Mechanics of thin elastic rods: engineering meets computer graphics
Event details
| Date | 10.02.2016 |
| Hour | 13:30 › 14:30 |
| Speaker |
Dr. M. Khalid Jawed, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge MA Bio: Khalid Jawed is a PhD candidate in mechanics at the Department of Mechanical Engineering, Massachusetts Institute of Technology. His research focuses on the mechanics of slender rods; e.g. fuel pipelines, knots in ropes, bacterial flagella. He attained his Master’s degree from the same institution in 2014. He received his undergraduate degrees in Aerospace Engineering and Engineering Physics from the University of Michigan in 2012. His research interest lies in developing numerical tools and computerized systems to exploit the functionality of materials. |
| Location | |
| Category | Conferences - Seminars |
Thin rods are ubiquitous in both nature (e.g. bacterial flagella, human hair) and engineering (ropes, cables), from the micron to the kilometer scale, and often undergo extreme deformation. The geometric nonlinearities that result from the deformation process pose enormous challenges to traditional analytical and numerical tools. Moreover, it is often unfeasible to perform experiments at the original length scale of these systems. We overcome these challenges by combining model experiments and cutting-edge computational tools ported from computer graphics, towards developing predictive physical understanding of these systems. The prominence of geometry in this class of systems enables the scaling (up or down) of the problem to the desktop scale, which allows for systematic experimental exploration of parameter space. In parallel, we conduct numerical simulations using the Discrete Elastic Rods (DER) method, which was originally developed for the animation industry for special effects of the visually dramatic dynamics of hair, fur, and other rod-like structures. For the first time, we port DER into engineering as a predictive computational tool and test ride it against our own model experiments by studying two a priori unrelated problems, at disparate length scales. The excellent agreement found between experiments and simulations illustrates the predictive power of our approach. Scaling (up or down) to the original application then offers unprecedented tools for rationalization and engineering design.
(i) Laying of submarine cables onto the seabed (kilometer scale). We developed a model system to study the nonlinear coiling patterns that emerge when a thin elastic rod is deployed onto a moving substrate (conveyor belt). Excellent quantitative agreement is found between experiments and the DER simulations, with no fitting parameters. We identify the characteristic length scales, systematically explore parameter space and map out phase diagrams. Particular emphasis is given to the sinusoidal patterns (the first mode of instability) for which we find a close-form analytical description.
(ii) Locomotion of single-flagellar bacteria (micron scale). We consider a macroscopic analog model to study the rotation of a helical elastic rod immersed in a viscous fluid, at low Reynolds numbers. We tackle this fluid-structure interaction problem (elastic forces couple to hydrodynamics) by implementing Lighthill’s slender body theory into DER to fully capture the geometrically nonlinear configurations of the rod. Our numerics are again in excellent quantitative agreement with experiments, with no fitting parameters. A novel mechanical instability is uncovered, whereby the flagellum buckles above a critical rotation frequency. We demonstrate that bacteria in nature swim close to this threshold frequency, and therefore can possibly exploit this instability for physiological purposes, e.g. to change its swimming direction.
This research was performed with Pedro Reis (MIT), Noor Khouri (MIT), Eitan Grinspun (Columbia University), and Fang Da (Columbia University).
(i) Laying of submarine cables onto the seabed (kilometer scale). We developed a model system to study the nonlinear coiling patterns that emerge when a thin elastic rod is deployed onto a moving substrate (conveyor belt). Excellent quantitative agreement is found between experiments and the DER simulations, with no fitting parameters. We identify the characteristic length scales, systematically explore parameter space and map out phase diagrams. Particular emphasis is given to the sinusoidal patterns (the first mode of instability) for which we find a close-form analytical description.
(ii) Locomotion of single-flagellar bacteria (micron scale). We consider a macroscopic analog model to study the rotation of a helical elastic rod immersed in a viscous fluid, at low Reynolds numbers. We tackle this fluid-structure interaction problem (elastic forces couple to hydrodynamics) by implementing Lighthill’s slender body theory into DER to fully capture the geometrically nonlinear configurations of the rod. Our numerics are again in excellent quantitative agreement with experiments, with no fitting parameters. A novel mechanical instability is uncovered, whereby the flagellum buckles above a critical rotation frequency. We demonstrate that bacteria in nature swim close to this threshold frequency, and therefore can possibly exploit this instability for physiological purposes, e.g. to change its swimming direction.
This research was performed with Pedro Reis (MIT), Noor Khouri (MIT), Eitan Grinspun (Columbia University), and Fang Da (Columbia University).
Practical information
- Informed public
- Free
- This event is internal
Organizer
- IGM
Contact
- Prof J. Botsis