Morphing origami & Geometric mechanics
We created a new origami-based pattern that can exhibit extremely tunable Poisson's ratio going theoretically from negative infinity to positive infinity as it folds and that can morph into a hybrid material system with re-programmable combination of contrasting metamaterials.
Acoustic metamaterials are lattice-based mechanical systems that exhibit unique elastic wave propagation behavior by virtue of frequency bandgaps or other related phenomenon. Presence of such bandgaps prevent elastic wave propagation through solid materials within particular ranges of frequencies. We developed a theoretical framework to study such lattices with non-local structural interactions and applied it to origami metamaterials to discover tunable frequency bandgaps by virtue of the foldable nature of origami.
High-performance parallel computing
Developed very efficient massively parallel frameworks to computationally simulate nanoscale systems with thousands of atoms using our linear scaling ab-initio method. This framework could lead to fundamental understanding of structural failure of metallic solids through first principles simulations.
The parallel scaling efficiency of the AAR solver that we developed was studied and found to be competitive with respect to the state-of-the-art methods used to solve very large, sparse linear systems of equations.
Linear/Non-linear solvers, Iterative methods
Developed iterative methods based on Jacobi iteration and Anderson extrapolation technique to solve very large, sparse linear systems of equations as well as non-linear equations. Competitive performance was demonstrated with respect to the state-of-the-art methods.
Instability prediction in atomic systems
Developed an instability prediction criterion for large atomic systems based on Lanczos iteration. Applied it to predict defect nucleation during nanoindentaton and hydrostatic cavitation.
Linear scaling Density Functional Theory
State-of-the-art software for quantum mechanical calculations of metallic atomic systems using Density Functional Theory (DFT) scale cubically with number of atoms and therefore are restricted to a few hundred atoms in routine calculations. We developed a linear scaling DFT framework that allows us to scale to very large atomic systems by employing massively parallel computer architectures. Eventually, such extreme calculations could be used to understand nanoscale mechanics of material failure that could lead to developing advanced high-performance materials.