skip to main content

This content will become publicly available on March 29, 2023

Title: Mechanical cloak via data-driven aperiodic metamaterial design
Mechanical cloaks are materials engineered to manipulate the elastic response around objects to make them indistinguishable from their homogeneous surroundings. Typically, methods based on material-parameter transformations are used to design optical, thermal, and electric cloaks. However, they are not applicable in designing mechanical cloaks, since continuum-mechanics equations are not form invariant under general coordinate transformations. As a result, existing design methods for mechanical cloaks have so far been limited to a narrow selection of voids with simple shapes. To address this challenge, we present a systematic, data-driven design approach to create mechanical cloaks composed of aperiodic metamaterials using a large precomputed unit cell database. Our method is flexible to allow the design of cloaks with various boundary conditions, multiple loadings, different shapes and numbers of voids, and different homogeneous surroundings. It enables a concurrent optimization of both topology and properties distribution of the cloak. Compared to conventional fixed-shape solutions, this results in an overall better cloaking performance and offers unparalleled versatility. Experimental measurements on additively manufactured structures further confirm the validity of the proposed approach. Our research illustrates the benefits of data-driven approaches in quickly responding to new design scenarios and resolving the computational challenge associated with multiscale designs of more » functional structures. It could be generalized to accommodate other applications that require heterogeneous property distribution, such as soft robots and implants design. « less
; ; ; ; ;
Award ID(s):
1835677 1835782 1835648
Publication Date:
Journal Name:
Proceedings of the National Academy of Sciences
Sponsoring Org:
National Science Foundation
More Like this
  1. Context. Radio relics are diffuse extended synchrotron sources that originate from shock fronts induced by galaxy cluster mergers. The particle acceleration mechanism at the shock fronts is still under debate. The galaxy cluster 1RXS J0603.3+4214 hosts one of the most intriguing examples of radio relics, known as the Toothbrush. Aims. In order to understand the mechanism(s) that accelerate(s) relativistic particles in the intracluster medium, we investigated the spectral properties of large-scale diffuse extended sources in the merging galaxy cluster 1RXS J0603.3+4214. Methods. We present new wideband radio continuum observations made with uGMRT and VLA. Our new observations, in combination with previously published data, allowed us to carry out a detailed high-spatial-resolution spectral and curvature analysis over a wide range of frequencies. Results. The integrated spectrum of the Toothbrush closely follows a power law over almost two orders of magnitude in frequency, with a spectral index of −1.16 ± 0.02. We do not find any evidence of spectral steepening below 8 GHz. The subregions of the Toothbrush also exhibit near-perfect power laws and identical spectral slopes, suggesting that the observed spectral index is rather set by the distribution of Mach numbers which may have a similar shape at different parts of the shockmore »front. Indeed, numerical simulations show an intriguing similar spectral index, indicating that the radio spectrum is dominated by the average over the inhomogeneities within the shock, with most of the emission coming from the tail of the Mach number distribution. In contrast to the Toothbrush, the spectra of the fainter relics show a high-frequency steepening. Moreover, the integrated spectrum of the halo also follows a power law from 150 MHz to 3 GHz with a spectral index of −1.16 ± 0.04. We do not find any evidence for spectral curvature, not even in subareas of the halo. This suggest a homogeneous acceleration throughout the cluster volume. Between the “brush” region of the Toothbrush and the halo, the color-color analysis reveals emission that was consistent with an overlap between the two different spectral regions. Conclusions. None of the relic structures, that is, the Toothbrush as a whole or its subregions or the other two fainter relics, show spectral shapes consistent with a single injection of relativistic electrons, such as at a shock, followed by synchrotron aging in a relatively homogeneous environment. Inhomogeneities in some combination of Mach number, magnetic field strength, and projection effects dominate the observed spectral shapes.« less

    Full-waveform inversion (FWI) methods rely on accurate numerical simulation of wave propagation in the analysed medium. Acoustic or elastic wave equations are often used to model seismic wave propagation. These types of simulations do not account for intrinsic attenuation effects due to material anelasticity, and thus correction techniques have been utilized in practice to partially compensate the anelasticity. These techniques often only consider the waveform amplitude correction based on averaging of overall amplitude response over the entire data set, and ignore the phase correction. Viscoelastic wave equations account for the anelastic response in both waveform amplitude and phase, and are therefore a more suitable alternative. In this study, we present a novel 3-D Gauss–Newton viscoelastic FWI (3-D GN-VFWI) method. To address the main challenge of the Gauss–Newton optimization, we develop formulas to compute the Jacobian efficiently by the convolution of virtual sources and backward wavefields. The virtual sources are obtained by directly differentiating the viscoelastic wave equations with respect to model parameters. In order to resolve complex 3-D structures with reasonable computational effort, a homogeneous attenuation (Q factor) is used throughout the analysis to model the anelastic effects. Synthetic and field experiments are performed to demonstrate the utility ofmore »the method. The synthetic results clearly demonstrate the ability of the method in characterizing a challenging velocity profile, including voids and reverse velocity layers. The field experimental results show that method successfully characterizes the complex substructure with two voids and undulating limestone bedrock, which are confirmed by invasive tests. Compared to 3-D elastic FWI results, the presented viscoelastic method produces more accurate results regarding depths of the voids and bedrock. This study suggests that the improvement of imaging accuracy would warrant the widespread use of viscoelastic wave equations in FWI problems. To our best knowledge, this is the first reported study on 3-D GN-VFWI at any scale. This study provides the new theory and formulation for the use of Gauss–Newton optimization on the 3-D viscoelastic problem.

    « less
  3. Abstract

    Origami, the ancient art of paper folding, has shown its potential as a versatile platform to design various reconfigurable structures. The designs of most origami-inspired architected materials rely on a periodic arrangement of identical unit cells repeated throughout the whole system. It is challenging to alter the arrangement once the design is fixed, which may limit the reconfigurable nature of origami-based structures. Inspired by phase transformations in natural materials, here we study origami tessellations that can transform between homogeneous configurations and highly heterogeneous configurations composed of different phases of origami unit cells. We find that extremely localized and reprogrammable heterogeneity can be achieved in our origami tessellation, which enables the control of mechanical stiffness and in-situ tunable locking behavior. To analyze this high reconfigurability and variable stiffness systematically, we employ Shannon information entropy. Our design and analysis strategy can pave the way for designing new types of transformable mechanical devices.

  4. Engineering structures that bridge between elements with disparate mechanical properties are a significant challenge. Organisms reap synergy by creating complex shapes that are intricately graded. For instance, the wear-resistant cusp of the chiton radula tooth works in concert with progressively softer microarchitectural units as the mollusk grazes on and erodes rock. Herein, we focus on the stylus that connects the ultrahard and stiff tooth head to the flexible radula membrane. Using techniques that are especially suited to probe the rich chemistry of iron at high spatial resolution, in particular synchrotron Mössbauer and X-ray absorption spectroscopy, we find that the upper stylus ofCryptochiton stelleriis in fact a mineralized tissue. Remarkably, the inorganic phase is nano disperse santabarbaraite, an amorphous ferric hydroxyphosphate that has not been observed as a biomineral. The presence of two persistent polyamorphic phases, amorphous ferric phosphate and santabarbaraite, in close proximity, is a unique aspect that demonstrates the level of control over phase transformations inC. stelleridentition. The stylus is a highly graded material in that its mineral content and mechanical properties vary by a factor of 3 to 8 over distances of a few hundred micrometers, seamlessly bridging between the soft radula and the hard tooth head. Themore »use of amorphous phases that are low in iron and high in water content may be key to increasing the specific strength of the stylus. Finally, we show that we can distill these insights into design criteria for inks for additive manufacturing of highly tunable chitosan-based composites.

    « less
  5. Abstract The data-driven approach is emerging as a promising method for the topological design of multiscale structures with greater efficiency. However, existing data-driven methods mostly focus on a single class of microstructures without considering multiple classes to accommodate spatially varying desired properties. The key challenge is the lack of an inherent ordering or “distance” measure between different classes of microstructures in meeting a range of properties. To overcome this hurdle, we extend the newly developed latent-variable Gaussian process (LVGP) models to create multi-response LVGP (MR-LVGP) models for the microstructure libraries of metamaterials, taking both qualitative microstructure concepts and quantitative microstructure design variables as mixed-variable inputs. The MR-LVGP model embeds the mixed variables into a continuous design space based on their collective effects on the responses, providing substantial insights into the interplay between different geometrical classes and material parameters of microstructures. With this model, we can easily obtain a continuous and differentiable transition between different microstructure concepts that can render gradient information for multiscale topology optimization. We demonstrate its benefits through multiscale topology optimization with aperiodic microstructures. Design examples reveal that considering multiclass microstructures can lead to improved performance due to the consistent load-transfer paths for micro- and macro-structures.