The Nonlinear Mechanics Research Group is housed in the George W. Woodruff School of Mechanical Engineering at the Georgia Institute of Technology. We perform research in traditional and emerging areas of mechanical engineering where we focus on nonlinear mechanics. Areas currently active in the research group: computational modeling of phonon spectra in nanostructured materials; computational design of phonon spectra band gaps; large deformation dynamic behavior of carbon nanotubes; mechanics of steel pushing-belt continuously variable transmissions; vehicle hybrid transmission architectures and their control; and the application of cellular automata in computational mechanics.
Phonon Spectra Modeling
We study phonon behavior in nanostructured materials, such as carbon nanotubes, using a multi-scale approach combining tensor-based continuum modeling, representative area elements, and interatomic potentials. Solutions are obtained via a small number of specially formulated shell-like finite elements. The method generalizes well to imperfections and non-idealized geometries, making it very attractive for studying real systems. Our present focus is on extending the method to predict dispersion relationships, and ultimately thermal properties of nano-scale materials.
We are just starting an effort to adapt our previous analytical and computational models of Front End Accessory Drives (FEADs) to model pushing-belt Continuously Variable Transmissions (CVTs). CVTs typically see application in hybrid vehicles, but can also replace standard automatic transmission with fuel savings of nearly 10%. Their operational behavior is significantly more complicated than conventional V-belt and serpentine drives due to hydraulically-controlled steady-state and shifting behavior. The current project aims to develop highly-accurate nonlinear mechanics models coupled to high-fidelity control modeling. The models are expected to yield higher torque-rated CVT designs which suffer from less slip, more efficiency, and greater longevity.
Cellular Automata Modeling
We have developed an alternative computational modeling technique for studying elastodynamic wave motions and other problems in linear and nonlinear elasticity. Cells can be rectangular for regular geometries (highest accuracy), or triangular for complex geometries.
The approach uses local rules dependent on a cell’s state and its neighbors’ states. Comparisons to staggered-grid finite difference and finite element simulations show that the cellulular automata approach is as accurate with less numerical ‘ringing’ and more symmetry in the left-ward and right-ward moving waves. We also avoid Gibbs phenomena present in finite element simulations.
Many future directions are being considered.
Multi-Scale Acoustic Absorption
We are developing multi-scale computational tools for predicting acoustic absorption and band-gap behavior in periodic porous materials. Our focus is on posing the multi-scale equations in a manner suitable for incorporation into commercial codes, such as COMSOL. Our present focus is on designing super lattice materials with acoustic band gaps at desired frequencies. These materials will be useful in applications such as wave guides, filters, and sound isolation.
Wave Propagation in Nonlinear Media
We have developed novel perturbation schemes for predicting, in closed-form, the dispersion relationships of waves traveling in one- and two-dimensional nonlinear materials. The materials considered are in discrete, lattice form, including crystalline materials. We have found that the nonlinear parameters present allow for amplitude-dependent tuning of the material response. In one-dimensional chains this allows for tunable filters. In two-dimensional lattices, we have observed tunable wave beaming, or steering.
Protein Folding and Biological Modeling
Follow the link entitled “Folding Sim” for a preliminary multi-scale simulation of a protein undergoing folding. More to follow soon…