Shape optimization in exoskeletons and endoskeletons: a biomechanics analysis

Abstract

This paper addresses the question of strength and mechanical failure in exoskeletons and endoskeletons. We developed a new, more sophisticated model to predict failure in bones and other limb segments, modelled as hollow tubes of radiusrand thicknesst. Five failure modes were considered: transverse fracture; buckling (of three different kinds) and longitudinal splitting. We also considered interactions between failure modes. We tested the hypothesis that evolutionary adaptation tends towards an optimum value ofr/t, this being the value which gives the highest strength (i.e. load-carrying capacity) for a given weight. We analysed two examples of arthropod exoskeletons: the crab merus and the locust tibia, using data from the literature and estimating the stresses during typical activities. In both cases, the optimumr/tvalue for bending was found to be different from that for axial compression. We found that the crab merus experiences similar levels of bending and compressionin vivoand that itsr/tvalue represents an ideal compromise to resist these two types of loading. The locust tibia, however, is loaded almost exclusively in bending and was found to be optimized for this loading mode. Vertebrate long bones were found to be far from optimal, having much lowerr/tvalues than predicted, and in this respect our conclusions differ from those of previous workers. We conclude that our theoretical model, though it has some limitations, is useful for investigating evolutionary development of skeletal form in exoskeletons and endoskeletons.