Nonlinear Elastodynamics Cloaking
Abstract
The technical objective of the proposed effort is to explore and create a precise formulation of nonlinear and linearized elastodynamics cloaking. The proposed effort is motivated by a unique opportunity to achieve and exploit cloaking in elastodynamics. While one of the original publications on the topic (Milton 2006), claimed that Navier s equations of linear elastodynamics are not invariant under coordinate transformations (in contrast to Maxwell s equations), concluded that cloaking for linear elastodynamics is not possible, other researchers have begun to question the claim which founds this conclusion. The proposed effort seeks to establish a mathematically precise formulation of this problem and will focus on four primary tasks. First, the proposed effort will seek to develop a rigorous formulation of the cloaking problem in elastodynamics. This will be explored in the framework of nonlinear elasticity to be able to distinguish between referential and spatial (coordinate) transformations, where cloaking transformations will be a particular class of time-independent referential di ffeomorphisms. Second, a careful study of invariance or lack of invariance of the governing equations of both nonlinear and linearized elasticity under referential diffeomorphisms will be undertaken. Third, the effect of push forward by referential diffeomorphisms on the type of anisotropy expected in the cloaking region will be captured. Finally, the possibility of neutral inclusions and neutral holes in nonlinear elasticity in both 2D and 3D will be determined. In this manner, the proposed effort will seek to establish the mathematical foundations necessary to guide a robust exploration of elastodynamics cloaking.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jan 12, 2017
- Source ID
- W911NF1610064
Entities
People
- Arash Yavari
Organizations
- Army Contracting Command
- Georgia Tech Research Corporation
- United States Army