A crack-bridging model considering microstructural randomness in biological composite materials

The macroscopic mechanical properties of biological composite materials, such as strength and fracture toughness, are determined by both their constituents and microstructure. Conventional researches often assume that these properties can be modeled using representative volume elements that features microstructural periodicity. However, in reality, such periodicity is absent, and the mechanical and geometric properties of the constituents exhibit spatial randomness, profoundly affecting the material's macroscopic behavior. In this study, we modify the classic crack-bridging model to account for microstructural randomness. Using the brick–mortar microstructure of nacre as an example, we investigate how microstructural randomness influences macroscopic fracture toughness and the mechanical properties of the crack-bridging zone. The results demonstrate that microstructural randomness weakens macroscopic fracture toughness, in line with the classic weakest-link principle. However, the randomness in macroscopic fracture toughness is significantly reduced compared to microstructural randomness, suggesting that the weakening effect induced by microstructural randomness is suppressed. Further analysis reveals that as the length of platelets increases, the weakening effect of microstructural randomness becomes less significant. This indicates that the microstructural stress transfer mechanism is responsible for suppressing the negative impact of microstructural randomness. Beyond the conventional strengthening and toughening effects, our results highlight a new advantage of well-designed microstructures in biological materials, offering deeper insights into how microscopic heterogeneity influences the macroscopic fracture toughness of these materials.