Acoustically transparent and acoustic wave steering materials for acoustic cloaking and methods of fabrication thereof
Disclosed an acoustically transparent material including an acoustic wave steering material, and methods for fabrication and use thereof. The materials are specially designed structures of homogenous isotropic metals. These structures are constructed to propagate waves according to Pentamode elastic theory. The metamaterial structures are two-dimensional, intended to propagate acoustic waves in the plane in a manner which closely emulates the propagation of waves in water. The acoustically transparent materials described herein have particular utility as acoustic wave steering materials and acoustic cloaks.
1. A computer-implemented method for designing an acoustic cloaking material having anisotropic stiffness and an isotropic mass, comprising the following steps:
selecting one or more material microstructures for a cloak;
defining a variation of one or more target material properties at a plurality of locations in the cloak, wherein the target material properties include anisotropic elastic tensor (C) and isotropic mass density (ρ) properties;
evaluating anisotropic elastic tensor (C) and isotropic mass density (ρ) properties of the selected material microstructures by comparison to the target material anisotropic elastic tensor (C) and isotropic mass density (ρ) properties, wherein the comparison of the material microstructures to the target material properties is performed using an elastic homogenization theory; and
refining or altering the selected material microstructures, on the basis of their deviation from the target material anisotropic elastic tensor (C) and isotropic mass density (ρ) properties;
Wherein the cloak includes multiple layers, and wherein the isotropic mass density (ρ) and anisotropic elastic tensor (C) properties for each layer are independently defined using separate mappings, wherein the mappings are constrained so that the material properties at the interface between layers in the volume of the cloak are substantially continuous.
2. The computer-implemented method of claim 1 , wherein defining the target material anisotropic elastic tensor (C) and isotropic mass density (ρ) properties for the cloak comprises:
defining a cloak using a specific mathematical transformation which results in a uniform isotropic mass density (ρ) throughout its volume.
3. The computer-implemented method of claim 1 , wherein defining the target material anisotropic elastic tensor (C) and isotropic mass density (ρ) properties for the cloak comprises:
defining a cloak using a specific mathematical transformation which results in a distribution of the anisotropic elastic tensor (C) such that the radial-direction elastic modulus is uniform throughout its volume.
4. The computer-implemented method of claim 1 , wherein defining the target material anisotropic elastic tensor (C) and isotropic mass density (ρ) properties for the cloak comprises:
defining a cloak using a specific mathematical transformation which results in a mass density (ρ) that varies as a function of a radial coordinate of a point of the cloak raised to an arbitrary power.
5. The computer-implemented method of claim 1 , wherein defining the target material anisotropic elastic tensor (C) and isotropic mass density (ρ) properties for the cloak comprises:
defining a cloak using a specific mathematical transformation which results in a distribution of the anisotropic elastic tensor (C) such that a radial elastic modulus is uniform throughout its volume, resulting in a distribution of the anisotropic elastic tensor (C) such that the radial-direction elastic modulus varies as a function of a radial coordinate of a point of the cloak, raised to an arbitrary power.
6. The computer-implemented method of claim 1 , wherein defining the target material anisotropic elastic tensor (C) and isotropic mass density (ρ) properties for the cloak comprises:
defining a cloak using a specific mathematical transformation which results in a minimization of the elastic anisotropy of the cloak.
7. The computer-implemented method of claim 1 , wherein the materials selected for the acoustic cloak structure comprise one or more of polymers, composites, or metals.
8. The computer-implemented method of claim 1 , wherein the structure of the acoustic cloak for d=2 consists of arrangements of regular hexagonal unit cells with equilateral sides, or irregular cells with sides of different lengths or unequal angles.
9. A system for designing an acoustic cloaking material, comprising a processor configured to:
select one or more material microstructures for a cloak;
define a variation of one or more target material properties at a plurality of locations in the cloak, wherein the target material properties include anisotropic elastic tensor (C) and isotropic mass density (ρ) properties;
evaluate anisotropic elastic tensor (C) and isotropic mass density (ρ) properties of the selected material microstructures by comparison to the target material anisotropic elastic tensor (C) and isotropic mass density (ρ) properties, wherein the comparison of the material microstructures to the target material properties is performed using an elastic homogenization theory; and
refine or alter the selected material microstructures on the basis of their deviation from the target material anisotropic elastic tensor (C) and isotropic mass density (ρ) properties;
Wherein the cloak includes multiple layers, and wherein the isotropic mass density (ρ) and anisotropic elastic tensor (C) properties for each layer are independently defined using separate mappings, wherein the mappings are constrained so that the material properties at the interface between layers in the volume of the cloak are substantially continuous.