The Overall Elastic Dielectric Properties of Fiber-Strengthened/Weakened Elastomers

2015 ◽  
Vol 82 (11) ◽  
Author(s):  
Victor Lefèvre ◽  
Oscar Lopez-Pamies
Keyword(s):  
Dielectric Properties ◽  
Volume Fraction ◽  
Exact Analytical Solution ◽  
Closed Form Solution ◽  
Dielectric Elastomer ◽  
Form Solution ◽  
Dielectric Elastomers ◽  
Filler Materials ◽  
Elastomer Composites ◽  
Elastic Dielectric

By employing recent results (Lopez-Pamies, O., 2014, “Elastic Dielectric Composites: Theory and Application to Particle-Filled Ideal Dielectrics,” J. Mech. Phys. Solids, 64, p. 6182 and Spinelli, S. A., Lefèvre, V., and Lopez-Pamies, O., “Dielectric Elastomer Composites: A General Closed-Form Solution in the Small-Deformation Limit,” J. Mech. Phys. Solids, 83, pp. 263–284.) on the homogenization problem of dielectric elastomer composites, an approximate solution is generated for the overall elastic dielectric response of elastomers filled with a transversely isotropic distribution of aligned spheroidal particles in the classical limit of small deformations and moderate electric fields. The solution for such a type of dielectric elastomer composites is characterized by 13 (five elastic, two dielectric, and six electrostrictive) effective constants. Explicit formulae are worked out for these constants directly in terms of the elastic dielectric properties of the underlying elastomer and the filler particles, as well as the volume fraction, orientation, and aspect ratio of the particles. As a first application of the solution, with the objective of gaining insight into the effect that the addition of anisotropic fillers can have on the electromechanical properties of elastomers, sample results are presented for the case of elastomers filled with aligned cylindrical fibers. These results are confronted to a separate exact analytical solution for an assemblage of differential coated cylinders (DCC), wherein the fibers are polydisperse in size, and to full-field simulations of dielectric elastomer composites with cylindrical fibers of monodisperse size. These results serve to shed light on the recent experimental findings concerning the dielectric elastomers filled with mechanically stiff fibers. Moreover, they serve to reveal that high-permittivity liquid-like or vacuous fibers—two classes of filler materials yet to be explored experimentally—have the potential to significantly enhance the electrostriction capabilities of dielectric elastomers.

Influence of Nanoparticles in Lubricants on the Load Capacity of Hydrostatic Thrust Bearings

2012 ◽  
Vol 486 ◽  
pp. 99-103
Author(s):  
Huei Chu Weng ◽  
Yuan Kang
Keyword(s):  
Volume Fraction ◽  
Load Capacity ◽  
Particle Volume Fraction ◽  
Closed Form Solution ◽  
Form Solution ◽  
Interparticle Interaction ◽  
Particle Volume ◽  
Thrust Bearings ◽  
Bearing Load ◽  
Thrust Pad

An analysis for the effect of nanoparticles in lubricants on load capacity is performed to study a rectangular thrust pad hydrostatic bearing with a central recess. The closed-form solution of the bearing load is derived analytically and presented for nanofluids with interparticle interaction. Results reveal that in the presence of nanoparticles, the enhanced viscosity could result in an increase in bearing load; moreover, this increase dramatically increases as particle volume fraction and/or interparticle interaction increases. The effect of nanoparticles on the bearing load can be magnified by decreasing the bearing gap.

A closed form solution for bending/stretching analysis of functionally graded circular plates under asymmetric loading using the Green function

2010 ◽  
Vol 224 (6) ◽  
pp. 1153-1163 ◽  
Author(s):  
A R Saidi ◽  
A Naderi ◽  
E Jomehzadeh
Keyword(s):  
Green Function ◽  
Closed Form ◽  
Volume Fraction ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Form Solution ◽  
Functionally Graded ◽  
Transverse Displacement ◽  
Circular Plates ◽  
Equilibrium Equations

In this article, a closed-form solution for bending/stretching analysis of functionally graded (FG) circular plates under asymmetric loads is presented. It is assumed that the material properties of the FG plate are described by a power function of the thickness variable. The equilibrium equations are derived according to the classical plate theory using the principle of total potential energy. Two new functions are introduced to decouple the governing equilibrium equations. The three highly coupled partial differential equations are then converted into an independent equation in terms of transverse displacement. A closed-form solution for deflection of FG circular plates under arbitrary lateral eccentric concentrated force is obtained by defining a new coordinate system. This solution can be used as a Green function to obtain the closed-form solution of the FG plate under arbitrary loadings. Also, the solution is employed to solve some different asymmetric problems. Finally, the stress and displacement components are obtained exactly for each problem and the effect of volume fraction is also studied.

Electroelastic Response of Isotropic Dielectric Elastomer Composites with Deformation-Dependent Apparent-Permittivity Matrix

2020 ◽  
Vol 87 (9) ◽  
Author(s):  
Victor Lefèvre
Keyword(s):  
Free Energy ◽  
Electric Fields ◽  
Dielectric Response ◽  
Dielectric Elastomer ◽  
Spherical Particles ◽  
Full Field ◽  
The Matrix ◽  
Elastomer Composites ◽  
Non Gaussian ◽  
Elastic Dielectric

Abstract This paper puts forth an approximate yet accurate free energy for the elastic dielectric response—under finite deformations and finite electric fields—of non-percolative dielectric elastomer composites made out of a non-Gaussian dielectric elastomer matrix with deformation-dependent apparent permittivity isotropically filled with nonlinear elastic dielectric particles that may exhibit polarization saturation. While the proposed free energy applies in its most general form to arbitrary isotropic non-percolative microstructures, closed-form specializations are recorded for the practically relevant cases of rigid or liquid-like spherical particles. The proposed free energy is exact by construction in the asymptotic context of small deformations and moderate electric fields and is shown to remain accurate for arbitrary large deformations and electric fields via comparisons with full-field finite-element simulations. The proposed constitutive model is deployed to probe the electrostriction response of these dielectric elastomer composites and corresponding results reveal that their elastic dielectric response strongly depends on the deformation-dependent apparent permittivity of the matrix they comprise.

scholarly journals The Sustainable Characteristic of Bio-Bi-Phase Flow of Peristaltic Transport of MHD Jeffrey Fluid in the Human Body

2018 ◽  
Vol 10 (8) ◽  
pp. 2671 ◽  
Author(s):  
Ahmed Zeeshan ◽  
Nouman Ijaz ◽  
Tehseen Abbas ◽  
Rahmat Ellahi
Keyword(s):  
Volume Fraction ◽  
Closed Form Solution ◽  
Pressure Rise ◽  
Expansion Method ◽  
Form Solution ◽  
Peristaltic Transport ◽  
Jeffrey Fluid ◽  
Physical Parameters ◽  
Phase Flow ◽  
Special Cases

This study deals with the peristaltic transport of non-Newtonian Jeffrey fluid with uniformly distributed identical rigid particles in a rectangular duct. The effects of a magnetohydrodynamics bio-bi-phase flow are taken into account. The governing equations for mass and momentum are simplified using the fact that wavelength is much greater than the amplitude and small Reynolds number. A closed-form solution for velocity is obtained by means of the eigenfunction expansion method whereby pressure rise is numerically calculated. The results are graphically presented to observe the effects of different physical parameters and the suitability of the method. The results for hydrodynamic, Newtonian fluid, and single-phase problems can be respectively obtained by taking the Hartmann number (M = 0), relaxation time (λ1=0), and volume fraction (C = 0) as special cases of this problem.

scholarly journals Dynamic Analysis of a Deeply Buried Tunnel Influenced by a Newly-built Adjacent Cavity with a Special Emphasis on the Minimum Seismically Safe Tunnel Distance

2021 ◽  
Author(s):  
Elefterija Zlatanović ◽  
Dragan Č. Lukić ◽  
Vlatko Šešov ◽  
Zoran Bonić
Keyword(s):  
Exact Analytical Solution ◽  
Closed Form Solution ◽  
Decomposition Theorem ◽  
Expansion Method ◽  
Addition Theorem ◽  
Transportation Systems ◽  
Form Solution ◽  
Infinite Length ◽  
Underground Structures ◽  
Plane Sv Waves

Contemporary life streams, more often than ever, impose the necessity for construction of new underground structures in the vicinity of existing tunnels, with an aim to accommodate transportation systems and utility networks. A previously uninvestigated case, in which a newly-constructed tunnel opening is closely positioned behind an existing tunnel, referred to as the tunnel–cavity configuration, has been considered in this study. An exact analytical solution is derived considering a pair of parallel circular cylindrical structures of infinite length, with the horizontal alignment, embedded in a boundless homogeneous, isotropic, elastic medium and excited by time-harmonic plane SV-waves under the plane-strain conditions. The Helmholtz decomposition theorem, the wave functions expansion method, the translational addition theorem for bi-cylindrical coordinates, and the pertinent boundary conditions are jointly employed in order to develop a closed-form solution of the corresponding boundary value problem. The primary goal of the present study is to examine the increase in dynamic stresses at an existing tunnel structure due to the presence of a closely driven unlined cavity, as well as in a localized region around the tunnel (at the position of the cavity in close proximity), under incident SV-waves. A new quantity called dynamic stress alteration factor is introduced and the aspect of the minimum seismically safe distance between the two structures is particularly considered.

Orthotropy Rescaling for the Fracture Problem in Anisotropic Piezoelectric Materials

2002 ◽  
Author(s):  
William S. Oates ◽  
Christopher S. Lynch
Keyword(s):  
Closed Form ◽  
Piezoelectric Materials ◽  
Stress Singularity ◽  
Closed Form Solution ◽  
Form Solution ◽  
Governing Equations ◽  
Closed Form Solutions ◽  
Order Polynomial ◽  
Work Done ◽  
Elastic Dielectric

To date, much of the work done on ferroelectric fracture assumes the material is elastically isotropic, yet there can be considerable polarization induced anisotropy. More sophisticated solutions of the fracture problem incorporate anisotropy through the Stroh formalism generalized to the piezoelectric material. This gives equations for the stress singularity, but the characteristic equation involves solving a sixth order polynomial. In general this must be accomplished numerically for each composition. In this work it is shown that a closed form solution can be obtained using orthotropy rescaling. This technique involves rescaling the coordinate system based on certain ratios of the elastic, dielectric, and piezoelectric coefficients. The result is that the governing equations can be reduced to the biharmonic equation and solutions for the isotropic material utilized to obtain solutions for the anisotropic material. This leads to closed form solutions for the stress singularity in terms of ratios of the elastic, dielectric, and piezoelectric coefficients. The results of the two approaches are compared and the contribution of anisotropy to the stress intensity factor discussed.

scholarly journals Multiscale instabilities in soft heterogeneous dielectric elastomers

2014 ◽  
Vol 470 (2162) ◽  
pp. 20130618 ◽  
Author(s):  
S. Rudykh ◽  
K. Bhattacharya ◽  
G. deBotton
Keyword(s):  
Large Volume ◽  
Electric Displacement ◽  
Closed Form Solution ◽  
Form Solution ◽  
Dielectric Elastomers ◽  
Layered Composites ◽  
Volume Fractions ◽  
Moderate Volume ◽  
Layered Dielectrics ◽  
New Type

The development of instabilities in soft heterogeneous dielectric elastomers is investigated. Motivated by experiments and possible applications, we use in our analysis the physically relevant referential electric field instead of electric displacement. In terms of this variable, a closed form solution is derived for the class of layered neo-Hookean dielectrics. A criterion for the onset of electromechanical multiscale instabilities for the layered composites with anisotropic phases is formulated. A general condition for the onset of the macroscopic instability in soft multiphase dielectrics is introduced. In the example of the layered dielectrics, the essential influence of the microstructure on the onset of instabilities is revealed. We found that: (i)  macroscopic instabilities dominate at moderate volume fractions of the stiffer phase, (ii) interface instabilities appear at small volume fractions of the stiffer phase and (iii) instabilities of a finite scale, comparable to the microstructure size, occur at large volume fractions of the stiffer phase. The latest new type of instabilities does not appear in the purely mechanical case and dominates in the region of large volume fractions of the stiff phase.

Exact Closed-Form Solution of the Nonlinear Fin Problem With Temperature-Dependent Thermal Conductivity and Heat Transfer Coefficient

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Mahdi Anbarloei ◽  
Elyas Shivanian
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Exact Analytical Solution ◽  
Closed Form Solution ◽  
Form Solution ◽  
Temperature Dependent ◽  
Fin Efficiency ◽  
Temperature Dependent Thermal Conductivity

In the current paper, the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient is revisited. In this problem, it has been assumed that the heat transfer coefficient is expressed in a power-law form and the thermal conductivity is a linear function of temperature. It is shown that its governing nonlinear differential equation is exactly solvable. A full discussion and exact analytical solution in the implicit form are given for further physical interpretation and it is proved that three possible cases may occur: there is no solution to the problem, the solution is unique, and the solutions are dual depending on the values of the parameters of the model. Furthermore, we give exact analytical expressions of fin efficiency as a function of thermogeometric fin parameter.

A Closed-Form Solution of Effective Young's Modulus for Composites Including Multi-Shape Inclusions Using Improved Mori-Tanaka Model

2013 ◽  
Vol 704 ◽  
pp. 343-348
Author(s):  
Dong Mei Luo ◽  
Hong Yang ◽  
Yi Ying Xiao ◽  
Wen Xue Wang
Keyword(s):  
Closed Form ◽  
Young’S Modulus ◽  
Volume Fraction ◽  
Hybrid Composites ◽  
Young's Modulus ◽  
Closed Form Solution ◽  
Form Solution ◽  
Homogenization Theory ◽  
Equivalent Inclusion ◽  
Improved Model

In this paper, an improved model is proposed by combining Mori-Tanaka method with Eshelbys equivalent inclusion concept to derive a closed-form solution of the effective Young's modulusE11for hybrid composites reinforced with multi-shapes inclusions. When only the fiber-like inclusions are considered in the model, the results are consistent with those from Tandons unidirectional aligned composites based on Mori-Tanaka theory. For composites reinforced with fiber-like and spherical inclusions, the homogenization theory is employed to verify the effects of the proposed model. The influence of volume fraction and Youngs modulus of each phase on effective Youngs modulusE11is investigated, and the results show thatE11is sensitive to the inclusion shapes, and the model is practicable to predict the effective mechanical properties of composites reinforced by several inclusions with different shapes.

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