Exploring anisotropic mechanical properties of lobster claw exoskeleton through fractal models

The outstanding mechanical properties of lobster claw exoskeletons are intricately tied to their internal microstructure. Investigating this relationship can offer vital insights for designing high-performance additive manufacturing structures. Fractal theory, with its fractional dimensional perspective, suits the complexity of real-world phenomena. Our study examines fully hydrated lobster claw exoskeletons using a multifaceted approach: four-point bending tests, scanning electron microscopy observations, and fractal models. Test results reveal superior mechanical properties in longitudinal specimens. Scanning electron microscopy shows non-uniform fiber helical structures and porous elements in the exoskeleton. Fracture mechanisms involve both breaking fiber fragments perpendicular to the cross-section and tearing between these fragments. The observed crack propagation paths exhibit statistical self-similarity. Consequently, we develop fractal models for the crack propagation paths in longitudinal and transverse specimens, calculating crack extension forces. Using the box-counting method and its improved variant, we determine the fractal dimensions of specimen sections. The fractal dimension of longitudinal models exceeds that of transverse models, and calculated crack extension forces are higher in longitudinal models. These findings align well with experimental data, demonstrating fractal theory's efficacy in analyzing the lobster claw exoskeleton's anisotropic mechanical properties.