Abstract: 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.

Biography: Dr Shreyas Mandre is an applied mathematician, an engineer and a scientist. Before moving to Warwick, he was an Assistant Professor in the School of Engineering at Brown University from 2010 to 2019. Dr Mandre was also a Lecturer in Applied Mathematics at Harvard University.

Dr Mandre received his PhD in Mathematics from the University of British Columbia in 2006 under the guidance of Professor Neil J Balmforth. Undergraduate education was in Mechanical Engineering from the Indian Institute of Technology Bombay followed by a Masters from Northwestern University in the same subject.

Dr Mandre’s research spans continuum mechanics, biomechanics and applied mathematics, with applications to biology and engineering.