Nonlocal Homogenization Model Research Articles

Spatiotemporally nonlocal homogenization method for viscoelastic porous metamaterial structures

The underlying size-dependent mechanism of viscoelastic porous metamaterial structures is still unclear, and the solution to their response using the high-fidelity numerical method is time-consuming, even prohibitive. This paper explores how the size-dependent effect of metamaterial structures emerges from the underlying nonlocal interactions in metamaterial microstructures, and then develops an accurate but efficient homogenization method for analyzing their size-dependent and time-dependent mechanical behaviors of viscoelastic porous metamaterial structures. By accounting for the nonlocal interaction between different representative volume elements and the history-dependent effect, a spatiotemporally nonlocal discrete element model is developed to analyze the mechanical behavior of viscoelastic porous metamaterial structures. With the help of the spatiotemporally nonlocal discrete element model, a spatiotemporally nonlocal homogenization method is proposed to accurately yet efficiently assess the size-dependent mechanical behavior of the porous metamaterial structure. The remarkable potential of the spatiotemporally nonlocal homogenization method is illustrated by simulating the stress relaxation of a viscoelastic porous metamaterial structure under axial strain. Results indicate that the size-dependent phenomenon can be significant, and the spatiotemporally nonlocal homogenization model can efficiently capture the size-dependent relaxation stress evaluated by the high-fidelity finite element model without loss of accuracy.

Cross-scale optimization of advanced materials for micro and nano structures based on strain gradient theory

Recently developed cross-scale optimization methods are mainly the macro equivalent calculation of performances based on the traditional homogenization method. However, the traditional homogenization is limited to the classic continuum of Cauchy–Boltzmann. Therefore, it is inadequate to interpret the size dependence of the optimal result. Hence, a new cross-scale optimization is proposed based on Wei–Hutchinson strain gradient theory by employing the non-local homogenization model, which could describe and explain the size dependence during optimization process when considering micro structures. The topological optimization procedure simultaneously has the ability of coupled computing by using subdomain parameterized coarse meshes. The numerical computations involved in the entire model can be solved in one iteration, which helps to eliminate mesh dependencies and greatly reduce the computation time. It is shown that the final stiffness of the optimized periodic structure can be significantly increased by considering the strain gradient theory compared with the classic homogenization scheme in the process of cross-scale optimization.

Multiscale nonlocal effective medium model for in-plane elastic wave dispersion and attenuation in periodic composites

This manuscript proposes a multiscale nonlocal homogenization and a nonlocal effective medium model for in-plane wave propagation in periodic composites accounting for dispersion and attenuation due to Bragg scattering. The nonlocal effective medium model is developed based on the spatial-temporal nonlocal homogenization model that is formulated to capture dispersion within the first Brillouin zone with particularly high accuracy along high symmetry directions. The homogenization model is derived by employing high order asymptotic expansions, extending the applicability of asymptotic homogenization to short wavelength regime, to capture wave dispersion and attenuation. The effective medium model is in the form of a second order PDE with a nonlocal effective moduli tensor that contains the nonlocal features of the homogenization model. The proposed models are derived and numerically verified for in-plane elastic wave propagation in two-dimensional periodic composites. It is shown that the dispersion curves of the spatial-temporal nonlocal homogenization model capture the acoustic branch, the first stop band and the optical branch of longitudinal and shear wave modes. The nonlocal effective medium model predicts transient elastic wave propagation in periodic composites and captures wave dispersion and attenuation within the limits of separation of scales.

Spatial–temporal nonlocal homogenization model for transient anti-plane shear wave propagation in periodic viscoelastic composites

This manuscript presents a spatial–temporal nonlocal homogenization model for transient anti-plane shear wave propagation in viscoelastic composites. The proposed model is formulated through asymptotic homogenization with higher order corrections incorporated to extend the applicability of the homogenization theory to shorter wavelength regime. A nonlocal homogenization model in the form of a fourth order PDE is consistently derived with all model parameters directly computed from the microstructure equilibrium. A reduced order model in the form of a second order PDE is then proposed for efficient transient wave propagation analysis. The reduced model retains the dispersive character of the original nonlocal model through the effective stiffness tensor. Transient shear wave propagation in two-dimensional domain with periodic elastic and viscoelastic microstructures is investigated and the proposed models were verified against direct numerical simulations. The spatial–temporal nonlocal homogenization model is shown to accurately capture shear wave dispersion in the first pass band and attenuation within the first stop band.

Nonlocal Homogenization Model for Wave Dispersion and Attenuation in Elastic and Viscoelastic Periodic Layered Media

This manuscript presents a new nonlocal homogenization model (NHM) for wave dispersion and attenuation in elastic and viscoelastic periodic layered media. Homogenization with multiple spatial scales based on asymptotic expansions of up to eighth order is employed to formulate the proposed nonlocal homogenization model. A momentum balance equation, nonlocal in both space and time, is formulated consistent with the gradient elasticity theory. A key contribution in this regard is that all model coefficients including high-order length-scale parameters are derived directly from microstructural material properties and geometry. The capability of the proposed model in capturing the characteristics of wave propagation in heterogeneous media is demonstrated in multiphase elastic and viscoelastic materials. The nonlocal homogenization model is shown to accurately predict wave dispersion and attenuation within the acoustic regime for both elastic and viscoelastic layered composites.

Local thickness-dependent permittivity model for nonlocal bounded wire-medium structures

A local thickness-dependent permittivity is derived in closed form for bounded nonlocal wire-medium structures. The model takes into account spatial dispersion (as an average per length of the wires) and the effect of the boundary, and shows that an effective local model of a nonlocal medium is thickness dependent. The permittivity is comprised of a local bulk (Drude) term and a boundary- and thickness-dependent term, the latter including the effect of spatial nonlocality. Results are obtained for different wire-medium topologies which possess strong spatial dispersion, demonstrating good agreement with a nonlocal homogenization model and full-wave simulation results.

Mushroom-type structures with the wires connected through diodes: Theory and applications

In this paper, we establish a general formalism to quantify the interaction of electromagnetic waves with mushroom-type structures (high impedance surface and bi-layer) with diodes inserted along the direction of the wires. The analysis is carried out using the nonlocal homogenization model for the mushroom structure with the generalized additional boundary conditions at the connection of the wires to diodes. We calculate numerically the magnitude and phase of the reflected/transmitted fields in the presence of an ideal and realistic PIN diodes. It is observed that the reflection/transmission characteristics of the mushroom-type structures can be controlled by tuning the working states of the integrated PIN diodes. We realize a structure with a multi-diode switch to minimize the undesired transmission for a particular incident angle. In addition, a dual-band subwavelength imaging lens is designed based on the resonant amplification of evanescent waves, wherein the operating frequency can be tuned by changing the states of the PIN diodes. The analytical results are verified with the full-wave electromagnetic solver CST Microwave Studio, showing a good agreement.

Tunable dual-band subwavelength imaging with a wire medium slab loaded with nanostructured graphene metasurfaces

In this paper, we demonstrate that a wire medium slab loaded with graphene-nanopatch metasurfaces (GNMs) enables the enhancement of evanescent waves for the subwavelength imaging at terahertz (THz) frequencies. The analysis is based on the nonlocal homogenization model for wire medium with the additional boundary condition at the connection of wires to graphene. The physical mechanism behind this lens can be described as the surface plasmons excitement at the lower and upper GNMs which are coupled by an array of metallic wires. The dual nature (capacitive/inductive) of the GNM is utilized in order to design a dual-band lens in which the unique controllable properties of graphene and the structural parameters of wire medium (WM) slab provide more degrees of freedom in controlling two operating frequency bands. The lens can support the subwavelength imaging simultaneously at two tunable distinct frequencies with the resolution better than λ/6 even if the distance between GNMs is a significant fraction of wavelength (>λ/5.5). The major future challenges in the fabrication of the lens have been demonstrated and a promising approach for the practical configuration of the lens has been proposed.

Partial focusing by a bulk metamaterial formed by a periodically loaded wire medium with impedance insertions

In this paper, a uniaxial wire medium periodically loaded with metallic patches and lumped impedance insertions is proposed for partial focusing of electromagnetic radiation due to a magnetic line source. The analysis is based on the nonlocal homogenization model for a bi-layer mushroom structure with generalized additional boundary conditions for loaded vias, and it is extended to a multilayered configuration with the transfer matrix approach. The proposed structure exhibits a high transmission and is nearly insensitive to the losses. The analytical results are validated against full-wave numerical simulations.

A nonlocal homogenization model for wave dispersion in dissipative composite materials

This manuscript presents a nonlocal homogenization model for the analysis of wave dispersion and energy dissipation in bimaterial viscoelastic composites subjected to dynamic loading conditions. The proposed model is derived based on the asymptotic homogenization method with multiple spatial scales applied in the Laplace domain. Asymptotic expansions of the associated response fields up to fourth order are employed to account for wave dispersions induced by the microscopic heterogeneities. The solution of the nonlocal homogenization approach is obtained in semi-analytical form in the Laplace domain and discrete inverse Laplace transform method is employed to approximate the response fields in the time domain. Numerical examinations are carried out to verify the proposed model and assess its capabilities compared to the standard (i.e., local) homogenization and the analytical solutions of composite beams subjected to dynamic loading conditions. Investigations reveal that the nonlocal model accurately accounts for wave dispersions and heterogeneity induced attenuation. A parametric analysis is conducted to identify the relationship between microstructure and heterogeneity induced attenuation under high-frequency loading.

Mushroom-Type High-Impedance Surface With Loaded Vias: Homogenization Model and Ultra-Thin Design

In this letter, we study the reflection properties and natural modes (surface waves and leaky waves) of the mushroom-type surfaces with impedance loadings (as lumped loads) at the connection of the vias to the ground plane. The analysis is carried out using the nonlocal homogenization model for the mushroom structure with a generalized additional boundary condition for loaded vias. It is observed that the reflection characteristics obtained with the homogenization model strongly depend on the type of the load (inductive or capacitive) and are in a very good agreement with the full-wave simulation results. The proposed concept of lumped loads enables the design of an ultrathin mushroom-type surface with high-impedance resonance characteristics (zero reflection phase) for oblique incidence at low frequencies with a broad stopband for surface waves.

Characterization of Surface-Wave and Leaky-Wave Propagation on Wire-Medium Slabs and Mushroom Structures Based on Local and Nonlocal Homogenization Models

In this paper, a nonlocal homogenization model is proposed for the analysis of the spectrum of natural modes on sub-wavelength mushroom-type high-impedance surfaces composed of a capacitive grid connected to a grounded wire-medium (WM) slab. Modal characteristics of mushroom structures are studied in conjunction with the surface-wave and leaky-wave propagation on WM slabs based on local and nonlocal homogenization models, showing the importance of spatial dispersion (SD) in WM. It is shown that mushroom structures support proper real (bound) forward and backward modes, whose dispersion determines the stopband properties of the mushroom structure, and proper (exponentially decaying from the surface) and improper (exponentially growing from the surface) complex leaky-wave modes related to the backward and forward radiation, respectively. Results obtained by different homogenization models are compared leading to important conclusions. Specifically, an interesting observation concerns the mushroom structures with short vias, wherein the SD of the WM slab is significantly reduced, and the results of local and nonlocal homogenization models are in excellent agreement.

Nonlocal homogenization of an array of cubic particles made of resonant rings

Here, we develop a nonlocal homogenization model to characterize the electrodynamics of an array of cubic particles made of resonant rings. The effective parameters are calculated from the microscopic fields produced by a periodic external excitation. It is confirmed that the spatial dispersion effects cannot be neglected in the regime where μ ≈ 0. We demonstrate that when the array of resonant rings is combined with a triple wire medium formed by connected wires, the structure may behave approximately as an isotropic left-handed material.