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 radius r and thickness t. 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 of r/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 optimum r/t value for bending was found to be different from that for axial compression. We found that the crab merus experiences similar levels of bending and compression in vivo and that its r/t value 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 lower r/t values 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.

Fatigue of insect cuticle

“…Cuticle in the tibiae contains a high proportion of chitin fibres, arranged in a complex layered pattern with a predominance of fibres lying parallel to the longitudinal axis of the leg (Neville, 1965). This ensures good resistance to the dominant type of loading, which is axial bending during jumping (Taylor and Dirks, 2012). This fibrous structure, like wood and some other natural materials, is very resistant to cracking when loaded parallel to its grain direction.…”

“…We used these results to estimate the ground reaction force and thus calculate the maximum stress in the tibia during jumping (Taylor and Dirks, 2012), obtaining a result of 42.2MPa, which is 55% of The Journal of Experimental Biology 216 (10) the UTS. Such estimates are inevitably approximate in nature given the various sources of error involved.…”

“…In a previous publication we presented a theoretical analysis that predicted that the locust tibia had evolved to an optimal design, in relation to its dimensions of length, diameter and thickness (Taylor and Dirks, 2012). One aspect of that analysis was the prediction that the two failure modes of tensile fracture and compressive buckling would be equally likely to occur.…”

“…During their migratory journeys across thousands of kilometres of deserts or oceans, their wings have to withstand many millions of cyclic loadings. The tibiae in the large hind legs experience stresses of more than half their tensile strength during jumping and kicking (Bayley et al, 2012;Taylor and Dirks, 2012). Mammalian bone subject to cyclic loading has been shown to resist fatigue failure by continuous repair, mediated by living cells (Martin, 1997;Taylor et al, 2007).…”

It's Not a Bug, It's a Feature: Functional Materials in Insects

“…Chemoreceptive sensilla Gypsy moths, [433][434][435] nun moths, [433] silk moths, [629] tobacco hawk moths [440,441] Collective materials Building and fungus cultivation Termites [630] Built structures Honeybees [2] Group thermoregulation Termites, [528] bees, [512,563] wasps [512,563] Wind harvesting Termites [511,631] Locomotion Locomotive appendages Jumping insects, [128] locust, [632,633] cicadas [634] Emulsions and biphasic solutions Adhesion Permanent adhesives Flies, [635,636] praying mantis, [68] asparagus beetle, [637] gum moths [57] Temporary adhesives Locusts, [58] grasshoppers, [59] flies, [65] beetles [65] Chemical sensing and defense…”