Design and Optimization of Nano-Bio-Inspired Hierarchical or Nano-Grained Materials

TL;DR

This paper introduces a mathematical model and optimization method for designing nano-bio-inspired hierarchical and nano-grained materials, predicting their mechanical properties and optimal grain sizes based on biomechanisms.

Contribution

It provides a novel mathematical framework and formulas for designing and optimizing nano-bio-inspired materials, including a new understanding of grain size effects beyond the Hall-Petch regime.

Findings

Derived formulas for strength, toughness, and stiffness dependence on size-scale.

Identified optimal grain size for nano-grained materials.

Explained deviation from Hall-Petch law based on material properties.

Abstract

In this letter a mathematical model to design nano-bio-inspired hierarchical materials is proposed. An optimization procedure is also presented. Simple formulas describing the dependence of strength, fracture toughness and stiffness on the considered size-scale are derived, taking into account the toughening biomechanisms. Furthermore, regarding nano-grained materials the optimal grain size is deduced: incidentally, it explains and quantitatively predicts the deviation from the well-known Hall-Petch regime. In contrast with the common credence, this deviation does not arise at a universal value of grain size but it is strongly dependent on the mechanical properties of the mixture.