A novel second-order reduced homogenization approach for nonlinear thermo-mechanical problems of axisymmetric structures with periodic micro-configurations

We present the theoretical analysis of a periodic structure based on a transformational design of an axisymmetric system from a two-dimensional (2D) Sonic Crystal (SC). Applying an axial rotation of a 2D SC, we obtain a three dimensional (3D) axisymmetric structure made up of toroidal scatterers. Based on the propagating properties of the 2D system, we interpret the scattering produced by the 3D axisymmetric structure, and one can also use the homogenization approach in the long wavelength regime to design a refractive media with controlled effective parameters. We use both the multiple scattering theory, for the analysis of the 2D systems, and the finite elements methods, for the case of 3D axisymmetric structures. This system, due to the axial symmetry, could be useful to manage the radiation properties of sources presenting that symmetry. Moreover it may be useful by transforming in scale to different sizes, and as a consequence, to be applied at different ranges of frequencies.

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A second‐order reduced asymptotic homogenization approach for nonlinear periodic heterogeneous materials

International Journal for Numerical Methods in Engineering ◽

10.1002/nme.6058 ◽

2019 ◽

Vol 119 (6) ◽

pp. 469-489 ◽

Cited By ~ 12

Author(s):

Jacob Fish ◽

Zhiqiang Yang ◽

Zifeng Yuan

Keyword(s):

Heterogeneous Materials ◽

Second Order ◽

Asymptotic Homogenization ◽

Homogenization Approach

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Second-Order Computational Homogenization Approach Using Higher-Order Gradients at Microlevel

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.665.181 ◽

2015 ◽

Vol 665 ◽

pp. 181-184 ◽

Cited By ~ 1

Author(s):

Tomislav Lesičar ◽

Zdenko Tonković ◽

Jurica Sorić

Keyword(s):

Heterogeneous Material ◽

Computational Homogenization ◽

Second Order ◽

Material Behavior ◽

Bending Test ◽

Present Contribution ◽

Three Point Bending ◽

Linear Elastic ◽

Homogenization Approach ◽

Realistic Description

Realistic description of heterogeneous material behavior demands more accurate modeling at macroscopic and microscopic scales. To observe strain localization phenomena and material softening occurring at the microstructural level, an analysis on the microlevel is unavoidable. Multiscale techniques employing several homogenization schemes can be found in literature. Widely used second-order homogenization requiresC1continuity at the macrolevel, while standardC0continuity has usually been hold at microlevel. However, due to theC1-C0transition macroscale variables cannot be defined fully consistently. The present contribution is concerned with a multiscale second-order computational homogenization employingC1continuity at both scales under assumptions of small strains and linear elastic material behavior. All algorithms derived are implemented into the FE software ABAQUS. The numerical efficiency and accuracy of the proposed computational strategy is demonstrated by modeling three point bending test of the notched specimen.

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Disappearance Voltage Determinations Using a Convergent Beam

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100064979 ◽

1971 ◽

Vol 29 ◽

pp. 184-185

Author(s):

W. L. Bell

Keyword(s):

Second Order ◽

Objective Method ◽

Uniform Thickness ◽

Rocking Curve ◽

Crystal Perfection ◽

Kikuchi Line ◽

Central Maximum ◽

Diffraction Patterns ◽

Convergent Beam ◽

Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

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