Electro-elastomers: Large deformation analysis of silicone membranes

Electro-elastomers are large strain smart materials capable of both sensing and actuation. Typical electro-elastomer setups consist of either a silicone or acrylic membrane sandwiched between two compliant grease electrodes. Silicone electro-elastomers have maximum elastic strains between 200% and 350%. Acrylic electro-elastomers are more widely employed due to larger actuation strains but are softer than silicone and have a lower force output [Goulbourne, N.C., Frecker, M., Mockensturm, E.M., Snyder, A.J., 2003. Modeling of a dielectric elastomer diaphragm for a prosthetic blood pump. In: Proceedings of SPIE, Smart Structures and Materials: EAPAD, San Diego; Goulbourne, N.C., Mockensturm, E.M., Frecker, M., 2005b. Quasi-static and dynamic inflation of a dielectric elastomer membrane. In: Proceedings of SPIE, Smart Structures and Materials: EAPAD, San Diego]. A numerical formulation for the large deformation response of electro-elastomer membranes subject to electromechanical loading is derived in this paper. The approach is based on modifying the elastic membrane theory of Green, Adkins, and Rivlin [Adkins, J.E., Rivlin, R.S., 1952. Large elastic deformations of isotropic materials IX. The deformation of thin shells. Philosophical Transactions of the Royal Society of London. Series A Mathematical and Physical Sciences 244, 505–531; Green, A.E., Adkins, J.E., 1970. Large Elastic Deformations. Oxford University Press, London]. The electro-elastic stress state is defined as the combination of the electrical Maxwell stress and the mechanical stress for hyperelastic materials [Goulbourne, N.C., Mockensturm, E.M., Frecker, M., 2005a. A nonlinear model for dielectric elastomer membranes. ASME Journal of Applied Mechanics 72, (6) 899–906]. This paper augments our previous work by presenting a mathematical solution procedure for simulating the field responsive behavior of silicone electro-elastomers configured for both in-plane and out-of-plane deformation. Thin axisymmetric membranes subject to electromechanical loads are the focus of this investigation. The numerical analysis shows that there is a delicate balance between the electrical and the mechanical portions of the stress, which must be maintained for the overall stress to remain tensile and by extension the electro-elastomer to remain stable. It is shown that at very high voltages the stress can become negative ultimately leading to transducer failure. For sensing applications, the varying capacitive behavior of electro-elastomers is used to extract information about the membrane’s deformed state.     

Measurement method of complex viscoelastic material properties

A measurement technique of viscoelastic properties of polymers is proposed to investigate complex Poisson’s ratio as a function of frequency. The forced vibration responses for the samples under normal and shear deformation are measured with varying load masses. To obtain modulus of elasticity and shear modulus, the present method requires only knowledge of the load mass, geometrical characteristics of a sample, as well as both the amplitude ratio and phase lag of the forcing and response oscillations. The measured data were used to obtain the viscoelastic properties of the material based on a 2D numerical deformation model of the sample. The 2D model enabled us to exclude data correction by the empirical form factor used in 1D model. Standard composition (90% PDMS polymer + 10% catalyst) of silicone RTV rubber (Silastic^® S2) were used for preparing three samples for axial stress deformation and three samples for shear deformation. Comprehensive measurements of modulus of elasticity, shear modulus, loss factor, and both real and imaginary parts of Poisson’s ratio were determined for frequencies from 50 to 320 Hz in the linear deformation regime (at relative deformations 10^?6 to 10^?4) at temperature 25 °C. In order to improve measurement accuracy, an extrapolation of the obtained results to zero load mass was suggested. For this purpose measurements with several masses need to be done. An empirical requirement for the sample height-to-radius ratio to be more than 4 was found for stress measurements. Different combinations of the samples with different sizes for the shear and stress measurements exhibited similar results. The proposed method allows one to measure imaginary part of the Poisson’s ratio, which appeared to be about 0.04–0.06 for the material of the present study.     

Influences of ions and temperature on performance of carbon nano-particulates in supercapacitors with neutral aqueous electrolytes

A commercial product of carbon nano-particles, Cabot MONACH 1300 pigment black (CMPB), was studied for basic structural information and electrochemical performance in neutral aqueous electrolytes, aiming at applications in supercapacitors. As confirmed by SEM and HRTEM, the CMPB had a hierarchical structure, containing basic 10 nm nano-spheres which combined into ca. 50 nm agglomerates which further aggregated into larger particles of micrometres. The capacitance of this commercial material was found to increase with decreasing the size of hydrous cation (Li⁺ → Na⁺ → K⁺), instead of the cation crystal radius (K⁺ → Na⁺ → Li⁺) when coupled with the same anion (Cl⁻). In electrolytes with the same cation concentration (K⁺), changing the anion from the larger dianion (SO₄²⁻) to the smaller monoanion (Cl⁻) also increased the capacitance at high potential scan rates (>50 mV/s). Increasing electrolyte concentration produced expected effect, including raising the electrode capacitance, but lowering the equivalent series resistance (ESR), charge transfer resistance (CTR), and the diffusion resistance. At higher temperatures, the CMPB exhibited slightly higher capacitance, which does not agree with the Gouy–Chapman theory on electric double layer (EDL). A hypothesis is proposed to account for the capacitance increase with temperature as a result of the CMPB opening up some micro-pores for more ions to access in response to the temperature increase.     

On the interplay between material flaws and dynamic necking

In this paper we investigate the interplay between material defects and flow localization in elastoplastic bars subjected to dynamic tension. For that task, we have developed a 1D finite difference scheme within a large deformation framework in which the material is modelled using rate-dependent J₂ plasticity. A perturbation of the initial yield stress is introduced in each node of the finite difference mesh to model localized material flaws. Numerical computations are carried out within a wide spectrum of strain rates ranging from 500 s⁻¹ to 2500 s⁻¹. On the one hand, our calculations reveal the effect of the material defects in the necking process. On the other hand, our results show that the necking inception, instead of being a random type process, is the deterministic result of the interplay between the mechanical behaviour of the material and the boundary conditions. This conclusion agrees with the experimental evidence reported by Rittel et al. [1] and Rotbaum et al. [2].     

Relating inhomogeneous deformation to local texture in zirconium through grain-scale digital image correlation strain mapping experiments

The effect of local texture on inhomogeneous plastic deformation is studied in zirconium subjected to uniaxial compression. Cross-rolled commercially pure Zr 702 plate that had a strong basal (0 0 0 1) texture through the plate thickness, and a non-basal texture in cross-section, was obtained. At a compressive strain rate of 1 s^?1, samples loaded either in the through-thickness or in-plane directions exhibited significant differences in yield strength, hardening response and failure mechanisms. These macroscopic differences are related to microstructural features by combining information from electron backscattered diffraction with real time in situ imaging and subsequent full-field strain measurements obtained using digital image correlation. Experimental results indicate that the through-thickness loaded zirconium samples, which show a strong basal-texture in the loading direction, do not deform homogeneously – implying the lack of a representative volume element. The detailed surface deformation fields provided by digital image correlation allow for a qualitative and quantitative analysis of the relationship between grain orientation and patterns of deformation bands that form as the precursors to development of an adiabatic shear band in the through-thickness loaded sample. For the in-plane loaded samples, inhomogeneities still exist at the microscale, but the collective behavior of several grains leads to a homogeneous response at the macroscale. It is observed that local texture for hcp polycrystals, which are significantly slip restricted, can directly affect both local and global response, even at low to moderate plastic strains.     

Resolving the stratification discrepancy of turbulent natural convection in differentially heated air-filled cavities – Part I: Reference solutions using Chebyshev spectral methods

The problem of the long established thermal stratification discrepancy between numerical and experimental results is investigated in three companion articles. The Part I article establishes reference solutions by means of three-dimensional (3D) spectral direct numerical simulations of a buoyancy-driven flow (Ra_H = 1.5 × 10⁹). Two configurations of differentially heated air-filled cavity are considered: an idealized cavity (perfectly adiabatic cavity, PAC) and an Intermediate Realistic Cavity (IRC) making use of experimentally measured temperature distributions (Salat, 2004) on its top and bottom walls. The IRC flow structure as well as its associated rms fluctuations correspond to the experimentally observed flow dynamics. However both configurations keep resulting in a core thermal stratification value equal to 1.0 whereas experiments lead to a stratification of about 0.5. It is proved that this stratification paradox is neither related to three-dimensional effects nor to the experimental thermal distributions applied on the horizontal walls. Resolving this stratification discrepancy is the subject of the parts II and III articles (Sergent et al., 2013, Xin et al., 2012).     

Use of zero-net-mass-flow for separation control in diffusing S-duct

Flow control using zero-net-mass-flow jets in an S-shaped diffusing duct was investigated. Experiments were conducted in a channel flow facility at a Reynolds number, Re = 4.1 × 10⁴ with particle image velocimetry measurements in the symmetry plane of the duct. In the natural configuration, separation of the boundary layer occurs in a region of the duct with an high degree of curvature. A stability analysis of the wall normal base flow at the location of the applied control is presented and estimates the most effective frequency of the actuator. Time-averaged velocity fields show total reattachment of the boundary layer using active flow control.     

Comparison of a quasi-Newtonian fluid with a viscoelastic fluid in planar contraction flow

The flow of a 5.0 wt.% solution of polyisobutylene in tetradecane through a planar 4 : 1 contraction exhibiting a shear thinning viscosity is simulated using the flow-type sensitive quasi-Newtonian fluid model. The shear viscosity is fitted by the Giesekus model, which, with the chosen parameters, leads to an extension thickening elongational viscosity. The stress and velocity fields of the numerical simulations are compared with the experimental results of Quinzani et al. [J. Non-Newtonian Fluid Mech. 52 (1994) 1–36] and the numerical results of the viscoelastic simulation using the Giesekus model of Azaiez et al. [J. Non-Newtonian Fluid Mech. 62 (1996) 253–277]. It can be shown that the quasi-Newtonian fluid qualitatively predicts the essential features of the flow in the vicinity of the contraction.     

Thermodynamic admissibility of the extended Pom-Pom model for branched polymers

The thermodynamic consistency of the eXtended Pom-Pom (XPP) model for branched polymers of Verbeeten et al. [W.M.H. Verbeeten, G.W.M. Peters, F.P.T. Baaijens, Differential constitutive equations for polymer melts: the extended pom-pom model, J. Rheol. 45 (4) (2001) 823–843; W.M.H. Verbeeten, G.W.M. Peters, F.P.T. Baaijens, Differential constitutive equations for polymer melts: the extended pom-pom model (vol 45, pg 823–843, 2001), J. Rheol. 45 (6) (2001) 1489] as well as its modified version [J. van Meerveld, Note on the thermodynamic consistency of the integral pom-pom model, J. Non-Newtonian Fluid Mech. 108 (1–3) (2002) 291–299] is investigated from the perspective of non-equilibrium thermodynamics, namely the General Equation for Non-Equilibrium Reversible–Irreversible Coupling (GENERIC) framework. The thermodynamic admissibility of the XPP model is shown for both its original and modified form. According to the GENERIC formalism, the parameter α introduced by Verbeeten et al. to predict non-zero second normal stress in shear flows must fulfill the condition 0 ≤ α ≤ 1.     

Time-, stress-, and temperature-dependent deformation in nanostructured copper: Creep tests and simulations

In the present work, we performed experiments, atomistic simulations, and high-resolution electron microscopy (HREM) to study the creep behaviors of the nanotwinned (nt) and nanograined (ng) copper at temperatures of 22 °C (RT), 40 °C, 50 °C, 60 °C, and 70 °C. The experimental data at various temperatures and different sustained stress levels provide sufficient information, which allows one to extract the deformation parameters reliably. The determined activation parameters and microscopic observations indicate transition of creep mechanisms with variation in stress level in the nt-Cu, i.e., from the Coble creep to the twin boundary (TB) migration and eventually to the perfect dislocation nucleation and activities. The experimental and simulation results imply that nanotwinning could be an effective approach to enhance the creep resistance of twin-free ng-Cu. The experimental creep results further verify the newly developed formula (Yang et al., 2016) that describes the time-, stress-, and temperature-dependent plastic deformation in polycrystalline copper.     

Experimental study on the effect of drag reducing polymer on flow patterns and drag reduction in a horizontal oil–water flow

In this study, a HMW anionic co-polymer of 40:60 wt/wt NaAMPS/acrylamide was used as a drag reducing polymer (DRP) for oil–water flow in a horizontal 25.4 mm ID acrylic pipe. The effect of polymer concentration in the master solution and after injection in the main water stream, oil and water velocities, and pipe length on drag reduction (DR) was investigated. The injected polymer had a noticeable effect on flow patterns and their transitions. Stratified and dual continuous flows extended to higher superficial oil velocities while annular flow changed to dual continuous flow. The results showed that as low as 2 ppm polymer concentration was sufficient to create a significant drag reduction across the pipe. DR was found to increase with polymer concentration increased and reached maximum plateau value at around 10 ppm. The results showed that the drag reduction effect tends to increase as superficial water velocity increased and eventually reached a plateau at U_sw of around 1.3 m/s. At U_sw > 1.0 m/s, the drag reduction decreased as U_so increased while at lower water velocities, drag reduction is fluctuating with respect to U_so. A maximum DR of about 60% was achieved at U_so = 0.14 m/s while only 45% was obtained at U_so = 0.52 m/s. The effectiveness of the DRP was found to be independent of the polymer concentration in the master solution and to some extent pipe length. The friction factor correlation proposed by Al-Sarkhi et al. (2011) for horizontal flow of oil–water using DRPs was found to underpredict the present experimental pressure gradient data.     

The high strain mechanical response of the wet Kelvin model for open-cell foams

Surface Evolver software was used to create the three-dimensional geometry of a Kelvin open-cell foam, to simulate that of polyurethane flexible foams. Finite Element Analysis (FEA) with 3D elements was used to model large compressive deformation in the [0 0 1] and [1 1 1] directions, using cyclic boundary conditions when necessary, treating the polyurethane as an elastic or elastic–plastic material. The predicted foam Young’s moduli in the [0 0 1] direction are double those of foams with uniform Plateau border cross-section edges, for the same foam density and material properties. For compression in the [1 1 1] direction, the normalized Young’s modulus increases from 0.9 to 1.1 with foam relative density, and the predicted stress–strain relationship can have a plateau, even for a linearly-elastic polymer. As the foam density increases, the predicted effects of material plasticity become larger. For foam of relative density 0.028, edge-to-edge contact is predicted to occur at a 66% strain for [1 1 1] direction compression. The foam is predicted to contract laterally when the [1 1 1] direction compressive strain exceeds 25%.     

Evaluation of subgrid-scale models in large-eddy simulation of flow past a two-dimensional block

Large-eddy simulations of flow past a two-dimensional (2D) block were performed to evaluate four subgrid-scale (SGS) models: (i) the traditional Smagorinsky model, (ii) the Lagrangian dynamic model, (iii) the Lagrangian scale-dependent dynamic model, and (iv) the modulated gradient model. An immersed boundary method was employed to simulate the 2D block boundaries on a uniform Cartesian grid. The sensitivity of the simulation results to grid refinement was investigated by using four different grid resolutions. The velocity streamlines and the vertical profiles of the mean velocities and variances were compared with experimental results. The modulated gradient model shows the best overall agreement with the experimental results among the four SGS models. In particular, the flow recirculation, the reattachment position and the vertical profiles are accurately reproduced with a relative coarse grid resolution of (N_x × N_y × N_z=) 160 × 40 × 160 (n_x × n_z = 13 × 16 covering the block). Besides the modulated gradient model, the Lagrangian scale-dependent dynamic model is also able to give reasonable prediction of the flow statistics with some discrepancies compared with the experimental results. Relatively poor performance by the Lagrangian dynamic model and the Smagorinsky model is observed, with simulated recirculating patterns that differ from the measured ones. Analysis of the turbulence kinetic energy (TKE) budget in this flow shows evidence of a strong production of TKE in the shear layer that forms as the flow is deflected around the block.     

Dynamic fracture of concrete compact tension specimen: Experimental and numerical study

Compared to quasi-static loading concrete loaded by higher loading rates acts in a different way. There is an influence of strain-rate and inertia on resistance, failure mode and crack pattern. With increase of loading rate failure mode changes from mode-I to mixed mode. Moreover, theoretical and numerical investigations indicate that after the crack reaches critical velocity there is progressive increase of resistance and crack branching. These phenomena have recently been demonstrated and discussed by O?bolt et al. (2011) on numerical study of compact tension specimen (CTS) loaded by different loading rates. The aim of the present paper is to experimentally verify the results obtained numerically. Therefore, the tests and additional numerical studies on CTS are carried out. The experiments fully confirm the results of numerical prediction discussed in O?bolt et al. (2011). The same as in the numerical study it is shown that for strain rates lower than approximately 50/s the structural response is controlled by the rate dependent constitutive law, however, for higher strain rates crack branching and progressive increase of resistance is observed. This is attributed to structural inertia and not the rate dependent strength of concrete. Maximum crack velocity of approximately 800 m/s is measured before initiation of crack branching. The comparison between numerical and experimental results shows that relatively simple modeling approach based on continuum mechanics, rate dependent microplane model and standard finite elements is capable to realistically predict complex phenomena related to dynamic fracture of concrete.     

Measuring soil compaction and soil behavior under the tractor tire using strain transducer

Soil compaction can occur due to machine traffic and is an indicator of soil physical structure degradation. For this study 3 strain transducers with a maximum displacement of 5 cm were used to measure soil compaction under the rear tire of MF285 tractor. In first series of experiments, the effect of tractor traffic was investigated using displacement transducers and cylindrical cores. For the second series, only strain transducers were used to evaluate the effect of moisture levels of 11%, 16% and 22%, tractor velocities of 1, 3 and 5 km/h, and three depths of 20, 30 and 40 cm on soil compaction, and soil behavior during the compaction process was investigated. Results showed that no significant difference was found between the two methods of measuring the bulk density. The three main factors were significant on soil compaction at a probability level of 1%. The mutual binary effect of moisture and depth was significant at 1%, and the interaction of moisture, velocity, and depth were significant at 5%. The soil was compressed in the vertical direction and elongated in the lateral direction. In the longitudinal direction, the soil was initially compressed by the approaching tractor, then elongated, and ultimately compressed again.     

Aerosol optical absorption by dust and black carbon in Taklimakan Desert,during no-dust and dust-storm conditions

Aerosol absorption coefficient σ_ap involves the additive contribution of both black carbon aerosol (BC) and dust aerosol. The linear statistical regression analysis approach introduced by Fialho et al. (2005) is used to estimate the absorption exponents of BC and dust aerosol absorption coefficients, and further to separate the contributions of these two types of aerosols from the total light absorption coefficient measured in the hinterland of Taklimakan Desert in the spring of 2006. Absorption coefficients are measured by means of a 7-wavelength Aethalometer from 1 March to 31 May and from 1 November to 28 December, 2006. The absorption exponent of BC absorption coefficient α is estimated as (?0.95 ± 0.002) under background weather (supposing the observed absorption coefficient is due only to BC); the estimated absorption exponent of dust aerosol absorption coefficient β during the 6 dust storm periods (strong dust storm) is (?2.55 ± 0.009). Decoupling analysis of the measured light absorption coefficients demonstrates that, on average, the light absorptions caused by dust aerosol and BC make up about 50.5% and 49.5% respectively of the total light absorption at 520 nm; during dust weather process periods (dust storm, floating dust, blowing dust), the contribution of dust aerosol to absorption extinction is 60.6% on average; in the hinterland of desert in spring, dust aerosol is also the major contributor to the total aerosol light absorption, more than that of black carbon aerosol.     

Dynamic response and energy dissipation characteristics of balsa wood: experiment and analysis

Dynamic response of a cellular sandwich core material, balsa wood, is investigated over its entire density spectrum ranging from 55 to 380 kg/m³. Specimens were compression loaded along the grain direction at a nominal strain rate of 3 × 10³ s⁻¹ using a modified Kolsky (split Hopkinson) bar. The dynamic data are discussed and compared to those of quasi-static experiments reported in a previous study (Mech. Mater. 35 (2003) 523). Results show that while the initial failure stress is very sensitive to the rate of loading, plateau (crushing) stress remains unaffected by the strain rate. As in quasi-static loading, buckling and kink band formation were identified to be two major failure modes in dynamic loading as well. However, the degree of dynamic strength enhancement was observed to be different for these two distinct modes. Kinematics of deformation of the observed failure modes and associated micro-inertial effects are modeled to explain this different behavior. Specific energy dissipation capacity of balsa wood was computed and is found to be comparable with those of fiber-reinforced polymer composites.     

Thermo-mechanical response of nylon 101 under uniaxial and multi-axial loadings: Part I,Experimental results over wide ranges of temperatures and strain rates

A comprehensive study of the thermo-mechanical response of a thermoplastic polymer, nylon 101 is presented. Quasi-static and dynamic compression uniaxial and multi-axial experiments (stress states) were performed at a wide range of strain rates (10⁻⁵ to 5000 s⁻¹) and temperatures (−60 to 177 °C or −76 to 350 °F). The material is found to be non-linearly dependent on strain rate and temperature. The change in volume after plastic deformation is investigated and is found to be negligibly small. The relaxation and creep responses at room temperature are found to be dependent on strain rate and the stress–strain level at which these phenomena are initiated. Total deformation is decomposed into visco-elastic and visco-plastic components; these components have been determined at different levels of deformation. Results from non-proportional uniaxial to biaxial compression, and torsion experiments, are also reported for three different strain rates at room temperature. It is shown that nylon 101 has a response dependent on the hydrostatic pressure.