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The design of broadband mechanical metamaterials in the context of acoustics can be driven by the invariance of the wave equation under a set of special coordinate transformations called transformation acoustics. A program of homogenization to design the metamaterial structure can be derived from these transformation functions subject to geometric constraints from the metamaterial’s intended application. The limits of homogenization in a nonperiodic, nonlinear environment however must be accounted for and corrected. This can be done by means of nonlinear manifold interpolation methods, the feedback into which is driven by the scattered wave field in the ambient medium. The feedback is minimized using statistical and machine learning techniques, dictating the final metamaterial structure. The performance of this algorithmic method is compared against a “brute force” optimization approach driven by a convolutional neural network with no transformation of the underlying wave equation.The design of broadband mechanical metamaterials in the context of acoustics can be driven by the invariance of the wave equation under a set of special coordinate transformations called transformation acoustics. A program of homogenization to design the metamaterial structure can be derived from these transformation functions subject to geometric constraints from the metamaterial’s intended application. The limits of homogenization in a nonperiodic, nonlinear environment however must be accounted for and corrected. This can be done by means of nonlinear manifold interpolation methods, the feedback into which is driven by the scattered wave field in the ambient medium. The feedback is minimized using statistical and machine learning techniques, dictating the final metamaterial structure. The performance of this algorithmic method is compared against a “brute force” optimization approach driven by a convolutional neural network with no transformation of the underlying wave equation.

Transformation acoustics uses invertible maps to transform a cloaked region to a region with a smaller scatterer. The “elastic” or Norris class of acoustic cloaking theory is inherently broadband, in that it does not rely on the presence of resonant effects. To achieve the properties required by the transformation theory, we utilize pentamode materials, which admit the use of finite mass but require anisotropic stiffness throughout the material. These types of materials do not exist naturally and must be fabricated through the use of metamaterials. One of the challenges associated with metamaterials for use in dynamic applications is the distribution of mass in a unit cell and its consequences for frequency-dependent behavior in the metamaterial. Various homogenization techniques for recovering wave speed properties of the metamaterial unit cells may predict contradictory wave speed values for pentamodal structures. These disagreements can be explained through the distribution of inertia in the material a...

Functionally graded acoustic metamaterials (FGAMs) can be designed to have specific waveguide properties dictated by a theory relevant to the application. Frequently, these material properties do not exist naturally, and must be fabricated by gradually layering manufactured unit cell microstructures, resulting in a (usually smooth) variation of properties. Tailoring these microstructures to the demands of the relevant theory requires assembling microstructures with very specific material properties—a process that often requires haphazardly searching a large domain space of unit cells for desirable parameter combinations. Moreover, the process of determining the material tensor of interest for a specific set of metamaterial cell design parameters typically involves solving a costly high dimensional finite element problem for each new microstructure cell of interest. This work presents a gradient-based, manifold interpolation technique to characterize acoustic metamaterial homogenized elastic tensors. An ad...

The field of acoustic metamaterial research has been driven, first, by transformation acoustics cloaking theory. This and other theoretical approaches optimize an acoustic effect through definition of artificial material properties which at present are only achievable using metamaterial technology. Metamaterials, however, present separate challenges in optimization for any desired acoustic effect: in particular, their dynamic behavior depends on parameters unrelated to acoustics, and exhibits wave propagation behavior more complex than elastic or acoustic continua. Homogenization methods which assume Cartesian symmetry are a staple in metamaterial design, but these only approximate a feasible optimal design. Moreover, total reliance on homogenized continuum models provides no information about the actual microstructure performance, and presents problems in functionally graded applications. To overcome this, we augment our Cartesian homogenization processes with high-resolution finite element models to optimize the design. Comparatively computationally expensive implicit FEM is avoided; specifically tailored time-domain wave propagation codes make the analyses feasible. Examples of the process, combining Cartesian homogenization estimates with high-resolution microstructural wave propagation solutions, will be shown.The field of acoustic metamaterial research has been driven, first, by transformation acoustics cloaking theory. This and other theoretical approaches optimize an acoustic effect through definition of artificial material properties which at present are only achievable using metamaterial technology. Metamaterials, however, present separate challenges in optimization for any desired acoustic effect: in particular, their dynamic behavior depends on parameters unrelated to acoustics, and exhibits wave propagation behavior more complex than elastic or acoustic continua. Homogenization methods which assume Cartesian symmetry are a staple in metamaterial design, but these only approximate a feasible optimal design. Moreover, total reliance on homogenized continuum models provides no information about the actual microstructure performance, and presents problems in functionally graded applications. To overcome this, we augment our Cartesian homogenization processes with high-resolution finite element models to opt...

Functionally graded acoustic metamaterials (FGAMs) can be designed to have specific waveguide properties. In sonar applications, FGAMs can be tailored to resist incident wave reflection. As these materials do not exist naturally, they must be fabricated by gradually layering manufactured, resulting in a (usually smooth) variation of properties. Validating material properties of FGAMs is difficult with conventional tests, as the distribution of material properties over the layered structure results in a non-unique solution if typical data (e.g., compressive strain) is measured. This talk will demonstrate an approach to characterize the functionally graded material properties by parameterizing how the functionally graded material changes throughout the specimen. Experiments designed to minimize the uncertainty surrounding the FGM model parameters are formulated and evaluated numerically. The FGM model parameters are estimated by Markov chain Monte Carlo so that a probability distribution surrounding each parameter is recovered. Probability distributions enable uncertainty quantification (UQ) surround the validated material parameters. UQ is important as uncertainty surrounding the parameter results directly translates into uncertainty surround the FGM performance. The approach is verified by bootstrap analyses of known FGAM distributions.

Acoustic metamaterials use sub-wavelength, anisotropic, and inhomogeneous microstructures. Macroscopic properties can be related to the microstructure using homogenization theory Hassani and Hinton [Comput. Struct. 69, 719–738 (1998), which allows an analyst to confirm the extent to which a candidate metamaterial microstructure meets the requirements for a pentamode cloaking material. Norris [Proc. R. Soc. Ser. A, 464, 2411–2434 (2008)] presented a theory of transformation acoustics that enables the realization of inhomogeneous pentamode acoustic materials having anisotropic elastic tensors, isotropic density and finite mass. This theory describes the spatially varying material properties in terms of a mapping, which for separable geometries may be generated using a scalar function. This function, the constraints on its behavior implicit in the Norris theory, and the material equations constitute the defining relations for pentamode transformation acoustics. Previously, analytic work in transformation acoustics developed the material properties after having fixed a transformation. By reversing the process, we create a number of new families of pentamode cloaking materials. We validate the concept with three-dimensional explicit transient finite element simulations.

Acoustic metamaterials need to be realized using subwavelength microstructures. By tailoring the microstructure of the underlying unit cell, different effective properties at the macroscopic scale may be achieved. These macroscopic properties can be related to the microstructure using homogenization theory. The problem of designing a pentamode acoustic metamaterial is formulated as the minimization of an objective functional representing the difference between the homogenized properties and the target pentamode acoustic metamaterial properties. A quasi‐Newton optimization approach is used to solve the optimization problem. Such an approach requires the gradient of the objective function with respect to the microstructural properties at every iteration, and hence the cost of gradient computation must be low. The gradient is calculated efficiently using the adjoint approach which requires the solution of only two (primal and dual) finite element problems, per homogenization deformation field, independent of...