Shape optimization in exoskeletons and endoskeletons: a biomechanics analysis

Area of Science:

• Biomechanics
• Evolutionary Biology
• Materials Science

Background:

• Skeletal structures, both exoskeletons and endoskeletons, are subject to mechanical failure.
• Understanding the relationship between skeletal form and strength is crucial for evolutionary and biomechanical studies.

Purpose of the Study:

• To develop and apply a sophisticated model for predicting mechanical failure in limb segments.
• To test the hypothesis that evolutionary adaptation optimizes the radius-to-thickness ratio (r/t) for maximum strength relative to weight.
• To compare the optimization of arthropod exoskeletons with vertebrate endoskeletons.

Main Methods:

• Modeled limb segments as hollow tubes with radius (r) and thickness (t).
• Considered five failure modes: transverse fracture, three types of buckling, and longitudinal splitting, including interactions.
• Analyzed arthropod exoskeletons (crab merus, locust tibia) and vertebrate long bones using literature data and estimated in vivo stresses.

Main Results:

• The optimal r/t ratio for bending differs from that for axial compression.
• The crab merus exhibits an r/t value that is a compromise for both bending and compression.
• The locust tibia is optimized for bending, its predominant loading mode.
• Vertebrate long bones have significantly lower r/t values than predicted optimal values.

Conclusions:

• The developed theoretical model is valuable for studying the evolutionary development of skeletal form in diverse organisms.
• Arthropod exoskeletons show evidence of evolutionary optimization for specific loading conditions.
• Vertebrate bones appear less optimized for strength relative to weight compared to arthropod exoskeletons.