By experimentally verifying the existence of Willis coupling, Mechanical Engineering Assistant Professor Michael Haberman and his team have laid a foundation for new research that makes use of its unique material response. The findings lend themselves to a wide range of applications in acoustical engineering ranging from sound diffusers in architectural acoustics to biomedical imaging using ultrasonic waves.
UT Austin Researchers:
Preston S. Wilson, Michael R. Haberman
Discovery:
This research provided experimental and theoretical demonstrations of a dynamic material behavior known as Willis coupling. Willis coupling is the acoustic analog to bianisotropy in electromagnetism and a result of a material having asymmetries in its small-scale structure. This research also focused on determining an experimental procedure to extract the effective material properties of a sample that has this Willis coupling parameter.
How It Works:
Willis coupling is an acoustical material property in which the pressure-strain relationship (Hooke’s law) is coupled to its momentum-velocity relation (Newton’s law). As a result, if you dynamically squeeze or stretch an object made from a material demonstrating Willis coupling, the object will want to translate due to an induced momentum. To achieve this coupling response, the small-scale structure of the object must be asymmetric. The microstructural asymmetry can be due to small-scale geometry, the distribution of material properties in a mixture of multiple materials, or both. The small-scale asymmetry produces non-uniform stress fields with a preferential direction when the object is uniformly squeezed or stretched. If the mechanical deformation is dynamic, the preferential stress fields will generate momentum.
Why It Matters:
Although theorized by J.R. Willis at the University of Cambridge in the UK several decades ago, Willis coupling had not been experimentally demonstrated prior to this work. Willis coupling represents a new material parameter that provides engineers and scientist with an additional degree of freedom in the design of acoustical devices. By experimentally verifying the existence of Willis coupling, Dr. Haberman and his team have laid a foundation for new research that makes use of this unique material response. The findings lend itself to a wide range of applications in acoustical engineering ranging from sound diffusers in architectural acoustics to biomedical imaging using ultrasonic waves.
Published: M.B. Muhlestein, C.F. Sieck, P.S. Wilson, M.R. Haberman, “Experimental evidence of Willis coupling in a one-dimensional effective material element,” Nature Communications, 8, 15625, (2017).
What's Next:
Dr. Haberman is currently working on National Science Foundation funded research to create non-reciprocal elastic materials that can allow sound to travel in one direction but prevent it from travelling back in the opposite direction. Using a material that has an asymmetric structure will serve as a critical step towards the goal of inducing momentum and therefore generating non-reciprocal elastic wave phenomena. That work is in collaboration with Dr. Seepersad in UTME and colleagues at Rutgers University (A. Norris) and The University of Missouri (G. Huang).
