Shreyas Mandre

Functional interpretation for transverse arches of the human foot

The fossil record indicates that the emergence of arches in human ancestral feet coincided with a transition from an arboreal to a terrestrial lifestyle. Propulsive forces exerted during walking and running load the foot under bending, which is distinct from those experienced during arboreal locomotion. I will present mathematical models with varying levels of detail to illustrate a simple function of the transverse arch. Just as we curve a dollar bill in the transverse direction to stiffen it while inserting it in a vending machine, the transverse arch of the human foot stiffens it for bending deformations. A fundamental interplay of geometry and mechanics underlies this stiffening -- curvature couples the soft out-of-plane bending mode to the stiff in-plane stretching deformation. This result overturns a century-old theory that the longitudinal arch underlies the bending rigidity of the human foot. In addition to presenting a functional interpretation of the transverse arch of the foot, this study also furnishes an interpretation of the fossil record implying that the evolution of the transverse arch may have preceded the longitudinal arch.