CAREER: Transformation Elastodynamics and its Application to Wave Control in Solids

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This Faculty Early Career Development (CAREER) project supports fundamental research needed to realize mechanisms of control of waves in solids. Information and energy in the world travel from one point to another in the form of waves. Examples include electromagnetic waves such as light and radio waves, sound waves in air and water, and elastic waves in solids. The ability to control the flow of these waves, therefore, indirectly leads to the ability to control the information and energy which these waves represent. Strong material design mechanisms have recently been developed to control the flow of electromagnetic and acoustic waves. However, controlling waves in solids has proven to be more difficult, and resolving associated challenges is the main focus of this project. This research will have beneficial impact on several U.S. economic, security, and energy interests. It will lead to improvements in the design of vibration sensors, transducers, and imaging devices with applications to various industries such as aerospace, automobile, civil infrastructure. It will lead to novel earthquake mitigation techniques for civil structures and vibration mitigation techniques for sensitive industry equipment. Through the various outreach efforts proposed here, this research will help in broadening the participation of the general public in the highly multi-disciplinary subject of waves and their control.Transformation methods have emerged as effective tools for the control of electromagnetic and acoustic waves. However, analogous successes have not been achieved for elastodynamics (waves in solids). This research aims to fill the knowledge gap by investigating a coupled constitutive form (Willis form) as the basis upon which the principles and applications of transformation elastodynamics can be built. Furthermore, this research aims to provide fundamental limits and bounds on the performance of any transformation device through the application of causality principle and scattering theory. The PI will conduct theoretical studies into elastodynamic homogenization, performance bounds of transformation-elastodynamic devices and will assess performance gains through the application of classes of Euclidean and non-Euclidean transformations. Level-set based parallel computational algorithms will be also developed for inverse design of transformation-based devices. Three-dimensional printed models of transformation-elastodynamic devices, at both the unit cell and the device levels, will be fabricated and tested through ultrasonic wave measurements for experimental verification.