Anisotropic elastic metamaterials

A method for manufacturing an elastic metamaterial for an acoustic radiator, the method comprising:

• defining an array of unit cells that form the acoustic radiator, the array including an elastic medium comprising a solid phase material selected from the group consisting of polymers, polymer-based materials, metals, and composite materials, and having an x-axis defining a longitudinal direction, a y-axis defining a transverse direction with respect to the x-axis, and a z-axis perpendicular to both the x-axis and the y-axis;
• determining a set of boundary conditions for a plurality of non-spherical apertures defined in the elastic medium of the array, with each non-spherical aperture disposed within a boundary defined by a single respective unit cell of the array;
• using a gradient-based algorithm to optimize a porous media model domain for the elastic medium, the gradient-based algorithm comprising a topology optimization problem solved according to constitutive laws associated with a linearly elastic medium, and where porosity is related to size dimensions of the non-spherical aperture and an anisotropic elastic modulus is related to an angle of orientation of the non-spherical aperture;
• optimizing an objective function, and obtaining a grayscale design that relates to the porosity and the anisotropic elastic modulus;
• using reaction diffusion equations to de-homogenize the grayscale design to obtain a pattern for the non-spherical apertures;
• and
• manufacturing the elastic metamaterial by forming the pattern for the non-spherical apertures in the solid phase material such that the non-spherical apertures extend through the solid phase material.