Toughening by crack deflection in the homogenization of brittle composites with soft inclusions

TL;DR

This paper demonstrates a toughening mechanism in brittle composites with soft inclusions, where crack deflection at the microscopic level enhances toughness, but standard homogenization methods fail to detect it due to irreversibility.

Contribution

It introduces a simple example showing how crack deflection contributes to toughening, highlighting limitations of traditional homogenization techniques.

Findings

Crack deflection at microscopic level increases composite toughness.

Standard $ ext{Gamma}$-convergence homogenization cannot detect the toughening mechanism.

Irreversibility of crack process is key to the toughening effect.

Abstract

We present a simple example of toughening mechanism in the homogenization of composites with soft inclusions, produced by crack deflection at microscopic level. We show that the mechanism is connected to the irreversibility of the crack process. Because of that it cannot be detected through the standard homogenization tool of the $\Gamma$-convergence.