Elastic Term Research Articles

Pattern selection in Rayleigh-Bénard convection with nonlinear viscoelastic fluids

A numerical investigation is conducted of Rayleigh-B\'enard convection in a rectangular enclosure of aspect ratio 2:1 filled by a class of nonlinear viscoelastic fluids represented by the Phan Thien-Tanner (PTT) constitutive equation. The objective is to provide a detailed interpretation of the physical mechanisms involved in Rayleigh-B\'enard convection for a viscoelastic fluid. An energy analysis highlights the different physical mechanisms involved in oscillatory convection. The results show the contribution of the elastic terms in the evolution of the kinetic energy of the structures. At a second critical Rayleigh number the oscillatory convection with two rollers becomes stationary again.

Precise Tuning and Characterization of Viscoelastic Interfaces for the Study of Early Epithelial-Mesenchymal Transition Behaviors.

There is growing evidence that cellular functions are regulated by the viscoelastic nature of surrounding matrices. This study aimed to investigate the impact of interfacial viscoelasticity on adhesion and epithelial-mesenchymal transition (EMT) behaviors of epithelial cells. The interfacial viscoelasticity was manipulated using spin-coated thin films composed of copolymers of ε-caprolactone and d,l-lactide photo-cross-linked with benzophenone, whose mechanical properties were characterized using atomic force microscopy and a rheometer. The critical range for the morphological transition of epithelial Madin-Darby canine kidney (MDCK) cells was of the order of 102 ms relaxation time, which was 1-2 orders of magnitude smaller than the relaxation times reported (10-102 s). An analysis of strain rate-dependent viscoelastic properties revealed that the difference was caused by the different strain rate/frequency used for the mechanical characterization of the interface and bulk. Furthermore, decoupling of the interfacial viscous and elastic terms demonstrated that E/N-cadherin expression levels were regulated differently by interfacial relaxation and elasticity. These results confirm the significance of precise manipulation and characterization of interfacial viscoelasticity in mechanobiology studies on EMT progression.

Equilibrium morphology of tactoids in elastically anisotropic nematics.

We study two dimensional tactoids in nematic liquid crystals by using a Q-tensor representation. A bulk free energy of the Maier-Saupe form with eigenvalue constraints on Q, plus elastic terms up to cubic order in Q are used to understand the effects of anisotropic anchoring and Frank-Oseen elasticity on the morphology of nematic-isotropic domains. Further, a volume constraint is introduced to stabilize tactoids of any size at coexistence. We find that anisotropic anchoring results in differences in interface thickness depending on the relative orientation of the director at the interface, and that interfaces become biaxial for tangential alignment when anisotropy is introduced. For negative tactoids, surface defects induced by boundary topology become sharper with increasing elastic anisotropy. On the other hand, by parametrically studying their energy landscape, we find that surface defects do not represent the minimum energy configuration in positive tactoids. Instead, the interplay between Frank-Oseen elasticity in the bulk, and anisotropic anchoring yields semi-bipolar director configurations with non-circular interface morphology. Finally, we find that for growing tactoids the evolution of the director configuration is highly sensitive to the anisotropic term included in the free energy, and that minimum energy configurations may not be representative of kinetically obtained tactoids at long times.

Nonlinear transmission line (NTL) model study of electromagnetic effects in high-frequency asymmetrically driven capacitive discharges

In this work, we generalize a nonlinear transmission line (NTL) model introduced in a previous work [Liu et al. Plasma Sources Sci. Technol. 30, 045017 (2021)] to achieve more comprehensive simulations. The improved NTL model allows a variable-sized (instead of a one grid cell) vacuum spacer between the powered and grounded electrodes and takes into account the (previously neglected) electron-neutral elastic collision frequency term in the plasma dielectric constant, and the radial variation of the plasma density. Using this model, we study the effects of the spatial and series resonances, associated with the (axially) z-antisymmetric and z-symmetric radially propagating surface wave modes, and the nonlinear harmonic excitations on the plasma uniformity. We conduct simulations in which we increase the driving frequency f from 30 to 120 MHz for an asymmetric capacitive argon discharge at a fixed pressure and electron power of pg=20 mTorr and Pe=40 W, respectively. The first antisymmetric mode resonance frequency fa1 occurs between 80 and 90 MHz, and the first symmetric mode resonance frequency fs1 occurs at about 100 MHz. The powered electrode sheath becomes smaller than the grounded electrode sheath for f≈fa1, and the source voltage reaches a minimum for f≈fs1. The radially varying electron power density shows a narrow center peak due to the finite mode wavelengths and the nonlinearly excited harmonics, which can be further enhanced by spatial or series resonances. A second peak appears above the vacuum spacer edge as f exceeds fs1 at 120 MHz because the shorter wavelengths at higher f allow secondary maxima of the surface waves to form within the reactor.

Chemomechanical equilibrium at the interface between a simple elastic solid and its liquid phase.

Applying diffusion coupled deformation theory, we investigate how the elastic properties of a solid body are modified when forced to keep its chemical potential aligned with that of its melt. The theory is implemented at the classical level of continuum mechanics, treating materials as simple continua defined by uniform constitutive relations. A phase boundary is a sharp dividing surface separating two continua in mechanical and chemical equilibrium. We closely follow the continuum theory of the swelling of elastomers (gels) but now applied to a simple two phase one-component system. The liquid is modeled by a local free energy density defining a chemical potential and hydrostatic pressure as usual. The model is extended to a solid by adding a non-linear shear elastic energy term with an effective modulus depending on density. Imposing chemomechanical equilibrium with the liquid reservoir reduces the bulk modulus of the solid to zero. The shear modulus remains finite. The stability of the hyper-compressible solid is investigated in a thought experiment. A mechanical load is applied to a rectangular bar under the constraintof fixed lateral dimensions. The linear elastic modulus for axial loading is evaluated and found to be larger than zero, implying that the bar, despite the zero bulk modulus, can support a weight placed on its upper surface. The weight is stabilized by the induced shear stress. The density dependence of the shear modulus is found to be a second order effect reducing the density of the stressed solid (chemostriction).

General decay and blow up of solutions for a class of inverse problem with elasticity term and variable‐exponent nonlinearities

In this paper, we study a class of Lamé inverse source problem with variable‐exponent nonlinearities. Under some suitable conditions on the coefficients and initial data, we proved general decay of solutions when the integral overdetermination tends to zero as time goes to infinity in appropriate range of variable exponents. Furthermore, in the absence of damping term, we show that there are solutions under some conditions on initial data and variable exponents which blow up in finite time.

Effect of the elastic hysteresis term formulation and response to non-harmonic periodic excitations of a non-linear SDOF dynamical model with weak frequency-dependency in the time domain

We elaborate a SDOF time-domain model for elastic hysteretic damping, by modifying the viscous damping model to introduce an instantaneous correction factor that recursively depends on the state variables of the system, such that the response exhibits weak dependency on frequency, corresponding to a large array of engineering materials. The effect of different formulations for calculating the instantaneous correction factor on the predicted hysteresis loops and the potential manifestation of singularities is studied. Hysteresis loops anticipated by the model are plotted and forced vibration responses to harmonic and other periodic non-harmonic excitations are simulated and discussed, also in comparison to the conventional viscous and Reid’s damping models.

Photoelastic Properties of Trigonal Crystals

All possible experimental geometries of the piezo-optic effect in crystals of trigonal symmetry are studied in detail through the interferometric technique, and the corresponding expressions for the calculation of piezo-optic coefficients (POCs) πim and some sums of πim based on experimental data obtained from the samples of direct and X/45°-cuts are given. The reliability of the values of POCs is proven by the convergence of πim obtained from different experimental geometries as well as by the convergence of some sums of POCs. Because both the signs and the absolute values of POCs π14 and π41 are defined by the choice of the right crystal-physics coordinate system, we here use the system whereby the condition S14 > 0 is fulfilled (S14 is an elastic compliance coefficient). The absolute value and the sign of S14 are determined by piezo-optic interferometric method from two experimental geometries. The errors of POCs are calculated as mean square values of the errors of the half-wave stresses and the elastic term. All components of the matrix of elasto-optic coefficients pin are calculated based on POCs and elastic stiffness coefficients. The technique is tested on LiTaO3 crystal. The obtained results are compared with the corresponding data for trigonal LiNbO3 and Ca3TaGa3Si2O14 crystals.

Viscoelastic response of impact process on dense suspensions

We numerically study impact processes on dense suspensions using the lattice Boltzmann method to elucidate the connection between the elastic rebound of an impactor and relations among the impact speed u0, maximum force acting on the impactor Fmax, and elapsed time tmax to reach Fmax. We find that tmax emerges in the early stage of the impact, while the rebound process takes place in the late stage. We find a crossover of Fmax from the u0 independent regime for low u0 to a power law regime satisfying Fmax∝u0α with α≈1.5 for high u0. Similarly, tmax satisfies tmax∝u0β with β≈−0.5 for high u0. Both power-law relations for Fmax and tmax vs u0 for high u0 are independent of the system size, but the rebound phenomenon strongly depends on the depth of the container for suspensions. Thus, we indicate that the rebound phenomenon is not directly related to the relations among u0, Fmax and tmax. We propose a floating + force chain model, where the rebound process is caused by an elastic term that is proportional to the number of the connected force chains from the impactor to the bottom plate. On the other hand, there are no elastic contributions in the relations for Fmax and tmax against u0 because of the absence of percolated force chains in the early stage. This phenomenology predicts Fmax∝u03/2 and tmax∝u0−1/2 for high u0 and also recovers the behavior of the impactor quantitatively even if there is the rebound process.

A regularized isothermal phase-field model of two-phase solid–fluid mixture and its spatial dissipative discretization equations

Abstract The present paper is devoted to a model describing a two-phase isothermal mixture, in which one of the phases obeys solid-like (namely, elastic) rheology. A fully Eulerian description is considered. To describe the stress–strain behaviour of the solid phase the elastic energy term is added to the Helmholtz free energy. The term depends on Almansi strain tensor. In its turn, the strain tensor is defined as the solution of the corresponding evolutionary equation. Considered model belongs to the phase field family. Formally it describes two-component mixture and uses mass densities of the components as order parameters. A distinctive feature of the considered model is its preliminary regularization according to the quasi-hydrodynamic framework. The dissipativity in total energy is proved when periodic boundary conditions are imposed. A spatial dissipative semi-discrete (continuous in time and discrete in space) scheme based on staggered grids is suggested. The theoretical results remain valid in the absence of the regularization. The results of a numerical study in a 2D setting are presented.

Effects of prolonged saline water exposure on the peel strength of polyurea/monel 400 interface

ABSTRACT This study investigates changes in the peel strength of polyurea/monel 400 interfaces after prolonged exposure to saline water. The monel family of alloys is extensively used on marine structures due to its resistance to corrosion, and polyurea has shown considerable promise as a coating material for marine structures to mitigate the damage from blast loading and provide corrosion resistance. In the present work, polyurea was cast on sandblasted and chemically treated Monel 400 bars, which were subsequently immersed in saline water at 70°C for 2, 5 and 8 weeks, respectively, to accelerate the aging process. This high-temperature exposure corresponded to 19, 48 and 76 weeks in the real-life service environment. The peel strengths of the interfaces were measured using the fixed arm peel test at two angles: 90° and 180°. The adhesive energy was computed from the experimentally determined peel strength using models developed by Kendall and Rivlin. The surfaces exposed by peeling were analyzed with the use of an optical microscope to determine the different failure modes at the interfaces. Finally, employing degradation kinetics, a degradation model was established and used to calculate long-term adhesive energy and the degradation rate of the interface. Results showed that prolonged exposure to saline water leads to a drop in the peel strength. For 180° peel test, an 83% decrease in the peel strength of the polyurea/monel 400 interface was observed after 8 weeks of exposure at 70°C. Both peel angles gave similar adhesive energies for the same exposure durations indicating the independence of the adhesive energy on the testing angle. The elastic term contribution to the adhesive energy for all experiments was less than 5.5%. Lastly, the exposure time dependence on the adhesive energy followed first-order degradation kinetics.

Pathfollowing of high-dimensional hysteretic systems under periodic forcing

The dynamic response and bifurcations of high-dimensional systems endowed with hysteretic restoring forces in all degrees of freedom are investigated. Two types of hysteresis models are considered, namely the Bouc–Wen model and a differential version of the so-called exponential model of hysteresis. The numerical technique tailored for tackling high-dimensional hysteretic systems is based on an enhanced pathfollowing approach based on the Poincare map. In particular, a five-dof mass-spring-damper-like system, with each rheological element described by the Bouc–Wen or the exponential model of hysteresis enriched by cubic and quintic nonlinear elastic terms, is investigated and a rich variety of nonlinear responses and bifurcations is found and discussed.

A novel ADRC-based design for a kind of flexible aerocraft

The paper presents a novel control design, which is based on the idea of active disturbance rejection control (ADRC), for a kind of flexible aerocraft whose controlled variable cannot be measured directly. Since the original frame of ADRC cannot be directly applied, the paper puts forward a new extended state observer (ESO) and the corresponding ADRC law. In order to assign the poles of the closed-loop system to ideal positions such that the vibration can be quickly suppressed, an elastic damping term is added into feedback law. The advantages of the new ESO for effectively estimating both the rigid mode and elastic mode from the measurements are discussed. Moreover, the analysis on the stability, the relative stability and the steady state of the closed-loop system is given. Finally, the effectiveness and robustness of the proposed ADRC are verified by simulations.

On the second order term asymptotic solution for sharp V-notch tip field in elasto-viscoplastic solids

A two-order asymptotic solution for sharp V-notch tip mechanics field in elasto-viscoplastic solids with power-law form under mode I loading is developed. The stress exponents and angular distributions for various notch angles and viscoplastic exponents for the second terms are reported. The stress exponent of the first order is singular and is non-singular except for low creep exponent with small notch opening angle. Compared with finite element results from several V-notched specimens, it is found that the two-order solution can have a better estimate for those cases with small notch opening angles, e.g., α = 30° under n = 5, than that of one-order solution regardless of viscoplastic extent, specimen type and loading level. One-order term solution is demonstrated to be sufficient to characterize the full field of sharp V-notch specimen for those conditions that elastic term is considered into higher order term, e.g., α = 60° under n = 5, in all specimens under various viscoplasticity extents.

Homotopy Analysis Method for a Conservative Nonlinear Oscillator with Fractional Power

In this paper, the homotopy analysis method is applied to deduce the periodic solutions of a conservative nonlinear oscillator for which the elastic force term is proportional to u1/3. By introducing the auxiliary linear operator and the initial guess of solution, the homotopy analysis solving is set up. By choosing the suitable convergence-control parameter, the accurate high-order approximations of solution and frequency for the whole range of initial amplitudes can easily be obtained. Comparison of the results obtained using this method with those obtained by different methods reveals that the former is more accurate, effective and convenient for these types of nonlinear oscillators.

Improved Mitigation Method for the Multipath Delays of BDS‐3 Code Observations with the Aid of a Sparse Modeling Algorithm

Global navigation satellite systems are essential for positioning, navigation, and timing services. The quality and reliability of satellite observations determine the system performance, especially in the case of the newly launched global BDS‐3 service. However, analyses of multipath delays in BDS‐3 satellite observations suggest that there are appreciable errors at different frequencies. Improvement of the accuracy and precision of positioning, navigation, and timing services provided by BDS‐3 requires the mitigation of multipath delays of the satellite observations. This paper models the multipath delays of BDS‐3 observations using a least‐squares combined autoregressive method. Furthermore, a sparse modeling algorithm is proposed to obtain a multipath delay series using total variation and elastic net terms for denoising and eliminating the effect of limited original observations. The estimated coefficients of multipath delays are then set as prior information to correct the next‐arc code observations, where the square‐root information filter is used in the coefficient estimation. Moreover, four groups of experiments are conducted to analyze the results of modeling the BDS‐3 multipath delay using the proposed methods, with single‐frequency precise point positioning (PPP) and real‐time PPP solutions being selected to test the correction of multipath delays in BDS‐3 code observations. The residuals of iGMAS and MGEX station coordinates indicate improvements in eastward, northward, and upward directions of at least 4.1%, 9.6%, and 1.2%, respectively, for the frequency B1I; 6.6%, 5.3%, and 0.2%, respectively, for B3I, 12.5%, 14.3%, and 3.8%, respectively, for B1C; and 5.9%, 7.4%, and 18.1%, respectively, for B2a relative to the use of the traditional method in BDS‐3 single‐frequency PPP. Furthermore, the real‐time double‐frequency PPP is optimized by at least 10% for B1I + B3I and B1C + B2a. An improved result was obtained with the proposed strategy in a standard point positioning experiment. The proposed multipath delay mitigation method is therefore effective in improving BDS‐3 satellite code observations.

Stress correlation function and linear response of Brownian particles

.We determine the non-local stress autocorrelation tensor in an homogeneous and isotropic system of interacting Brownian particles starting from the Smoluchowski equation of the configurational probability density. In order to relate stresses to particle displacements as appropriate in viscoelastic states, we go beyond the usual hydrodynamic description obtained in the Zwanzig-Mori projection-operator formalism by introducing the proper irreducible dynamics following Cichocki and Hess, and Kawasaki. Differently from these authors, we include transverse contributions as well. This recovers the expression for the stress autocorrelation including the elastic terms in solid states as found for Newtonian and Langevin systems, in case that those are evaluated in the overdamped limit. Finally, we argue that the found memory function reduces to the shear and bulk viscosity in the hydrodynamic limit of smooth and slow fluctuations and derive the corresponding hydrodynamic equations.Graphical abstract

The Politics of Humour in Kafkaesque Cinema: A World-Systems Approach

Kafka's work has exercised immense influence on cinema and his reflections on diminished human agency in modernity and the dominance of oppressive institutions that perpetuate individual or social alienation and political repression have been the subject of debates by philosophers such as Theodor Adorno, Walter Benjamin, Gilles Deleuze, Félix Guattari, and Alexander Kluge. Informed by a world-systems approach and taking a cue from Jorge Luis Borges’ point that Kafka has modified our conception of the future, and André Bazin's suggestion that literary concepts, characters and styles can exceed “novels from which they emanate”, I understand the Kafkaesque as an elastic term that can refer to diverse films that might share thematic preoccupations, but also aesthetic and formal differences. In this article, I explore the politics of humour in Kafkaesque cinema with reference to the following films: The Overcoat ( Шинель, 1926, Gregor Koznitzev and Leo Trauberg), The Shop on Main Street ( Obchod na korze, 1965, Ján Kadár), and Death of a Bureaucrat ( La muerte de un burócrata, 1966, Tomás Gutiérrez Alea). I draw attention to the dialectics of humour and the connection between the Kafkaesque and slapstick so as to show how humour is deployed as a means of political critique.

Calculations of vibration isolation systems by means of SCAS KiDyM in a nonlinear setting

The problem of vibration isolation of a device installed on four three-degree elastic shock absorbers with nonlinear characteristics, as an example of vibration isolation of a discrete system of arbitrary structure with several nonlinear elastic shock absorbers is considered in given paper. An analytical description of mechanical models is applied According to this description a special computer algebra system KiDyM (SCAS KiDyM) constructs differential equations of motion, linearizes inertial and elastic terms by means of elimination of the first small terms, carrying out harmonic linearization of the second one. After getting linear multi-mass mathematical model, the KiDyM software package performs calculations of free vibrations and presents the results in the form of skeletal curves. It allows to determine their sensitivity to the values of elastic and inertial parameters, It makes possible to carry out a cycle of calculations with varying model parameters to achieve optimal characteristics of the vibration protection system by shear and deformation of skeletal curves. An example of the problem analysis solution to the above-mentioned vibration protection system of a device performing spatial vibrations is given. Thus, the system contains 12 nonlinearities. The method for determining the experimental elastic characteristics for specimens of two types of shock absorbers is described. The possibilities of narrowing the spectrum of free vibrations by taking into account the nonlinearity of shock absorbers and the problem of skeletal curves construction of systems with several nonlinearities with generalized coordinates as the main coordinates of the oscillatory system.

Anisotropic disclination cores in nematic liquid crystals modeled by a self-consistent molecular field theory.

Disclination configurations of a nematic liquid crystal are studied within a self-consistent molecular field theory. The theory is based on a tensor order parameter, and can accommodate anisotropic elastic energies without the known divergences in the Landau-de Gennes formulation. Our results agree with the asymptotic results of Dzyaloshinskii for the Frank-Oseen energy far from the defect core, but reveal biaxial order at intermediate distances from the core, crossing over to uniaxial but axisymmetric configurations as the core is approached. The elastic terms considered in our energy allow for the separate control of surface tension, anchoring, and elasticity contrast, and are used to analyze recent results for lyotropic chromonic liquid crystals. The latter display unusually large defect cores (on the order of tens of microns) which can be used for a quantitative comparison with the theory. Both ±1/2 disclination configurations are well reproduced by our calculations. Elastic anisotropy is also shown to lead to qualitative changes in the disclination polarization, a quantity that is proportional to the active stress in models of active matter.