IGM Colloquium: Prof. Shreyas Mandre, Brown University

© 2018 Prof. Shreyas Mandre

© 2018 Prof. Shreyas Mandre

Functional interpretation for transverse arches of human foot
About 8 million years ago, the common ancestor of the human and chimpanzee lineages had feet without arches and with a structure similar to our hands. In this talk, we consider the function of the transverse arch of the human foot as a structural element and juxtapose the results in the context of fossilized feet from human ancestors.

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. In addition to presenting a functional interpretation of the transverse arch of the foot, this study also identifies a classification of flat feet based on the skeletal geometry and mechanics.

Dr. Mandre is an Assistant Professor in the School of Engineering at Brown University. He has a Bachelors degree in Mechanical Engineering from the Indian Institute of Technology Bombay, a Masters in Mechanical Engineering from Northwestern University, a PhD from the University of British Columbia in Mathematics. Like his degrees, Dr. Mandre's research straddles engineering and mathematics, including on esoteric topics such as the waving of grass, the splashing of droplets, and the structure of fish fins and human feet.