Research

Our research is focused on the development of new numerical methods that enable the investigation of emerging theories in applied mechanics, with a particular emphasis on the important role played by interfaces and defects. Our work is interdisciplinary and combines civil and mechanical engineering, applied mathematics, computer science, and materials science.

Research Areas

Our lab is interested in understanding the behavior of systems that fail suddenly when subjected to extreme loading conditions.

Shock Wave and Laster Lithotripsy are highly effective treatments for the removal of kidney stones. Numerical modeling of the damage and fragmentation of kidney stones during these processes are the goals of this project. Finite element approach in combination with phase field damage model are employed for the numerical modeling of experiments performed at Duke University.

Multiphase flow through granular and porous materials exhibits complex behavior, and the understanding of the underlying physical phenomena remains an ongoing challenge.  These systems routinely exhibit a complex coupling of phenomena linking pore-scale mechanisms to dynamics at the macro-scale.  A current example concerns the connection between the mode of gas invasion in sediments at the pore level governing whether methane hydrate forms as concentrated veins that are useful for energy production, or instead in a much more disperse manner.  

When a densely packed monolayer of hydrophobic particles is placed on the surface of a liquid, the particles interact through capillary bridges, leading to the formation of particle rafts. The macroscopic properties of these rafts reflect an interplay between fluid and solid mechanics, giving rise to novel physics. This interplay is relevant to a wide range of applications, from the synthesis of ‘‘liquid marbles’’ to the design of drug delivery systems to the stabilization of drops.

Researchers in the DCML are actively developing models and simulations of stimulus-responsive hydrogels (SRHs). These materials exhibit dramatic volume changes in response to small changes in external stimuli, such as temperature, solvent concentration, and light. They are biologically inspired materials, and are of interest for use in a number of micro-scale devices.

Researchers in the DCML are actively developing new computational methods to treat fluid-structure interaction. This is an important class of problems that has come to the forefront recently with the emphasis on wave energy conversion systems. These systems translate wave motion into structural motion, that is eventually used to generate electricity.

One of the main research thrusts in our laboratory concerns computational fracture mechanics. Fracture and failure at large scales represent fascinating phenomena. When material systems and structures fail, they often do so in catastrophic ways. We seek to develop simulations of fracture and failure that are physically faithful and robust, such that models can be both calibrated against experimental observations and also have the potential to be genuinely predictive. Toward these goals, gradient damage and phase-field models of fracture have proven to be one of our workhorses over the past decade. These methods have been demonstrated to reliably capture fracture and failure phenomena in three dimensions for quasi-brittle systems.

Researchers in Duke's Computational Mechanics Laboratory are actively developing new methodologies and algorithms to robustly capture the physics of evolving interfaces. Our work is distinguished by the use of the finite element method for this class of problems. Typically, the FEM is only used to capture evolving interfaces when the mesh is continuously adapted (re-meshed) to "fit" the interface. This can be incredibly costly and usually requires the use of many heuristics, particularly when topology changes are frequent.