Bloch-mode analysis for retrieving effective parameters of metamaterials

We introduce a new approach for retrieving effective parameters of metamaterials based on the Bloch-mode analysis of quasi-periodic composite structures. We demonstrate that, in the case of single-mode propagation, a complex effective refractive index can be assigned to the structure, being restored by our method with a high accuracy. We employ both surface and volume averaging of the electromagnetic fields of the dominating (fundamental) Bloch modes to determine the Bloch and wave impedances, respectively. We discuss how this method works for several characteristic examples, and demonstrate that this approach can be useful for retrieval of both material and wave effective parameters of a broad range of metamaterials.Comment: 12 pages, 10 figure

Design of metallic nanoparticles gratings for filtering properties in the visible spectrum

Plasmonic resonances in metallic nanoparticles are exploited to create efficient optical filtering functions. A Finite Element Method is used to model metallic nanoparticles gratings. The accuracy of this method is shown by comparing numerical results with measurements on a two-dimensional grating of gold nanocylinders with elliptic cross section. Then a parametric analysis is performed in order to design efficient filters with polarization dependent properties together with high transparency over the visible range. The behavior of nanoparticle gratings is also modelled using the Maxwell-Garnett homogenization theory and analyzed by comparison with the diffraction by a single nanoparticle. The proposed structures are intended to be included in optical systems which could find innovative applications.Comment: submitted to Applied Optic

Multiscale Surrogate Modeling and Uncertainty Quantification for Periodic Composite Structures

Computational modeling of the structural behavior of continuous fiber composite materials often takes into account the periodicity of the underlying micro-structure. A well established method dealing with the structural behavior of periodic micro-structures is the so- called Asymptotic Expansion Homogenization (AEH). By considering a periodic perturbation of the material displacement, scale bridging functions, also referred to as elastic correctors, can be derived in order to connect the strains at the level of the macro-structure with micro- structural strains. For complicated inhomogeneous micro-structures, the derivation of such functions is usually performed by the numerical solution of a PDE problem - typically with the Finite Element Method. Moreover, when dealing with uncertain micro-structural geometry and material parameters, there is considerable uncertainty introduced in the actual stresses experienced by the materials. Due to the high computational cost of computing the elastic correctors, the choice of a pure Monte-Carlo approach for dealing with the inevitable material and geometric uncertainties is clearly computationally intractable. This problem is even more pronounced when the effect of damage in the micro-scale is considered, where re-evaluation of the micro-structural representative volume element is necessary for every occurring damage. The novelty in this paper is that a non-intrusive surrogate modeling approach is employed with the purpose of directly bridging the macro-scale behavior of the structure with the material behavior in the micro-scale, therefore reducing the number of costly evaluations of corrector functions, allowing for future developments on the incorporation of fatigue or static damage in the analysis of composite structural components.Comment: Appeared in UNCECOMP 201

Kernel Analog Forecasting: Multiscale Test Problems

Data-driven prediction is becoming increasingly widespread as the volume of data available grows and as algorithmic development matches this growth. The nature of the predictions made, and the manner in which they should be interpreted, depends crucially on the extent to which the variables chosen for prediction are Markovian, or approximately Markovian. Multiscale systems provide a framework in which this issue can be analyzed. In this work kernel analog forecasting methods are studied from the perspective of data generated by multiscale dynamical systems. The problems chosen exhibit a variety of different Markovian closures, using both averaging and homogenization; furthermore, settings where scale-separation is not present and the predicted variables are non-Markovian, are also considered. The studies provide guidance for the interpretation of data-driven prediction methods when used in practice.Comment: 30 pages, 14 figures; clarified several ambiguous parts, added references, and a comparison with Lorenz' original method (Sec. 4.5

Finite Strain Homogenization Using a Reduced Basis and Efficient Sampling

The computational homogenization of hyperelastic solids in the geometrically nonlinear context has yet to be treated with sufficient efficiency in order to allow for real-world applications in true multiscale settings. This problem is addressed by a problem-specific surrogate model founded on a reduced basis approximation of the deformation gradient on the microscale. The setup phase is based upon a snapshot POD on deformation gradient fluctuations, in contrast to the widespread displacement-based approach. In order to reduce the computational offline costs, the space of relevant macroscopic stretch tensors is sampled efficiently by employing the Hencky strain. Numerical results show speed-up factors in the order of 5-100 and significantly improved robustness while retaining good accuracy. An open-source demonstrator tool with 50 lines of code emphasizes the simplicity and efficiency of the method.Comment: 28 page