Nonlinear and Linear Elastodynamics Transformation Cloaking
Abstract
Major Goals: The main goal of this project was to lay the mathematical and physical foundations of transformation elasticity and elastodynamic cloaking. Understanding the transformation properties of the governing equations of nonlinear and linearized elasticity for different types of materials is a crucial task for systematic design of elastic cloaks. This study was done in the settings of both linear and nonlinear elasticity. In elastic cloaking one would like to hide an object (a hole, inhomogeneity, inclusion, etc.) from elastic waves. Accomplishments: We formulated transformation cloaking as a bijective map between the boundary-value problems of the physical body and a virtual body that is homogenous and has no holes/inhomogeneities. We carefully studied this problems for nonlinear elasticity, classical linear elasticity, small-on-large theory, gradient solids, and (generalized) Cosserat solids. We have proved several no-go theorems for transformation cloaking. It turns out that the balance of angular momentum is the obstruction to exact elastic cloaking. However, we have found an example of a cylindrical cloak that can exactly cloak a cylindrical cloak under any in-plate excitations. We also studied the problem of cloaking for elastic plates. It turns out that exact transformation cloaking is not possible for elastic plates either. Our final conclusions are: i) Exact transformation cloaking is not possible in elastic materials. ii) The existing works in the literature in the past fifteen years have some fundamental flaws. iii) The path forward for cloaking applications is approximate cloaking.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 30, 2022
- Accession Number
- AD1222774
Entities
People
- Arash Yavari
Organizations
- Georgia Tech