Testing Weibull as a viable statistical strength distribution for Nacre

Abstract

Nacre, a composite layer present in sea-shells, exhibits a remarkable combination of toughness, strength, and stiffness through its brick–mortar micro-structure, acting as a template for novel materials. Strength, one of nacre’s important properties is highly variable due to distribution of underlying material’s properties as well as various defects present in its micro-structure. Presently, researchers assume the Weakest-link hypothesis and consequently use the Weibull distribution to model this variability. However, this assumption is theoretically unproven for biological materials such as Nacre and extrapolation of the same to predict rare but catastrophic behavior would be incorrect. In this article, the suitability of Weibull distribution to account for the variability of strength in nacre is tested, using multi-scale models, developed using FEM. Through Monte Carlo based numerical experiments and Renormalization Group (RG) based arguments, it is shown that the Weakest-link hypothesis, which is commonly used to justify the use of the Weibull distribution, does not seem to hold for nacre. Micromechanics and non-local homogenization based distributions such as the one suggested by Luo and Bazant (2019) might be more appropriate for accurate extrapolation to the low probability tail.