# Research

I am particularly interested in generating and mathematically testing ideas in sister disciplines of continuum mechanics that pose a high risk for the practitioners who specialize in those disciplines but also yield a high reward if borne out. Here by high reward I mean a transformation in the perspective of the practitioners. The use of mathematical modeling, when carried out competently, significantly reduces the cost and the risk associated with such investigations.
And, of course, who could resist the allure of research driven purely by curiosity? The pleasure of discovery -- a topic so much written about that it needs no elaboratioon -- is the reward itself and one of the highest reward for the animal intellect.

#### Foot in motion

The overarching question is the structure-function relation of propulsive appendages of animals, such as the human foot. The arched structure is the hallmark of the human foot, and is considered to have evolved alongside bipedalism. For the foot to act as a propulsive lever to push off on the ground when the heel is lifted, a common stage in the walking and running gait, the foot must be sufficiently stiff under longitudinal bending. The arch along the length of the foot is considered to be the primary structural feature in the foot imparting this stiffness, and the one in the transverse direction is thought to arise due to geometric constraints. In recent work, we have uncovered the structural role of the transverse arch to be even more than the longitudinal one. Much like a currency note stiffens when curled transversely, the foot also stiffens due to the transverse arch. The underlying mechanical principle is the coupling between soft bending mode and the stiff stretching mode brought about by the curved geometry. We posited this type of curvature-induced stiffening to also be present in the fins of fish (see adjoining video).

In fact, we found that a fin that is geometrically flat can exhibit a coupling between bending and stretching by virtue of its microstructure. It appears that since a curved geometry imparts stiffness without any additional biomass, this adaptation could be applicable in any load-bearing appendage that demands stiffness.

For more details see:

1. Venkadesan, M., Dias, M., Singh, D., Bandi, M. M., Mandre, S., (2017) “Stiffness of the human foot and evolution of the transverse arch”. Nature 579, 97-100, 2020.
2. Dhawale, N., Mandre, S., and Venkadesan, M. (2019). Dynamics and stability of running over rough terrain. Royal Society Open Science, 6 (3), 181729.
3. Nguyen, K., Yu, N., Bandi, M. M., Venkadesan, M. and Mandre, S. (2017). Curvature-induced stiffening of a fish fin. Journal of Royal Society Interface, 14, 20170247.
4. Venkadesan, M., Mandre, S., and Bandi, M. M. (2017). Biological feet: evolution, mechanics and applications. in M. A. Sharbafi and A. Seyfarth. Bio-inspired Legged Locomotion. Oxford, UK: Butterworth-Heinemann.