Curvature of the transverse arch governs stiffness of the human foot

Abstract eng:
Humans are unique among primates in having arched feet that provide a stiff propulsive lever for locomotion. Using mathematical and physical models of the foot as a curved elastic shell, we show that the transverse curvature is the primary determinant of foot stiffness. The stiffness of shallow thin shells has two asymptotic regimes, one that resembles a soft thin plate, and the other that shows a power- law dependence of stiffness with an exponent of 3/2. Curvature induced coupling between bending and in—plane stretching underlies the power-law dependence. Analysis of discrete realizations of a shell also show a similar transition, but with an exponent of 2. We present implications of our work to understanding the mechanical origins of stiff human feet, and to the evolution of human feet through an analysis of extant and fossil feet.

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