My main interest lies in understanding and modeling the behavior of materials and structures across length and time scales, ranging from atomistic to macroscopic, and over a variety of conditions, from quasistatic to extremes of pressure, temperature and rate of deformation. I am particularly interested in multiscale aspects of material behavior and the structure/property relation, including the development and evolution of microstructure during deformation and its role in shaping the macroscopic response of materials and structures.
I am also interested in understanding the limits of usability of materials, e.g., formability limits, failure mechanisms, fatigue life prediction, plastic deformation, fracture and fragmentation, material and structural instabilities, and others. From a methodological point of view, the main goal is to develop mathematical and computational methods enabling the application of high-fidelity multiscale material models to engineering systems, with a particular view to predicting their behavior under operational conditions with quantified uncertainties. Modern nonlinear analysis and high-performance computing are two disciplines that I find particularly useful in that regard and that have provided, and continue to provide, the basis and the focus for much of my work.
Some of the currently funded research projects that I am involved in at Caltech are:
- U.S. Army Research Laboratory through the Materials in Extreme Dynamic Environments Collaborative Research Alliance (University lead PI: K.T. Ramesh). The purpose of this work is to deploy a rigorous methodology of uncertainty quantification in which the requisite uncertainty bounds are supplied by concentration-of-measure (CoM) inequalities. These inequalities exploit the so-called concentration-of-measure phenomenon, which is a non-linear generalization of the law of large numbers.
- Office of Naval Research: Constitutive Modeling of Glass at Extreme Pressure and Loading Rates. Glass is attractive for armor applications because of its low density (~2.2 g/cm3), high strength (~5-6 GPa), volume expansion following fracture and energy dissipation due to densification. To date, no model exists that predicts these properties of glass, which hampers efforts to evaluate the true potential of glass for armor applications. The proposed work addresses this gap and is concerned with the development of a finite-deformation model of the inelasticity of glass under general multiaxial deformation histories, including irreversible dilation and densification, mixed states and microstructure, hysteresis and dissipation, rate-dependency and thermal softening, for use in terminal ballistics simulations.
- Office of Naval Research: Unlocking the unexpected behaviors of polyurea. Polyurea exhibits extraordinary behavior at high pressures and strain rates of deformation. However, the root causes of that behavior as still imperfectly understood. The work under the grant is directed at evaluating a number of micromechanical hypotheses and ascertaining their ability to explain the observed anomalous behavior of polyurea under extreme conditions of pressure and rate of deformation. The expected outcome of the research will be a fundamental understanding of the root causes of the unexpected behaviors of polyurea.
- US National Institutes of Health (NIH): Oncotripsy, Molecular Functional Ultrasound for Non-Invasive Imaging and Image-Guided Recording and Modulation of Neural Activity. Ultrasonic neuromodulation (UNM) is among the most significant new technologies being developed for hu-man neuroscience because it can provide non-invasive control of neural activity in deep-brain regions with mil-limeter spatial precision. This capability complements human imaging techniques for studying brain connectivity and function in basic and clinical applications. However, despite a surge of interest in UNM, the lack of knowledge about its mechanisms and recent findings of off-target sensory effects accompanying direct neuromodulation pose significant challenges to the use of this technology in human neuroscience. To overcome these challenges, we leverage a mechanistic understanding of ultrasonic neuromodulation to engineer methods for direct, spatially selective control of human brain function.