Elasticity of one-dimensional nanostructures – a multiscale approach
November 9 @ 2:30 pm - November 10 @ 3:30 pm
Prakhar Gupta, born on 12th March 1992 in Agra, received his primary education from Bal Bharati School, Agra and Air Force School, Agra. In 2009, he joined Dayalbagh Educational Institute, Agra to pursue his B.Tech. degree in Mechanical Engineering. During his Bachelors studies, he received Prof. V.G. Sastry Memorial Prize for best overall performance from the institute. He also received the Director’s Medal for securing highest marks. In July 2013, he joined the Department of Applied Mechanics, Indian Institute of Technology Delhi as a PhD student with MHRD fellowship. In November 2013, he also received DST-INSPIRE fellowship to pursue his PhD. His broad research interests are: nanomechanics, computational material science, nonlinear elasticity, bifurcation and stability.
Interest in one-dimensional nanostructures (e.g., carbon nanotubes, DNA, nanorods etc.) has surged dramatically due to their exceptional optical, thermal, electrical, magnetic and mechanical properties. The deformations of these nanostructures have been studied using both fully molecular approach as well as continuum formulations. These nanostructures have been modeled using two- dimensional shell theory as well as several one-dimensional theories such as Euler-Bernoulli and Timoshenko beam theories. However, the one-dimensional theories fail to model large cross- sectional rotation in these nanostructures. To overcome this limitation, the talk focuses on modeling of elasticity of such nanostructures using the one-dimensional continuum theory of Cosserat rods. In this talk, we discuss two different techniques to obtain nonlinear elastic constitutive relations of these nanostructures: (1) a multiscale technique (Helical cauchy-Born rule) to obtain nonlinear elastic constitutive relations through molecular statics of the smallest repeating cell of nanostructures (2) a fully continuum approach to obtain extensional and twisting stiffnesses of circular nanorods incorporating also the surface effects.