Inverse band gap design of elastic metamaterials for P and SV wave control

Goh, Heedong; Kallivokas, Loukas F.

doi:10.1016/j.cma.2020.113263

Cited by 15 publications

(6 citation statements)

References 26 publications

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“…Geometries and partitioning of boundary nodes of discretized microstructures of RVE (blue color denotes the negative nodes and red color denotes the positive nodes). RVE, representative volume element which satisfies the constraints in Equation ( 8) and also constraints in Equations ( 3) or (5). The corresponding functional space  l for the kinematically admissible displacement fluctuation field reads…”

Section: Linear Displacement Boundary Conditionmentioning

confidence: 99%

“…( 8) and also constraints in Eqns. (3) or (5). The corresponding functional space 𝒱 j for the kinematically admissible displacement fluctuation field reads…”

Section: Linear Displacement Boundary Conditionmentioning

confidence: 99%

“…In recent years, architected materials have received much attention and are expected to have a significant impact on how the materials are designed and discovered in future. By designing the underlying periodic microstructures, the architected materials can achieve desired engineering properties that are often not observed in nature materials, for example, high strength-to-weight ratio, 1 negative Poisson's ratio, 2,3 desirable band-gaps, 4,5 high energy absorption, 6,7 and so forth. For this reason, architected materials are also known as metamaterials.…”

Section: Introductionmentioning

confidence: 99%

“…By designing the underlying periodic microstructures, the architected materials can achieve desired engineering properties that are often not observed in nature materials, e.g. high strength-to-weight ratio [1], negative Poisson's ratio [2,3], desirable band-gaps [4,5], high energy absorption [6,7], etc. For this reason, architected materials are also known as metamaterials.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A computational framework for homogenization and multiscale stability analyses of nonlinear periodic materials

Zhang

Feng

Khandelwal

2021

Numerical Meth Engineering

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This article presents a consistent computational framework for multiscale first-order finite strain homogenization and stability analyses of rate-independent solids with periodic microstructures. The homogenization formulation is built on a priori discretized microstructure, and algorithms for computing the matrix representations of the homogenized stresses and tangent moduli are consistently derived. The homogenization results lose their validity at the onset of first bifurcation, which can be computed from multiscale stability analysis. The multiscale instabilities include: (a) microscale structural instability calculated by Bloch wave analysis; and (b) macroscale material instability calculated by rank-1 convexity checks on the homogenized tangent moduli.Implementation details of the Bloch wave analysis are provided, including the selection of wave vector space and the retrieval of real-valued buckling mode from complex-valued Bloch wave. Three methods are detailed for solving the resulted constrained eigenvalue problem-two condensation methods and a null-space projection method. Both the homogenization and stability analyses are verified using numerical examples including hyperelastic and elastoplastic periodic materials. Various microscale buckling phenomena are demonstrated. Aligned with theoretical results, the numerical results show that the microscopic long wavelength buckling can be equivalently detected by the loss of rank-1 convexity of the homogenized tangent moduli.

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Section: Linear Displacement Boundary Conditionmentioning

confidence: 99%

“…( 8) and also constraints in Eqns. (3) or (5). The corresponding functional space 𝒱 j for the kinematically admissible displacement fluctuation field reads…”

Section: Linear Displacement Boundary Conditionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A computational framework for homogenization and multiscale stability analyses of nonlinear periodic materials

Zhang

Feng

Khandelwal

2021

Numerical Meth Engineering

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“…Early studies on acoustic metamaterials are mainly concentrated on the band gap formation mechanisms and low-frequency broadband properties (Cai et al, 2022; El-Borgi et al, 2020; Goh and Kallivokas, 2020; Li et al, 2017; Pai et al, 2014; Van Belle et al, 2019; Wen et al, 2020). Xiao et al (2011) proposed a simple locally resonant continuous elastic system and provided analytical models with explicit formulations involving non-dimensional parameters to understand the underlying physics.…”

Section: Introductionmentioning

confidence: 99%

Vibration transmission characteristic prediction and structure inverse design of acoustic metamaterial beams based on deep learning

Chen

et al. 2023

Journal of Vibration and Control

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In this paper, an intelligent prediction and design method of acoustic metamaterial beams based on deep learning is presented. A theoretical model of acoustic metamaterial beams is derived by using the spectral element method to calculate the band structure and transmission characteristic of beam-type acoustic metamaterial. A high-degree-of-freedom design space dataset of band structure and transmission characteristics is constructed. In addition, the vibration transmission characteristics of acoustic metamaterial beams are predicted and the on-demand inverse design of acoustic metamaterial beams is realized by constructing a fully connected deep learning neural network model. Furthermore, the forward prediction and reverse design network model is verified by using the autoencoder neural network model. Results show that the predicted value of the autoencoder neural network structure is in good agreement with the target value, which indicates the feasibility of the intelligent design method of acoustic metamaterials based on deep learning. The presented intelligent design method could be potentially utilized in the field of fast and efficient acoustic metamaterial design for low frequency vibration isolation in engineering structures.

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Generative Inverse Design of Metamaterials with Functional Responses by Interpretable Learning

Chen,

Sun,

Lee

et al. 2024

Advanced Intelligent Systems

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Metamaterials with functional responses can exhibit varying properties under different conditions (e.g., wave‐based responses or deformation‐induced property variation). This work addresses rapid inverse design of such metamaterials to meet target qualitative functional behaviors, a challenge due to its intractability and nonunique solutions. Unlike data‐intensive and noninterpretable deep‐learning‐based methods, this work proposes the random‐forest‐based interpretable generative inverse design (RIGID), a single‐shot inverse design method for fast generation of metamaterials with on‐demand functional behaviors. RIGID leverages the interpretability of a random forest‐based “design → response” forward model, eliminating the need for a more complex “response → design” inverse model. Based on the likelihood of target satisfaction derived from the trained random forest, one can sample a desired number of design solutions using Markov chain Monte Carlo methods. RIGID is validated on acoustic and optical metamaterial design problems, each with fewer than 250 training samples. Compared to the genetic algorithm‐based design generation approach, RIGID generates satisfactory solutions that cover a broader range of the design space, allowing for better consideration of additional figures of merit beyond target satisfaction. This work offers a new perspective on solving on‐demand inverse design problems, showcasing the potential for incorporating interpretable machine learning into generative design under small data constraints.

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Inverse band gap design of elastic metamaterials for P and SV wave control

Cited by 15 publications

References 26 publications

A computational framework for homogenization and multiscale stability analyses of nonlinear periodic materials

A computational framework for homogenization and multiscale stability analyses of nonlinear periodic materials

Vibration transmission characteristic prediction and structure inverse design of acoustic metamaterial beams based on deep learning

Generative Inverse Design of Metamaterials with Functional Responses by Interpretable Learning

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