Conditional Generative Adversarial Network Enabled Localized Stress Recovery of Periodic Composites

Structural damage in heterogeneousmaterials typically originates frommicrostructures where stress concentration occurs.Therefore,evaluating the magnitude and location of localized stress distributions within microstructures under external loading is crucial.Repeating unit cells(RUCs)are commonly used to represent microstructural details and homogenize the effective response of composites.This work develops a machine learning-based micromechanics tool to accurately predict the stress distributions of extracted RUCs.The locally exact homogenization theory efficiently generates the microstructural stresses of RUCs with a wide range of parameters,including volume fraction,fiber/matrix property ratio,fiber shapes,and loading direction.Subsequently,the conditional generative adversarial network(cGAN)is employed and constructed as a surrogate model to establish the statistical correlation between these parameters and the corresponding localized stresses.The stresses predicted by cGAN are validated against the remaining true data not used for training,showing good agreement.This work demonstrates that the cGAN-based micromechanics tool effectively captures the local responses of composite RUCs.It can be used for predicting potential crack initiations starting from microstructures and evaluating the effective behavior of periodic composites.

A novel implementation algorithm of asymptotic homogenization for predicting the effective coefficient of thermal expansion of periodic composite materials

Asymptotic homogenization (AH) is a general method for predicting the effective coefficient of thermal expansion (CTE) of periodic composites. It has a rigorous mathematical foundation and can give an accurate solution if the macrostructure is large enough to comprise an infinite number of unit cells. In this paper, a novel implementation algorithm of asymptotic homogenization (NIAH) is developed to calculate the effective CTE of periodic composite materials. Compared with the previous implementation of AH, there are two obvious advantages. One is its implementation as simple as representative volume element (RVE). The new algorithm can be executed easily using commercial finite element analysis (FEA) software as a black box. The detailed process of the new implementation of AH has been provided. The other is that NIAH can simultaneously use more than one element type to discretize a unit cell, which can save much computational cost in predicting the CTE of a complex structure. Several examples are carried out to demonstrate the effectiveness of the new implementation. This work is expected to greatly promote the widespread use of AH in predicting the CTE of periodic composite materials.

PLASTIC LIMIT ANALYSIS OF DUCTILE COMPOSITE STRUCTURES FROM MICRO-TO MACRO-MECHANICAL ANALYSIS

The load-bearing capacity of ductile composite structures comprised of periodic composites is studied by a combined micro/macromechanicai approach. Firstly, on the microscopic level, a representative volume element （RVE） is selected to reflect the microstructures of the composite materials and the constituents are assumed to be elastic perfectly-plastic. Based on the homogenization theory and the static limit theorem, an optimization formulation to directly calculate the macroscopic strength domain of the RVE is obtained. The finite element modeling of the static limit analysis is formulated as a nonlinear mathematical programming and solved by the sequential quadratic programming method, where the temperature parameter method is used to construct the self-stress field. Secondly, Hill＇s yield criterion is adopted to connect the micromechanicai and macromechanical analyses. And the limit loads of composite structures are worked out on the macroscopic scale. Finally, some examples and comparisons are shown.

Refraction characteristics of phononic crystals

Some of the most interesting refraction prop- erties of phononic crystals are revealed by examining the anti-plane shear waves in doubly periodic elastic composites with unit cells containing rectangular and/or elliptical multi- inclusions. The corresponding band structure, group velocity, and energy-flux vector are calculated using a powerful mixed variational method that accurately and efficiently yields all the field quantities over multiple frequency pass-bands. The background matrix and the inclusions can be anisotropic, each having distinct elastic moduli and mass densities. Equifrequency contours and energy-flux vectors are read- ily calculated as functions of the wave-vector components. By superimposing the energy-flux vectors on equifrequency contours in the plane of the wave-vector components, and supplementing this with a three-dimensional graph of the corresponding frequency surface, a wealth of information is extracted essentially at a glance. This way it is shown that a composite with even a simple square unit cell con- taining a central circular inclusion can display negative or positive energy and phase velocity refractions, or simply performs a harmonic vibration （standing wave）, depending on the frequency and the wave-vector. Moreover, that the same composite when interfaced with a suitable homoge- neous solid can display： （1） negative refraction with negative phase velocity refraction; （2） negative refraction with pos- itive phase velocity refraction; （3） positive refraction with negative phase velocity refraction; （4） positive refraction with positive phase velocity refraction; or even （5） completereflection with no energy transmission, depending on the fre- quency, and direction and the wavelength of the plane-wave that is incident from the homogeneous solid to the interface. For elliptical and rectangular inclusion geometries, analyti- cal expressions are given for the key calculation quantities. Expressions for displacement, velocity, linear momentum, strain, and stress components, as well as the energy-flux and group velocity components are given in series form. The general results are illustrated for rectangular unit cells, one with two and the other with four inclusions, although any number of inclusions can be considered. The energy-flux and the accompanying phase velocity refractions at an inter- face with a homogeneous solid are demonstrated. Finally, by comparing the results of the present solution method with those obtained using the Rayleigh quotient and, for the lay- ered case, with the exact solutions, the remarkable accuracy and the convergence rate of the present solution method are demonstrated.

Interfacial effects in electromagnetic coupling within piezoelectric phononic crystals

In this paper, we discuss waves in piezoelectric periodic composite, with the emphasis on the connection between the electromechanical coupling and the effects of dispersion of Bloch-Floquet waves. A particular attention is given to structures containing interfaces between dissimilar media and localization of the electrical fields near such interfaces.

Band-gap Properties of Elastic Sandwich Metamaterial Plates with Composite Periodic Rod Core

A novel elastic sandwich metamaterial plate with composite periodic rod core is designed,and the frequency band-gap characteristics are numerically and experimentally investigated.The finite element and spectral element hybrid method(FE-SEHM)is developed to obtain the dynamic stiffness matrix of the sandwich metamaterial plate.The frequency response curves of the plate structure under the harmonic excitation are calculated using the presented numerical method and validated by the vibration experiment.By comparing with the frequency response curves of sandwich metamaterial plate with pure elastic rod core,improved band-gap properties are achieved from the designed metamaterial plate with composite periodic rod core.The elastic metamaterial plate with composite periodic rod core can generate more band-gaps,so it can suppress the vibration and elastic wave propagation in the structure more effectively.

Concurrent Analysis and Design of Structure and Its Periodic Material

The specific good properties of cellular materials and composite materials, such as low density and high permeability, make the optimal design of such materials necessary and at- tractive. However, the given materials for the structures may not be optimal or suitable, since the boundary condition and applied loads vary in practical applications; hence the macro-structure and its material micro-structure should be considered simultaneously. Although abundant studies have been reported on the structural and material optimization at each level, very few of them considered the mutual coordination on both scales. In this paper, two FE models are built for the macro-structure and the micro-structure, respectively; and the effective elastic properties of the periodic micro-structure are blended into the analysis of macro-structure by the homogenization theory. Here, a topological optimum is obtained by gradually re-distributing the constituents within the micro-structure and updating the topological shape at the macro-structure until converges are achieved on both scales. The mutual coordination between the roles of micro-scale and macro-scale is considered. Some numerical examples are presented, which illustrate that the proposed optimization algorithm is effective and highly efficient for the micro-structure design and macro-structure optimization. For the composite design, one can see reasonable effects of the stiffness of base materials on the resultant topologies.

Elastic metamaterials and dynamic homogenization: a review

In this paper,we review the recent advances which have taken place in the understanding and applications of acoustic/elastic metamaterials.Metamaterials are artificially created composite materials which exhibit unusual properties that are not found in nature.We begin with presenting arguments from discrete systems which support the case for the existence of unusual material properties such as tensorial and/or negative density.The arguments are then extended to elastic continuums through coherent averaging principles.The resulting coupled and nonlocal homogenized relations,called the Willis relations,are presented as the natural description of inhomogeneous elastodynamics.They are specialized to Bloch waves propagating in periodic composites and we show that the Willis properties display the unusual behavior which is often required in metamaterial applications such as the Veselago lens.We finally present the recent advances in the area of transformation elastodynamics,charting its inspirations from transformation optics,clarifying its particular challenges,and identifying its connection with the constitutive relations of the Willis and the Cosserat types.

Theoretical aspects of selecting repeated unit cell model in micromechanical analysis using displacement-based finite element method

Repeated Unit Cell（RUC）is a useful tool in micromechanical analysis of composites using Displacement-based Finite Element（DFE）method,and merely applying Periodic Displacement Boundary Conditions（PDBCs）to RUC is almost a standard practice to conduct such analysis.Two basic questions arising from this practice are whether Periodic Traction Boundary Conditions（PTBCs,also known as traction continuity conditions）are guaranteed and whether the solution is independent of selection of RUCs.This paper presents the theoretical aspects to tackle these questions,which unify the strong form,weak form and DFE method of the micromechanical problem together.Specifically,the solution’s independence of selection of RUCs is dealt with on the strong form side,PTBCs are derived from the weak form as natural boundary conditions,and the validity of merely applying PDBCs in micromechanical Finite Element（FE）analysis is proved by referring to its intrinsic connection to the strong form and weak form.Key points in the theoretical aspects are demonstrated by illustrative examples,and the merits of setting micromechanical FE analysis under the background of a clear theoretical framework are highlighted in the efficient selection of RUCs for Uni Directional（UD）fiber-reinforced composites.

Composite quantile regression estimation for P-GARCH processes

We consider the periodic generalized autoregressive conditional heteroskedasticity(P-GARCH) process and propose a robust estimator by composite quantile regression. We study some useful properties about the P-GARCH model. Under some mild conditions, we establish the asymptotic results of proposed estimator.The Monte Carlo simulation is presented to assess the performance of proposed estimator. Numerical study results show that our proposed estimation outperforms other existing methods for heavy tailed distributions.The proposed methodology is also illustrated by Va R on stock price data.

Ultrasensitive liquid level sensor based on slice-shaped composite long period fiber grating

In this paper,a novel liquid level sensor with ultra-high sensitivity is proposed.The proposed sensor is configured by a sliceshaped composite long period fiber grating(SSC-LPFG).The SSC-LPFG is prepared by polishing two opposite sides of a composite multimode-single-mode-multimode fiber structure using a CO;laser.The method improves the sensitivity of the sensor to external environment.Based on the simulation calculation,a liquid level sensor with a length of 3 mm is designed.The experimental transmission spectrum agrees well with the simulation result.The experimental results show that the sensitivity reaches 7080 pm/mm in the liquid level range of 0-1400 μm in water.The temperature sensitivity is24.52 pm/℃ in the range of 20℃-90℃.Due to the ultra-high sensitivity,good linearity,and compact structure,the SSC-LPFG has potential application in the field of high-Drecision liquid level measurement.

China's Commodity Composition of Exports in the Various Periods of Time

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