Biomechanical factors in the adaptations of insect tibia cuticle

Insects are among the most diverse groups of animals on Earth. Their cuticle exoskeletons vary greatly in terms of size and shape, and are subjected to different applied forces during daily activities. We investigated the biomechanics of the tibiae of three different insect species: the desert locust (Schistocerca gregaria), American cockroach (Periplaneta americana) and Death's Head cockroach (Blaberus discoidalis). In a previous work, we showed that these tibiae vary not only in geometry (length, radius and thickness) but also in material quality (Young's modulus) and in the applied stress required to cause failure when loaded in bending. In the present work we used kinematic data from the literature to estimate the forces and stresses arising in vivo for various different activities, and thus calculated factors of safety defined as the ratio between the failure stress and the in vivo stress, adjusting the failure stress to a lower value to allow for fatigue failure in the case of frequently repeated activities. Factors of safety were found to vary considerably, being as little as 1.7 for the most strenuous activities, such as jumping or escaping from tight spaces. Our results show that these limbs have evolved to the point where they are close to optimal, and that instantaneous failure during high-stress activities is more critical than long-term fatigue failure. This work contributes to the discussion on how form and material properties have evolved in response to the mechanical functions of the same body part in different insects.