, to date, is still a challenge due in part to fabrication challenges as well as a lack of models that can predict its properties or properties of a bulk material given specific constituent materials and material structure. Previous attempts to create analytical models for nacre include tablet sliding but don't account for the waviness of the tablets. In this work, a mathematical model is proposed to account for the waviness of the tablet. Using this model, a better prediction of the elastic modulus is obtained that agrees with experimental values found in the literature. In addition, the waviness angle can be predicted which is within the recommended range. Having a good representative model aids in designing a bio-mimicked nacre.