Related papers: Multiband homogenization of metamaterials in real-…
Temporal metamaterials are artificially manufactured materials with time-dependent material properties that exhibit interesting phenomena when waves propagate through them. The propagation of electromagnetic waves in such time-varying…
This paper considers a time-fractional diffusion-wave equation with a high-contrast heterogeneous diffusion coefficient. A numerical solution to this problem can present great computational challenges due to its multiscale nature.…
The focus of our work is dispersive, second-order effective model describing the low-frequency wave motion in heterogeneous (e.g.~functionally-graded) media endowed with periodic microstructure. For this class of quasi-periodic medium…
The design of band-gap metamaterials, i.e., metamaterials with the capability to inhibit wave propagation of a specific frequency range, has numerous potential engineering applications, such as acoustic filters and vibration isolation…
A unified homogenization procedure for split ring metamaterials taking into account time and spatial dispersion is introduced. The procedure is based on two coupled systems of equations. The first one comes from an approximation of the…
The present paper is concerned with a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main results consist of a homogenization theorem (i.e., convergence of…
It is well known that the classical energetically consistent micropolar model has limits in simulating the frequency band structure of packed granular materials (see Merkel et al., 2011). It is here shown that if a standard continualization…
We propose a novel numerical homogenization method based on the edge multiscale approach for solving indefinite time-harmonic Maxwell equations in heterogeneous media with large wavenumber. Numerical methods for these equations in…
Time-evolving perforated domains arise in many engineering and geoscientific applications, including reactive transport, particle deposition, and structural degradation in porous media. Accurately capturing the macroscopic behavior of such…
The conception of new metamaterials showing unorthodox behaviors with respect to elastic wavepropagation has become possible in recent years thanks to powerful dynamical homogenization techniques. Such methods effectively allow to describe…
We consider the scattering of elastic waves by highly oscillating anisotropic periodic media with bounded support. Applying the two-scale homogenization, we first obtain a constant coefficient second-order partial differential elliptic…
A multifield asymptotic homogenization technique for periodic thermo-diffusive elastic materials is provided in the present study. Field equations for the first-order equivalent medium are derived and overall constitutive tensors are…
We use a simple effective model, obtained through the application of high-frequency homogenisation, to tackle the fundamental question of how the choice of gradient function affects the performance of a graded metamaterial. This approach…
In this paper, we consider a parabolic problem with time-dependent heterogeneous coefficients. Many applied problems have coupled space and time heterogeneities. Their homogenization or upscaling requires cell problems that are formulated…
A non-local dynamic homogenization technique for the analysis of a viscoelastic heterogeneous material which displays a periodic microstructure is herein proposed. The asymptotic expansion of the micro-displacement field in the transformed…
A recently developed upscaling technique, the multicontinuum homogenization method, has gained significant attention for its effectiveness in modeling complex multiscale systems. This method defines multiple continua based on distinct…
We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive effective medium approximation. One-dimensional materials with…
We present a method for two-scale model derivation of the periodic homogenization of the one-dimensional wave equation in a bounded domain. It allows for analyzing the oscillations occurring on both microscopic and macroscopic scales. The…
This paper aims at an accurate and efficient computation of effective quantities, e.g., the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods…
In this paper, we discuss a general framework for multicontinuum homogenization. Multicontinuum models are widely used in many applications and some derivations for these models are established. In these models, several macroscopic…