Nonlinear and Linear Elastodynamics Transformation Cloaking
Abstract
Invisibility has been a dream for centuries. The idea of cloaking has been explored in many fields of science and engineering, e.g., conductivity, electrical impedance tomography, electromagnetism, acoustics, thermodynamics (design of thermal cloaks), diffusion, and elastodynamics. The least understood among these applications is elastodynamics. The first ideas of hiding holes (cavities) from static stress fields go back to the 1930s and 1940s. However, the first theoretical work on hiding cavities from elastic waves is only eleven years old (Milton, G. W., Briane, M. and Willis, J. R., On cloaking for elasticity and physical equations with a transformation invariant form. New Journal of Physics 8: 248, 2006.). This proposed research program will lay the mathematical foundations of elastodynamics cloaking in the settings of both nonlinear and linear elasticity. The practical outcome of this project will be some design guidelines for hiding cavities from elastic waves. The specific problems of interest in this research program can be summarized as follows: i) A mathematical formulation of cloaking transformations in nonlinear and linear elastodynamics and providing rigorous proofs that the proposed cloaks will work. ii) Providing formulas and algorithms for finding the inhomogeneous and anisotropic mechanical properties of nonlinear and linear elastic cloaks. iii) Analytical and computational examples of linear and nonlinear elastic cloaks. iv) Cloaking multiple cavities in infinite media and cloaking multiple cavities or half-cavities in semi-infinite domains (carpet cloaking). v) Design of elastic cloaks in thin plates. vi) Development of new perfectly-matched layers (PML) with symmetric elastic constants for computational modeling of cloaks. Cloaking objects from stress waves will have significant applications, some of which will be extremely important for Army. Design of the next generation armor capable of redirecting stress waves, shielding and protecting critical structures from surface (Rayleigh) waves, e.g. explosions and earthquakes, hiding multiple objects from elastic waves, and cloaking holes in shell structures are some examples.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Mar 04, 2019
- Source ID
- W911NF1810003
Entities
People
- Arash Yavari
Organizations
- Army Contracting Command
- Georgia Tech Research Corporation
- United States Army