Comparison of simple and pure shear for an incompressible isotropic hyperelastic material under large deformation

The concepts of simple and pure shear are well known in continuum mechanics. For small deformations, these states differ only by a rotation. However, correlations between them are not well defined in the case of large deformations. The main goal of this study is to compare these two states of deformation by means of experimental and theoretical approaches. An incompressible isotropic hyperelastic material was used. The experimental procedures were performed using digital image correlation (DIC). The simple shear deformation was obtained by single lap joint testing, while the pure shear was achieved by means of planar tension testing. Classical hyperelastic constitutive equations available in the literature were used. As a consequence, the results indicate that simple shear cannot be considered as pure shear combined with a rotation when large deformation is assumed, as widely considered in literature.     

Bubble shapes and orientations in low Re simple shear flow

We present measurements of shape and orientation of air bubbles in a viscous Newtonian fluid deformed by simple shear. The apparatus is a variation of the "parallel band" device developed by G. I. Taylor. Previous experimental studies on low viscosity ratio, low Reynolds number (Re < 1) bubble deformation have focussed on either small or large deformations (mostly small deformation) and have only qualitatively examined the orientation of bubbles except for small deformations. Our data set spans both the theoretical small deformation and high deformation limits. With these data we confirm theoretical relationships and assess the range of capillary numbers (Ca) over which theoretical relationships for shape and orientation of bubbles are appropriate. We also examine the geometry of deformed bubbles as they relax to a spherical shape once shear stresses are removed. Our data indicate that for extremely small Reynolds numbers and viscosity ratios, the small deformation theoretical relationship first developed by Taylor, is a good approximation for Ca<0.5. The large deformation results for both shape and bubble orientation derived by Hinch and Acrivos agree with our data for Ca>1 and Ca>0.5, respectively.     

Rheology of interfacial layers

The response of interfacial layers to deformations in size and shape depends on their composition. The corresponding main mechanical quantities are elasticity and viscosity of dilation and shear, respectively. Hence, the interfacial rheology represents a kind of two-dimensional equivalent to the traditional bulk rheology. Due to growing interest in the quantitative understanding of foams and emulsions, more works are dedicated to studies on interfacial rheology. This overview presents the theoretical basis for traditional and recently developed experimental tools and discusses their application to different interfacial systems. While dilational rheology provides information on the composition of mixed interfacial layers, the shear rheology gives answers essentially on structures formed at an interface. The most frequently used methods at present are the oscillating drop and bubble tensiometry methods for dilational deformations and oscillating ring/bicone rheometers for shear deformations.     

6,6-dimethyl-1-oxa-spiro[2.5]octane. Conformational equilibrium in the gas phase as studied by microwave spectroscopy and molecular mechanics calculations

The gas-phase molecular structure of 6,6-dimethyl-1-oxa-spiro[2.5]octane has been investigated by joint analysis of the microwave spectrum and molecular mechanics calculations. Both experimental and theoretical data concur showing the presence of two stable conformational isomers having a chair cyclohexane ring. A set of structural parameters which reproduce the ground state rotational constants has been derived. The influence of 1,4 disubstitution is discussed in terms of deformations of the cyclohexane ring.     

Effect of capillary pressure and surface tension on the deformation of elastic surfaces by sessile liquid microdrops: an experimental investigation

Sessile liquid drops are predicted to deform an elastic surface onto which they are placed because of the combined action of the liquid surface tension at the periphery of the drop and the capillary pressure inside the drop. Here, we show for the first time the in situ experimental confirmation of the effect of capillary pressure on this deformation. We demonstrate micrometer-scale deformations made possible by using a low Young's modulus material as an elastic surface. The experimental profiles of the deformed surfaces fit well the theoretical predictions for surfaces with a Young's modulus between 25 and 340 kPa.     

The umbrella motion of core-excited CH3 and CD3 methyl radicals

An accurate experimental and theoretical study of the lowest core excitation of CH(3) and CD(3) methyl radicals is presented. The complex vibrational structure of the lowest band of the x-ray absorption spectrum (XAS) is due to the large variation of the molecular geometry, which is planar in the ground state and pyramidal in the core-excited state. The XAS spectra of the two radicals were recorded at high resolution and assigned by theoretical simulations of the spectra, taking into account the coupling of symmetrical stretching and symmetrical bending (umbrellalike) deformations of the radicals. An excellent agreement between experimental and theoretical spectral profiles allowed us to accurately characterize the vibrational structure of the electronic transition. The similarities, as well as the differences, of the peculiar vibrational progression observed for the two radicals are explained by the strong anharmonicity along the umbrella coordinate and by the isotopic variation, leading to a different probing of the double-well potential energy surface of the core excited state during the nuclear motion.     

Theory of non-equilibrium force measurements involving deformable drops and bubbles

Over the past decade, direct force measurements using the Atomic Force Microscope (AFM) have been extended to study non-equilibrium interactions. Perhaps the more scientifically interesting and technically challenging of such studies involved deformable drops and bubbles in relative motion. The scientific interest stems from the rich complexity that arises from the combination of separation dependent surface forces such as Van der Waals, electrical double layer and steric interactions with velocity dependent forces from hydrodynamic interactions. Moreover the effects of these forces also depend on the deformations of the surfaces of the drops and bubbles that alter local conditions on the nanometer scale, with deformations that can extend over micrometers. Because of incompressibility, effects of such deformations are strongly influenced by small changes of the sizes of the drops and bubbles that may be in the millimeter range. Our focus is on interactions between emulsion drops and bubbles at around 100 μm size range. At the typical velocities in dynamic force measurements with the AFM which span the range of Brownian velocities of such emulsions, the ratio of hydrodynamic force to surface tension force, as characterized by the capillary number, is ~ 10^{− 6} or smaller, which poses challenges to modeling using direct numerical simulations. However, the qualitative and quantitative features of the dynamic forces between interacting drops and bubbles are sensitive to the detailed space and time-dependent deformations. It is this dynamic coupling between forces and deformations that requires a detailed quantitative theoretical framework to help interpret experimental measurements. Theories that do not treat forces and deformations in a consistent way simply will not have much predictive power. The technical challenges of undertaking force measurements are substantial. These range from generating drop and bubble of the appropriate size range to controlling the physicochemical environment to finding the optimal and quantifiable way to place and secure the drops and bubbles in the AFM to make reproducible measurements. It is perhaps no surprise that it is only recently that direct measurements of non-equilibrium forces between two drops or two bubbles colliding in a controlled manner have been possible. This review covers the development of a consistent theory to describe non-equilibrium force measurements involving deformable drops and bubbles. Predictions of this model are also tested on dynamic film drainage experiments involving deformable drops and bubbles that use very different techniques to the AFM to demonstrate that it is capable of providing accurate quantitative predictions of both dynamic forces and dynamic deformations. In the low capillary number regime of interest, we observe that the dynamic behavior of all experimental results reviewed here are consistent with the tangentially immobile hydrodynamic boundary condition at liquid–liquid or liquid–gas interfaces. The most likely explanation for this observation is the presence of trace amounts of surface-active species that are responsible for arresting interfacial flow.     

A study of the elastoplastic properties of polymer-silicate nanocomposites with allowance for the change in their volumes during deformation

The results of experimental and theoretical studies of the elastoplastic properties of medium-density polyethylene and nanocomposites formed on its basis with a filler of layered clay minerals are described. It is found that the deformation of these materials is accompanied by a significant change in their volumes, which is primarily caused by the development of internal damage of the system (the formation of pores and cracks at the microlevel). A component that takes into account the change in volume during deformation is introduced into the previously proposed model of a heterogeneous medium that can undergo significant non-linear elastic and plastic deformations. For this purpose, we use a differential approach to the construction of constitutive equations and an additive decomposition of the total strain-rate tensor of the medium into strainrate tensors of the elastic and plastic components. Using an improved model, we describe the experimental curves of uniaxial stretching for pure PE and two PE-based polymer-silicate nanocomposites. The introduction of filler particles into the polymer matrix leads to enhancement of the role of two structural mechanisms in the formation of plastic properties: The presence of the filler contributes to the development of internal structural damage; the same particles decrease the orientation ability of the PE matrix, thereby hindering the development of plastic deformations in it. The use of tensor variables in the model makes it appropriate for describing not only stretching but also other types of loading of the material.     

Pressure-induced amorphization in mayenite (12CaO·7Al2O3)

We report a joint experimental and theoretical study on high pressure structures of nanoporous mayenite (12CaO·7Al(2)O(3)). A pressure-induced amorphization was identified at ～13 GPa by in situ high pressure x-ray experiments. The amorphous product can be decompressed to ambient conditions. Ab initio calculations reveal that the anisotropic deformations of empty cages break the crystallographic long-range orders, leading to the formation of high-pressure amorphous state. Furthermore, the deformation routes of empty cages are found fully dependent on their individual locally structural geometry relevant to the distribution of extra-framework oxygen ions.     

Relaxation of surfactants adsorption layers at liquid interfaces

The relaxation behaviour of surfactant layers provides a deep insight into the composition and structure of adsorbed layers at liquid interfaces. The development of professional experimental tools created a helpful basis for an increasing interest in these studies. In addition, the theoretical basis has been improved in many aspects such that for several surfactant systems a quantitative understanding is already possible. In particular the consideration of the changes in molar area of adsorbed molecules, introduced into the thermodynamics of adsorbed layers first by Fainerman in 1995, due to changes in the surface coverage allowed a considerably better, in many cases even quantitative understanding of the surface relaxation. Another important additional property, introduced into the thermodynamics and consequently also into the mechanisms of relaxation processes in interfacial layers, is the two-dimensional compressibility, important for the response to deformations of rather packed interfacial layers. The experimentally observed negative dilational viscosity is discussed only briefly and considered essentially in terms of experimental and theoretical shortcomings. The relaxation behaviour of nano- and microparticles, in literature often addressed is compounds able to act “instead of surfactants” are also addressed and some peculiarities discussed, while the obvious interrelation between the dilational rheology and stability of foams and emulsions is not analysed in detail.     

The Effects of Chemical Bonding at Subatomic Resolution: A Case Study on α-Boron

Similar to classical asphericity shifts, aspherical deformations of the electron density in the atomic core region can result in core asphericity shifts in refinements using a Hansen-Coppens multipolar model (HCM), especially when highly precise experimental datasets with resolutions far beyond sin(θ)/λ ≤ 1.0 Å⁻¹ are employed. These shifts are about two orders of magnitude smaller than their counterparts caused by valence shell deformations, and their underlying deformations are mainly of dipolar character for 1st row atoms. Here, we analyze the resolution dependence of core asphericity shifts in α-boron. Based on theoretical structure factors, an appropriate Extended HCM (EHCM) is developed, which is tested against experimental high-resolution (sin(θ)/λ ≤ 1.6 Å⁻¹) single-crystal diffraction data. Bond length deviations due to core asphericity shifts of α-boron in the order of 4–6·10⁻⁴ Å are small but significant at this resolution and can be effectively compensated by an EHCM, although the correlation of the additional model parameters with positional parameters prevented a free refinement of all core model parameters. For high quality, high resolution data, a proper treatment with an EHCM or other equivalent methods is therefore highly recommended.     

Structural remodeling and mechanical function in heart failure

The cardiac extracellular matrix (ECM) is the three-dimensional scaffold that defines the geometry and muscular architecture of the cardiac chambers and transmits forces produced during the cardiac cycle throughout the heart wall. The cardiac ECM is an active system that responds to the stresses to which it is exposed and in the normal heart is adapted to facilitate efficient mechanical function. There are marked differences in the short- and medium-term changes in ventricular geometry and cardiac ECM that occur as a result of volume overload, hypertension, and ischemic cardiomyopathy. Despite this, there is a widespread view that a common remodeling "phenotype" governs the final progression to end-stage heart failure in different forms of heart disease. In this review article, we make the case that this interpretation is not consistent with the clinical and experimental data on the topic. We argue that there is a need for new theoretical and experimental models that will enable stresses acting on the ECM and resultant deformations to be estimated more accurately and provide better spatial resolution of local signaling mechanisms that are activated as a result. These developments are necessary to link the effects of structural remodeling with altered cardiac mechanical function.     

Phonons in suspensions of hard sphere colloids: volume fraction dependence

The propagation of sound waves in suspensions of hard sphere colloids is studied as a function of their volume fraction up to random close packing using Brillouin light scattering. The rich experimental phonon spectra of up to five phonon modes are successfully described by theoretical calculations based on the multiple scattering method. Two main types of phonon modes are revealed: Type A modes are acoustic excitations which set up deformations in both the solid (particles) and the liquid (solvent) phases; for type B modes the stress and strain are predominantly localized near the interface between the solid particles and the surrounding liquid (interface waves). While the former become harder (increase their effective sound velocity) as the particle volume fraction increases the latter become softer (the corresponding sound velocity decreases).     

A 2D electrohydrodynamic model for electrorotation of fluid drops

A theoretical analysis of spontaneous electrorotation of deformable fluid drops in a DC electric field is presented with a 2D electrohydrodynamic model. The fluids in the system are assumed to be leaky dielectric and Newtonian. If the rotating flow is dominant over the cellular convection type of electrohydrodynamic flow, closed-form solutions for drops of small deformations can be obtained. Because the governing equations are in general nonlinear even when drop deformations are ignored, the general solution for even undeformed drop takes a form of infinite series and can only be evaluated by numerical means. Both closed-form solutions for special cases and numerical solutions for more general cases are obtained here to describe steady-state field variables and first-order drop deformations. In a DC electric field of strength beyond the threshold value, spontaneous electrorotation of a drop is shown to occur when charge relaxation in the surrounding fluid is faster than the fluid inside the drop. With increasing the strength of the applied electric field from the threshold for onset of electrorotation, the axis of drop contraction deviates from from that of the applied electric field in the direction of the rotating flow with an angle increasing with the field strength.     

Some electrohydrodynamic effects in fluid dispersions

Under the combined influence of applied shear and electric fields, the macroscopic behavior of suspensions reflects coupling of the two fields which produces stresses at the phase boundaries. These stresses in turn cause motion and/or deformation of the suspended phase. Electrohydrodynamic (EHD) factors which govern these motions and deformations are reviewed in detail. both in a general theoretical context and also in terms of extensive experimental observations. Throughout an attempt has been made to relate the microscopic behaviour (including interactions) of the suspended phase to macroscopically observable or bulk properties of the suspension as a whole.The phenomena reviewed here are important to a large number of colloidal problems of interest to the physical, biological and earth sciences.     

Modified slotted shear test for a thin sheet of solid polymer under large deformations

A modified slotted shear test based on ASTM B831 is proposed and used for determining the mechanical behavior of a solid polymer at large deformations. The shear stress-strain response of a thin sheet of polytetrafluoroethylene was experimentally investigated and a V-notched rail shear test was carried out to validate the experimental results obtained with the proposed approach. Displacement and strain fields of the test specimens were estimated by the Digital Image Correlation method. The results indicate agreement between both tests for small deformations, while for large deformations significant discrepancies in shear stress-strain responses are observed. These discrepancies can be attributed to unwanted distortions of the gage section observed in the V-notched specimens. The modified slotted shear test provided a uniform shear strain distribution across the gauge section of specimens. In addition, the principal advantages of the proposed approach over V-notched rail shear test are a wide range of shear strains and absence of unwanted distortions.     

Theory of capillary-induced interactions beyond the superposition approximation

Within a general theoretical framework, we study the effective, deformation-induced interaction between two colloidal particles trapped at a fluid interface in the regime of small deformations. In many studies, this interaction has been computed with the ansatz that the actual interface configuration for the pair is given by the linear superposition of the interface deformations around the single particles. Here, we assess the validity of this approach and compute the leading term of the effective interaction for a large interparticle separation beyond this so-called superposition approximation. As an application, we consider the experimentally relevant case of interface deformations owing to the electrostatic field emanating from charged colloidal particles. In mechanical isolation, i.e., if the net force acting on the total system consisting of the particles plus the interface vanishes, the superposition approximation is actually invalid. The effective capillary interaction is governed by contributions beyond this approximation and turns out to be attractive. For sufficiently small surface charges on the colloids, such that linearization is strictly valid, and at asymptotically large separations, the effective interaction does not overcome the direct electrostatic repulsion between the colloidal particles.