The Reproducing Kernel DMS-FEM: 3D Shape Functions and Applications to Linear Solid Mechanics

We propose a family of 3D versions of a smooth finite element method (Sunilkumar and Roy 2010), wherein the globally smooth shape functions are derivable through the condition of polynomial reproduction with the tetrahedral B-splines (DMS-splines) or tensor-product forms of triangular B-splines and ID NURBS bases acting as the kernel functions. While the domain decomposition is accomplished through tetrahedral or triangular prism elements, an additional requirement here is an appropriate generation of knotclouds around the element vertices or corners. The possibility of sensitive dependence of numerical solutions to the placements of knotclouds is largely arrested by enforcing the condition of polynomial reproduction whilst deriving the shape functions. Nevertheless, given the higher complexity in forming the knotclouds for tetrahedral elements especially when higher demand is placed on the order of continuity of the shape functions across inter-element boundaries, we presently emphasize an exploration of the triangular prism based formulation in the context of several benchmark problems of interest in linear solid mechanics. In the absence of a more rigorous study on the convergence analyses, the numerical exercise, reported herein, helps establish the method as one of remarkable accuracy and robust performance against numerical ill-conditioning (such as locking of different kinds) vis-a-vis the conventional FEM.

Synthesis of Layered Perovskite Oxides, ACa2-xLaxNb3-xTix010 (A = K, Rb, Cs), and Characterization of New Solid Acids, HCa2-xLaxNb3-xTixOlo (0 < x d 2), Exhibiting Variable Bronsted Acidity?

Layered perovskite oxides of the formula ACa~,La,Nb3-,Ti,010 (A = K, Rb, Cs and 0 < x d 2) have been prepared. The members adopt the structures of the parent ACazNb3010. Interlayer alkali cations in the niobium-titanium oxide series can be ion-exchanged with Li+, Na+, NH4+, or H+ to give new derivatives. Intercalation of the protonated derivatives with organic bases reveals that the Bronsted acidity of the solid solution series, HC~ ~ , L ~ ,N~ ~ , T ~ ,dOep~eOnd, s on the titanium content. While the x = 1 member (HCaLaNbzTiOlo) is nearly as acidic as the parent HCazNb3010, the x = 2 member (HLazNbTizOlo) is a weak acid hardly intercalating organic bases with pKa - 11.3. The variation of acidity is probably due to an ordering of Nb/Ti atoms in the triple octahedral perovskite slabs, [Ca~,La,Nb~,Ti,0~0], such that protons are attached to NbO6 octahedra in the x = 1 member and to Ti06 octahedra in the x = 2 member.

Thermodynamic Study of Mixed Anionic Solid Solutions Using Gradient Solid Electrolytes System K2CO3 - K2SO4

The thermodynamic properties of K2CO3 -KSO, solid solutions with hexagonal structure have been measured using a solid-state cell, incorporating a composite solid electrolyte with step-changes in composition. The cell with the configuration Pt, CO2' + O2' || K2CO3 | K2(CO3)x(SO4)1-x || CO2'' + O2'' + Pt X =1 X=X was investigated in the temperature range of 925 to 1165 K. The composite gradient solid electrolyte consisted of pure K2CO3 at one extremity and the solid solution under study at the other. The Nernstian response of the cell to changes in partial pressures of CO2 and O2 at the electrodes and temperature was demonstrated. The activity of K2CO3 in the solid solution was measured by three techniques. All three methods gave identical results, indicating unit transport number for K+ ions and negligible diffusion potential due to concentration gradients of carbonate and sulfate ions. The activity of K2CO3 exhibits positive deviation from Raoult's law. The excess Gibbs energy of mixing of the solid solution can be represented using a subregular solution model DELTAG(E) = X(1 - X)[5030X + 4715(1 - X)] J mol-1 By combining this information with the phase diagram, mixing properties of the liquid phase were obtained.

The scratch hardness and friction of a soft rigid-plastic solid

The paper describes an experimental and analytical study of the normal and scratch hardnesses of a model soft rigid-plastic solid. The material known as ‘Plasticine’, a mixture of dry particles and a mineral oil, has been deformed with a range of rigid conical indentors with included angles of between 30° and 170°. The sliding velocity dependence of the computed scratch hardness and friction has been examined in the velocity range 0.19 mm/s to 7.3 m/s. Data are also described for the time dependence of the normal hardness and also the estimated rate dependence of the intrinsic flow stress. The latter values were estimated from data obtained during the upsetting of right cylinders. Three major conclusions are drawn from these data and the associated analysis. (1) A first-order account of the scratching force may be provided by adopting a model which sums the computed plastic deformation and interfacial sliding contributions to the total sliding work. This is tantamount to the adoption of the two-term non-interacting model of friction. (2) For this system during sliding, at high sliding velocities at least, the interface shear stress which defines the boundary condition is not directly related to the bulk shear stress. The interface rheological characteristics indicate an appreciable dependence on the imposed strain or strain rate. In particular, the relative contributions of the slip and stick boundary conditions appear to be a function of the imposed sliding velocity. (3) The computed normal and scratch hardness values are not simply interrelated primarily because of the evolving boundary conditions which appear to exist in the scratching experiments.

Instability and dewetting of ultrathin solid viscoelastic films on homogeneous and heterogeneous substrates

Instability and dewetting engendered by the van der Waals force in soft thin (<100 nm) linear viscoelastic solid (e. g., elastomeric gel) films on uniform and patterned surfaces are explored. Linear stability analysis shows that, although the elasticity of the film controls the onset of instability and the corresponding critical wavelength, the dominant length-scale remains invariant with the elastic modulus of the film. The unstable modes are found to be long-wave, for which a nonlinear long-wave analysis and simulations are performed to uncover the dynamics and morphology of dewetting. The stored elastic energy slows down the temporal growth of instability significantly. The simulations also show that a thermodynamically stable film with zero-frequency elasticity can be made unstable in the presence of physico-chemical defects on the substrate and can follow an entirely different pathway with far fewer holes as compared to the viscous films. Further, the elastic restoring force can retard the growth of a depression adjacent to the hole-rim and thus suppress the formation of satellite holes bordering the primary holes. These findings are in contrast to the dewetting of viscoelastic liquid films where nonzero frequency elasticity accelerates the film rupture and promotes the secondary instabilities. Thus, the zero-frequency elasticity can play a major role in imposing a better-defined long-range order to the dewetted structures by arresting the secondary instabilities. (C) 2011 American Institute of Physics. doi: 10.1063/1.3554748]

Enhanced ionic conductivity in nano-composite solid polymer electrolyte: (PEG) (x) LiBr: y(SiO2)

In this paper, we report an enhancement in ionic conductivity in a new nano-composite solid polymer electrolyte namely, (PEG) (x) LiBr: y(SiO2). The samples were prepared, characterized, and investigated by XRD, IR, NMR, and impedance spectroscopy. Conductivity as a function of salt concentration shows a double peak. Five weight percent addition of silica nanoparticles increases the ionic conductivity by two orders of magnitude. Conductivity exhibits an Arrhenius type dependence on temperature. IR study has shown that the existence of nanoparticles in the vicinity of terminal OaEuro center dot H group results in a shift in IR absorption frequency and increase in amplitude of vibration of the terminal OaEuro center dot H group. This might lead to an enhancement in conductivity due to increased segmental motion of the polymer. Li-7 NMR spectroscopic studies also seem to support this. Thus addition of nanoparticle inert fillers still seems to be a promising technique to enhance the ionic conductivity in solid polymer electrolytes.

Crystallography of solid-liquid interface and evolution of texture during directional solidification of Tb0.3Dy0.7Fe1.95 alloy

The effect of growth texture on the magnetostriction of ternary Tb0.3Dy0.7Fe1.95 was studied by conducting unidirectional solidification experiments using a zoning set-up. Detailed texture evolutions were studied using X-ray diffraction on samples obtained by varying growth rates from 18 to 72 cm/h, under a temperature gradient of 100 degrees C/cm. The estimated texture co-efficient and pole figures of the samples indicate that during the onset of the solidification, < 110 > and < 331 >/'rotated < 110 >' texture components nucleate and grow in all the samples. However, as the solidification progresses, < 112 > texture component becomes dominant at higher growth rate. This results in an improvement of magnetostriction from 1000 to 1300 microstrains for samples grown at growth rates of 18 and 72 cm/h respectively. The transition of preferred growth direction occurs through intermediate orientations < 123 >. An attempt has been made in this paper to explain the occurrence of different growth texture by considering the stability of growing interface, its planar packing fraction and atomic stacking sequence of several low index planes. (C) 2010 Elsevier Ltd. All rights reserved.

Interdiffusion study on Co(W) solid solution and topological close-packed mu phase in Co-W system

An interdiffusion study is conducted on the Co-W system by a diffusion couple technique. The interdiffusion coefficient of the Co(W) solid solution and the Co7W6 mu phase is determined. The activation energy is found to increase with the W content of the Co(W) solid solution. (C) 2010 Elsevier Ltd. All rights reserved.

Mechanistic studies on the effect of ferrocene bonding agents in composite solid propellents

Five compounds, viz. 1,1'-ferrocenediyldiethylidene bis(thiocarbonohydrazide) (DAFT), 1,1-diacetylferrocene disemicarbazone (DAFS), 1,1-diacetylferrocenebenzoyl hydrazone (FDBAH), 1,1-diacetylferrocene-p-nitrobenzoyl hydrazone (FDNBAH), and p-toluenesulfonic acid 1,1'-ferrocenediyldiethylidene dihydrazide (TFDD) were found to be bonding agents as well as burning-rate modifiers for the ammonium perchlorate + hydroxy-terminated polybutadiene system. The tensile strength and percentage elongation significantly increased in the presence of these bonding agents (except FDBAH). The bonding agents generally did not adversely affect the slurry viscosity during processing. The bonding sites were located by infrared spectroscopy, supported by determination of the dissolution kinetics of the bonding agents and scanning electron microscopy. The bonding agents did not undergo any side-reactions with the curing agents.

Gradient solid electrolytes for thermodynamic measurements: System Na2CO3-Na2SO4

The thermodynamic properties of Na2CO3-Na2SO4 solid solution with hexagonal structure have been measured in the temperature range of 873 to 1073 K, using a composite-gradient solid electrolyte. The cell used can be represented as The composite-gradient solid electrolyte consisted of pure Na2CO3 at one extremity and the solid solution under study at the other, with variation in composition across the electrolyte. A CO2 + O2 + Ar gas mixture was used to fix the chemical potential of sodium at each electrode. The Nernstian response of the cell to changes in partial pressures of CO2 and O2 at the electrodes has been demonstrated. The activity of Na2CO3 in the solid solution was measured by two techniques. In the first method, the electromotive force (emf) of the cell was measured with the same CO2 + O2 + Ar mixture at both electrodes. The resultant emf is directly related to the activity of Na2CO3 at the solid solution electrode. By the second approach, the activity was calculated from the difference in compositions Of CO2 + O2 + Ar mixtures at the two electrodes required to produce a null emf. Both methods gave identical results. The second method is more suitable for gradient solid electrolytes that exhibit significant electronic conduction. The activity of Na2CO3 exhibits positive deviation from Raoult's law. The excess Gibbs' energy of mixing of the solid solution can be represented using a subregular solution model such as the following: DELTAG(E) = X(1 - X)[6500(+/-200)X + 3320(+/-80)(1 - X)J mol-1 where X is the mole fraction of Na2CO3. By combining this information with the phase diagram, mixing properties of the liquid phase are obtained.

Highly selective sulfur transfer reaction in the solid state

Benzyltriethylammonium tetrathiomolybdate 1 reacts readily with benzyl halides, alkyl iodides and acyl halides in the solid state to give the corresponding disulfides in good yields and with remarkable selectivity.

Mechanistic studies on the effect of ferrocene bonding agents in composite solid propellents

Five compounds, viz. 1,1'-ferrocenediyldiethylidene bis(thiocarbonohydrazide) (DAFT), 1,1-diacetylferrocene disemicarbazone (DAFS), 1,1-diacetylferrocenebenzoyl hydrazone (FDBAH), 1,1-diacetylferrocene-p-nitrobenzoyl hydrazone (FDNBAH), and p-tolenesulfonic acid, 1,1'-ferrocenediyldiethylidene dihydrazide (TFDD) were found to be bonding agents as well as burning-rate modifiers for the ammonium perchlorate + hydroxy-terminated polybutadiene system. The tensile strength and percentage elongation significantly increased in the presence of these bonding agents (except FDBAH). The bonding agents generally did not adversely affect the slurry viscosity during processing. The bonding sites were located by infrared spectroscopy, supported by determination of the dissolution kinetics of the bonding agents and scanning electron microscopy. The bonding agents did not undergo any side-reactions with the curing agents.

Diffusion path during internal displacement reactions in multi-component oxides: Reaction between Fe and (Co,Mg)TiO3 solid solution at 1273 K

The reaction between Fe foil and a disc of ilmenite solid solution (Co-0.48 Ni-0.52) TiO3 was studied at 1273 K. At the metal/oxide interface, the displacement reaction, Fe + (Co,Mg)TiO3 = Co + (Fe,Mg)TiO3 occurs, resulting in an ilmenite solid solution containing three divalent cations. Ferrous ions diffuse into the oxide solid solution and cause the precipitation of Co-Fe alloy as discrete particles inside the oxide matrix. The morphology of the product layer was characterized by SEM. Only two phases, alloy and ilmenite, were detected in the reaction zone. This suggests that the local flux condition imposed by ilmenite stoichiometry (Co + Fe + Mg):Ti = 1:1] was satisfied during the reactive diffusion: (J(Co) + J(Fe) + J(Mg)) = J(Ti). The composition of the alloy and the oxide was determined using EPMA as a function of distance in the direction of diffusion. Although Mg does not participate in the displacement reaction, its composition in the ilmenite phase was found to be position dependent inside the reaction zone. The up-hill diffusion of inert Mg is caused by the development of chemical potential gradients as a result of displacement reaction. The evolution of composition gradients inside the reaction zone and the diffusion path in a ternary composition diagram of the system CoTiO3-FeTiO3-MgTiO3 are discussed. (C) 2010 Elsevier B.V. All rights reserved.

Reaction of normal and pseudo 2-formylbenzenesulfonyl chlorides with amines:experimental and theoretical studies on the structure of 2-formyl benzenesulfonamides in solid, solution and gas phases

The reaction of 2-formylbenzenesulfonyl chloride 1 and its pseudo isomer 2 with primary amines give either the corresponding sulfonamido Schiff bases or the corresponding 2-formylbenzenesulfonamide depending on the concentration of the amine used. The derivatives exist as an equilibrium mixture of the corresponding sulfonamide and 2-alkyl-3-hydroxy(or 3-aminoalkyl)-benzisothiazole-1,1-dioxide. Spectroscopic studies suggest that 2-formylbenzenesulfonamides exist as benzisothiazole-1,1-dioxides in the solid state, as a mixture of 2-formylbenzenesulfonamide and the corresponding benzisothiazole-1,1-dioxide in solution and as 2-formyl-benzenesulfonamides in the gas phase.