Internal friction and the Stieltjes analytic representation of the effective properties of two-dimensional viscoelastic composites

2019 ◽  
Vol 89 (3) ◽  
pp. 591-607 ◽  
Author(s):  
Elena Cherkaev
Keyword(s):  
Internal Friction ◽  
Effective Properties ◽  
Analytic Representation ◽  
Two Dimensional ◽  
Viscoelastic Composites

Effective properties of composite materials containing voids

1993 ◽  
Vol 440 (1909) ◽  
pp. 461-473 ◽  
Keyword(s):  
Young’S Modulus ◽  
Poisson’S Ratio ◽  
Effective Properties ◽  
Young's Modulus ◽  
Matrix Material ◽  
Practical Importance ◽  
Three Dimensional ◽  
Poisson's Ratio ◽  
Two Dimensional ◽  
Isotropic Composite

Recent results of theoretical and practical importance prove that the two-dimensional (in-plane) effective (average) Young’s modulus for an isotropic elastic material containing voids is independent of the Poisson’s ratio of the matrix material. This result is true regardless of the shape and morphology of the voids so long as isotropy is maintained. The present work uses this proof to obtain explicit analytical forms for the effective Young’s modulus property, forms which simplify greatly because of this characteristic. In some cases, the optimal morphology for the voids can be identified, giving the shapes of the voids, at fixed volume, that maximize the effective Young’s modulus in the two-dimensional situation. Recognizing that two-dimensional isotropy is a subset of three-dimensional transversely isotropic media, it is shown in this more general case that three of the five properties are independent of Poisson’s ratio, leaving only two that depend upon it. For three-dimensionally isotropic composite media containing voids, it is shown that a somewhat comparable situation exists whereby the three-dimensional Young’s modulus is insensitive to variations in Poisson’s ratio, v m , over the range 0 ≤ v m ≤ ½, although the same is not true for negative values of v m . This further extends the practical usefulness of the two-dimensional result to three-dimensional conditions for realistic values of v m .

Giant Magneto-Piezoresistance and Internal Friction in a Two-Dimensional Electron System

2007 ◽  
Vol 46 (No. 27) ◽  
pp. L658-L660 ◽  
Author(s):  
Hiroshi Yamaguchi ◽  
Hajime Okamoto ◽  
Yuki Maruta ◽  
Sunao Ishihara ◽  
Sen Miyashita ◽  
...  
Keyword(s):  
Internal Friction ◽  
Electron System ◽  
Two Dimensional ◽  
Dimensional Electron ◽  
Dimensional Electron System

Modeling of Piezoelectric Bimorph Nano-Actuators With Surface Effects

2013 ◽  
Vol 80 (6) ◽  
Author(s):  
Chunli Zhang ◽  
Chuanzeng Zhang ◽  
Weiqiu Chen
Keyword(s):  
Effective Properties ◽  
Surface Effect ◽  
Surface Elasticity ◽  
Driving Voltage ◽  
Two Dimensional ◽  
Piezoelectric Bimorph ◽  
Simply Supported ◽  
Size Dependent ◽  
Spring Force ◽  
Plate Type

Two-dimensional (2D) equations of piezoelectric bimorph nano-actuators are presented which take account of the surface effect. The surface effect of the bimorph structure is treated as a surface layer with zero thickness. The influence on the plate's overall properties resulted from the surface elasticity and piezoelectricity is modeled by a spring force exerting on the boundary of the bulk core. Using the derived 2D equations, the anti-parallel piezoelectric bimorph nano-actuators of both cantilever and simply supported plate type are investigated theoretically. Numerical results show that the effective properties and the deflections of the antiparallel bimorph nano-actuators are size-dependent. The deflection at the resonant frequency achieves nearly 50 times as that under the static driving voltage.

Simulation and Modelling the Heterogeneous Effects of the Microstructure MOX Fuels on their Effective Properties in Nominal Pressure Water Reactor Conditions

2010 ◽  
Vol 73 ◽  
pp. 91-96 ◽  
Author(s):  
Rodrigue Largenton ◽  
Victor Blanc ◽  
Philippe Thevenin ◽  
Daniel Baron
Keyword(s):  
Effective Properties ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Numerical Representation ◽  
Two Dimensional ◽  
Heterogeneous Microstructure ◽  
Heterogeneous Effects ◽  
Nominal Pressure ◽  
Sequential Absorption ◽  
The Moment

The experimental Electron Probe Micro Analysis (EPMA) characterizations on the MOX fuels evidence a heterogeneous microstructure, containing several phases. This heterogeneity must be accounted for in the numerical simulation. The first phase of this work, presented here, concerns exclusively the numerical representation of the MOX microstructure in three dimensions. Three identified steps were realized. The first one consisted in the acquisition and the treatment of two-dimensional experimental pictures thanks to a soft-ware already developed [1]. From the made treatments, the following bi-dimensional data were acquired: the surface fraction of every phase, the various diameters of inclusions within a phase as well as their surfaces fractions. However, within the framework of our study, we wished to represent our heterogeneous microstructure in three dimensions. Except, the data, supplied by this soft-ware, were bi-dimensional. Therefore, the second step of our works deal with the stereological domain. The model of Saltykov [2] was used to go back up the two-dimensional statistical information in three-dimensional. Finally, the last step of our works was to develop a tool able to build a meshed periodic numerical representation of the MOX microstructure. This innovative tool, based on a Random Sequential Absorption technique, represents MOX fuels already irradiated in reactor or any heterogeneous fuels envisaged in the future as well. For example it models two or three phases MOX fuel or any multi-phases fuels as well. Moreover, the sizes of the inclusions can vary within each phase. At the moment, the tool models spherical inclusions but nothing prevents from evolving towards more complex morphologies.

Two-dimensional lattice Boltzmann modeling for effective thermal conductivity in carbon black filled composites

2017 ◽  
Vol 52 (15) ◽  
pp. 2047-2053 ◽  
Author(s):  
Yong-Jun Kim ◽  
Yu-Fei Tan ◽  
Sok Kim
Keyword(s):  
Experimental Data ◽  
Thermal Conductivity ◽  
Carbon Black ◽  
Effective Thermal Conductivity ◽  
Lattice Boltzmann ◽  
Volume Fraction ◽  
Effective Properties ◽  
Lattice Boltzmann Model ◽  
Two Dimensional ◽  
Boltzmann Model

Polymer composites filled with thermally conductive particles are widely used in thermo-electronic industry, and the prediction of effective properties is still important for design and use of composites. Thus, we propose a lattice Boltzmann model to predict the effective thermal conductivity of composites filled with carbon black. First, a method for reconstructing numerical material having filler distribution characteristic similar to that of actual material is introduced, and the process for obtaining the phase function and the volume fraction of grain filler is described. The energy transport governing equation is then solved through the two-dimensional discrete structure by using a lattice Boltzmann model. The effective thermal conductivity of two-phase composite is expressed by the conductivity of each phase and the temperature distribution in discrete rectangle. The resultant prediction is compared with theoretical and experimental data and indicates good agreement with experimental data.

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