GRIDS-Net: Inverse shape design and identification of scatterers via geometric regularization and physics-embedded deep learning

This study presents a deep learning based methodology for both remote sensing and design of acoustic scatterers. The ability to determine the shape of a scatterer, either in the context of material design or sensing, plays a critical role in many practical engineering problems. This class of inverse problems is extremely challenging due to their high-dimensional, nonlinear, and ill-posed nature. To overcome these technical hurdles, we introduce a geometric regularization approach for deep neural networks (DNN) based on non-uniform rational B-splines (NURBS) and capable of predicting complex 2D scatterer geometries in a parsimonious dimensional representation. Then, this geometric regularization is combined with physics-embedded learning and integrated within a robust convolutional autoencoder (CAE) architecture to accurately predict the shape of 2D scatterers in the context of identification and inverse design problems. An extensive numerical study is presented in order to showcase the remarkable ability of this approach to handle complex scatterer geometries while generating physically-consistent acoustic fields. The study also assesses and contrasts the role played by the (weakly) embedded physics in the convergence of the DNN predictions to a physically consistent inverse design.Comment: 23 pages of main text, 10 figure

Nonlocal elastic metasurfaces: enabling broadband wave control via intentional nonlocality

While elastic metasurfaces offer a remarkable and very effective approach to the subwalength control of stress waves, their use in practical applications is severely hindered by intrinsically narrow band performance. This work introduces the concept of intentional nonlocality as a fundamental mechanism to design passive elastic metasurfaces capable of an exceptionally broadband operating range. The nonlocal behavior is achieved by exploiting nonlocal forces, conceptually akin to long-range interactions in nonlocal material microstructures, between subsets of resonant unit cells forming the metasurface. These long-range forces are obtained via carefully crafted flexible elements whose specific geometry and local dynamics are designed to create remarkably complex transfer functions between multiple units. The resulting nonlocal coupling forces enable achieving phase gradient profiles that are function of the wavenumber of the incident wave.The identification of relevant design parameters and the assessment of their impact on performance are explored via a combination of semi-analytical and numerical models. The nonlocal metasurface concept is tested, both numerically and experimentally, by embedding a total-internal-reflection design in a thin plate waveguide. Results confirm the feasibility of the intentionally nonlocal design concept and its ability to achieve a fully passive and broadband wave control

Localization of a Breathing Crack Using Super-Harmonic Signals due to System Nonlinearity

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76712/1/AIAA-38947-457.pd

Improving the performance of structure-embedded acoustic lenses via gradient-index local inhomogeneities

We investigate the use of graded inhomogeneities in order to enhance the focusing and collimation performance of structure-embedded acoustic metamaterial lenses. The type of inhomogeneity exploited in this study consists in axial symmetric exponential-like gradients of either material or geometric properties that create gradient-index inclusions able to bend and redirect propagating waves. In particular, we exploit the concept of gradient index inclusions to achieve focusing and collimation of ultrasonic beams created by embedded drop-channel lenses in both bulk and thin-walled structures. In the latter, the implementation is possible thanks to geometric exponential tapers known as Acoustic Black Holes (ABH). ABH tapers allow accurate control of the characteristics of the acoustic beam emanating from the lens channel which in the conventional design is severely affected by diffraction. The concept of beam control via graded inclusions is numerically illustrated and validated by using a combination of methodologies including geometric acoustics, finite difference time domain, and finite element methods

On the detection of closing delaminations in laminated composite plates using the structural intensity method

{In recent years, the concept of Nonlinear Structural Intensity (NSI) has been applied to detect fatigue cracks and loose joints in isotropic structures. This paper extends the NSI concept to orthotropic and anisotropic materials and investigates the possibility to use NSI for the localization of a closing delamination in thin laminated plates. When the delamination is excited by a high frequency interrogation signal, the periodic contact occurring between the delaminated plies produces Contact Acoustic Nonlinear (CAN) effects that are associated with the generation of both higher order and fractional harmonics. The closing delamination acts as a mechanism of redistribution of energy from the driving frequency to the nonlinear harmonics. The structural intensity associated with the nonlinear harmonics is an effective metric to identify size and location of the damage. NSI is computed using a combined approach based on a Finite Element (FE) model and a 13 point finite differencing scheme. Using this approach, we performed a numerical investigation on a thin laminated plate to analyze the effect that the material orthotropy has on the propagation of vibration energy and to understand the impact that preferential directions of energy propagation have on the ability to interrogate the damage. Then, the approach is extended for application to an anisotropic symmetric laminated plate.

Displacement-driven approach to nonlocal elasticity

This study presents a physically-consistent displacement-driven reformulation of the concept of action-at-a-distance, which is at the foundation of nonlocal elasticity. In contrast to the class of existing approaches that adopts an integral stress–strain constitutive relation, the displacement-driven approach is predicated on an integral strain–displacement relation. One of the most remarkable consequence of this reformulation is that the (total) strain energy is guaranteed to be a convex and positive-definite function without imposing any constraint on the symmetry of the nonlocal kernel. This feature is critical to enable the application of nonlocal formulations to general continua exhibiting asymmetric interactions; ultimately a manifestation of material heterogeneity. Remarkably, the proposed approach also enables a strong (point-wise) satisfaction of the locality recovery condition and of the laws of thermodynamics, which are not foregone conclusions in most classical nonlocal elasticity theories. Additionally, the formulation is frame-invariant and the nonlocal operator remains physically consistent at material interfaces and domain boundaries. The study is complemented by a detailed analysis of the dynamic response of the nonlocal continuum and of its intrinsic dispersion, leading to the consideration that the choice of a nonlocal kernel should depend on the specific material. Examples of either exponential or power-law kernels are presented in order to demonstrate the applicability of the method to different classes of nonlocal media. The ability to admit generalized kernels reinforces the generalized nature of the displacement-driven approach over existing integral methodologies, which typically lead to simplified differential models based on exponential kernels. The theoretical formulation is also leveraged to perform numerical simulations of the linear static response of nonlocal beams and plates further illustrating the intrinsic consistency of the approach, which is free from unwanted and unrealistic boundary effects. © 2021 Elsevier Masson SA