Multiband homogenization of metamaterials in real-space: Higher-order nonlocal models and scattering at external surfaces

J., Deshmukh, Kshiteej; Breitzman, Timothy; Dayal, Kaushik

doi:10.1016/j.jmps.2022.104992

Cited by 7 publications

(1 citation statement)

References 67 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, nonlocal surrogate models have also received lots of attentions [7][8][9], where integral operators are employed which embeds all time and length scales in their definitions. Comparing with continuum PDE counterparts, the nonlocal surrogate models provide a more natural affinity with the dispersive waves in a microstructure, and successfully reproduce many features of the decay and spreading of stress waves [9]. Moreover, in nonlocal homogenization models the choice of kernel functions contains information about the smallscale response of the system.…”

Section: Introductionmentioning

confidence: 99%

MetaNOR: A Meta-Learnt Nonlocal Operator Regression Approach for Metamaterial Modeling

Zhang¹,

You²,

Yu³

2022

Preprint

View full text Add to dashboard Cite

We propose MetaNOR, a meta-learnt approach for transfer-learning operators based on the nonlocal operator regression. The overall goal is to efficiently provide surrogate models for new and unknown materiallearning tasks with different microstructures. The algorithm consists of two phases: (1) learning a common nonlocal kernel representation from existing tasks; (2) transferring the learned knowledge and rapidly learning surrogate operators for unseen tasks with a different material, where only a few test samples are required. We apply MetaNOR to model the wave propagation within 1D metamaterials, showing substantial improvements on the sampling efficiency for new materials.

show abstract

Section: Introductionmentioning

confidence: 99%

MetaNOR: A Meta-Learnt Nonlocal Operator Regression Approach for Metamaterial Modeling

Zhang¹,

You²,

Yu³

2022

Preprint

View full text Add to dashboard Cite

show abstract

A reduced-order computational homogenization framework for locally resonant metamaterial structures

Russillo,

Kouznetsova,

Failla

et al. 2024

Comput Mech

View full text Add to dashboard Cite

A computational homogenization framework is presented to study the dynamics of locally resonant acoustic metamaterial structures. Modelling the resonant units at the microscale as representative volume elements and building on well-established scale transition relations, the framework brings as a main novelty a reduced-order macroscopic homogenized continuum whose governing equations involve no additional variables to describe the microscale dynamics unlike micromorphic homogenized continua obtained by alternative computational homogenization approaches. This model-order reduction is obtained by formulating the governing equations of the micro- and macroscale problems in the frequency domain, introducing a finite-element discretization of the two problems and performing an exact dynamic condensation of all the degrees of freedom at the microscale. An appropriate inverse Fourier transform approach is implemented on the frequency-domain equations to capture transient dynamics as well; notably, the implementation involves the Exponential Window Method, here applied for the first time to calculate the time-domain response of undamped locally resonant acoustic metamaterial structures. The framework may handle arbitrary geometries of micro- and macro-structures, any transient excitations and any boundary conditions on the macroscopic domain.

show abstract

Peridynamic neural operators: A data-driven nonlocal constitutive model for complex material responses

Jafarzadeh,

Silling,

Liu

et al. 2024

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

Multiband homogenization of metamaterials in real-space: Higher-order nonlocal models and scattering at external surfaces

Cited by 7 publications

References 67 publications

MetaNOR: A Meta-Learnt Nonlocal Operator Regression Approach for Metamaterial Modeling

MetaNOR: A Meta-Learnt Nonlocal Operator Regression Approach for Metamaterial Modeling

A reduced-order computational homogenization framework for locally resonant metamaterial structures

Peridynamic neural operators: A data-driven nonlocal constitutive model for complex material responses

Contact Info

Product

Resources

About