This page contains some highlights from my past and current research.

Finite Temperature Quasi-Continuum analysis of nano-void growth in Magnesium.

Standard tools for atomistic simulation like molecular dynamics (MD) have significant shortcomings involving spurious size and rate effects owing to the highly restrictive length and time scales that can be studied using them. Among the host of solutions that have been proposed to tackle this problem, the quasi-continuum (QC) method has emerged as an elegant procedure to achieve spatial coarse-graining while still retaining a fully atomistic description in regions of interest.

Spatial coarse-graining in QC is based on the observation that atoms in a crystalline solid exhibit highly complex behavior only in the vicinity of regions with defects (like cracks, voids, dislocations etc.), but have a rather smooth behavior otherwise. Hence, the behavior of atoms in the defect-free bulk of a material can be effectively approximated with the choice of a few representative atoms.

The essential insight that permits temporal coarse-graining is the observation that atoms in solids exhibit oscillatory motion about a mean position, and to a first approximation, it is only the evolution of the mean positions that is important for understanding the physics at the mesoscale. This is rigorously formulated using the maximum entropy principle and a variational mean field theory that imposes local restrictions on the atomic energies, resulting in a local version of the classical canonical ensemble. An attractive outcome of this thermalization process is that slower atomic processes that are inaccessible to MD can be studied using QC.

Part of my current research at Caltech, funded by the Materials in Extreme Dynamical Environments (MEDE) program, focuses on using this framework to study spallation in magnesium (Mg). The interest in Mg is primarily due to its promise as a lightweight alternative to conventional metals for various engineering applications. Mg naturally occurs in the hexagonal close packed (HCP) crystal structure. The HCP structure has low symmetry in comparison to other crystal structures like the face centered cubic (FCC) structure, and this has specific implications on how plastic deformation is accommodated at the atomic scale. Unlike FCC materials where slip systems dominate, the role of twinning is crucial for understanding the plastic response of HCP materials. 

To understand the atomistic basis of spall, I studied the time evolution of nano-voids in single crystal Mg subject to tensile strain loads, in collaboration with Maurico Ponga, Kaushik Bhattacharya and Michael Ortiz. This study led to the important conclusion that the absence of any significant interactions between dislocation activity on the basal plane, involving basal slip and prismatic loop formation, and <c+a> dislocations that accommodate deformation perpendicular to the basal plane, plays a crucial role in the observed lower spall strength of Mg.

Reference:
M. Ponga, A. A. Ramabathiran, K. Bhattacharya, M. Ortiz
Dynamic behavior of nano-voids in Magnesium under hydrostatic tensile stress
Modelling Simul. Mater. Sci. Eng. 24 065003 (2016)