Presence Of Elasticity Research Articles

Differential kinematics of a single-point-suspended manipulator with center-of-mass shift compensation

The single cable-suspended manipulator is suitable for special occasions such as aerial operation tasks of unmanned aerial vehicles (UAVs) and deep-well search and rescue. However, due to the lack of complete constraints at the base, the manipulator will have errors in end position due to the center-of-mass offset during the motion. In this paper, the model of CoM shifting is established, and the Jacobian matrix is improved based on this model, to realize the differential kinematics solution for the single cable-suspended manipulator. In addition, by introducing the constraint of CoM shift in the Jacobian matrix, it makes it possible to synchronize the planning of the motion of the end and the center of mass. This can effectively avoid the wobbling of the manipulator in the presence of elasticity or instability at the suspension point. Both simulation and prototype experiments effectively verify the effectiveness of the proposed method. Using the method of this paper, the average error of the trajectories in the z-axis and x-axis can be reduced from 27.0 ± 2.6 mm to 5.6 ± 3.4 mm, and 43.0 ± 64.2 mm to 3.3 ± 4.8 mm, respectively.

Viscoelasticity, logarithmic stresses, and tensorial transport equations

We introduce models for viscoelastic materials, both solids and fluids, based on logarithmic stresses to capture the elastic contribution to the material response. The matrix logarithm allows to link the measures of strain, that naturally belong to a multiplicative group of linear transformations, to stresses, that are additive elements of a linear space of tensors. As regards the viscous stresses, we simply assume a Newtonian constitutive law, but the presence of elasticity and plastic relaxation makes the materials non‐Newtonian. Our aim is to discuss the existence of weak solutions for the corresponding systems of partial differential equations in the nonlinear large‐deformation regime. The main difficulties arise in the analysis of the transport equations necessary to describe the evolution of tensorial measures of strain. For the solid model, we only need to consider the equation for the left Cauchy–Green tensor, while for the fluid model, we add an evolution equation for the elastically‐relaxed strain. Due to the tensorial nature of the fields, available techniques cannot be applied to the analysis of such transport equations. To cope with this, we introduce the notion of charted weak solution, based on non‐standard a priori estimates, that lead to a global‐in‐time existence of solutions for the viscoelastic models in the natural functional setting associated with the energy inequality.

Coherent structures in elastic turbulent planar jets

At low Reynolds numbers, the flow of a Newtonian planar jet remains laminar, thus easy to characterize. In contrast, the presence of elasticity (e.g., attained dissolving polymers in a Newtonian solvent) enables a highly-complex turbulent-like behavior termed elastic turbulence. In this work, we run data-driven modal decomposition algorithms on high-fidelity data collected from the simulation of an elastic turbulent planar jet. The large-scale motions are expressed as a finite expansion of modes that condense the dominant dynamics. The modes associated with lower frequencies weight the most on the reconstruction of the original data, thus they are further decomposed in space to investigate their implications on the sustainment of the elastic turbulent state. Our findings suggest that slower dynamics are crucial for the sustainment of elastic turbulence, which is connected to the interaction of spanwise-coherent structures, steady in space, with spanwise-periodic traveling waves, causing the breakdown of the structures close to the inlet.

Ductile rupture under cyclic loadings at high triaxiality: The influence of strain hardening and elasticity

Previous works (Devaux et al., 1997; Cheng et al., 2017) have emphasized the effects of strain hardening and elasticity upon ductile rupture of metals under cyclic loading conditions. This work pursues the study and modelling of these two effects by distinct theoretical methods, each coupled with micromechanical finite element simulations of the behaviour of some “representative cell”. For the effect of strain hardening, we employ Morin et al. (2017)’s approach, based on the theory of sequential limit-analysis (Yang, 1993; Leu, 2007; Leblond et al., 2018). This approach is applied to various types of hardening of the metallic matrix: isotropic, linear kinematic, nonlinear kinematic with one or two kinematic variables (Armstrong and Frederick, 2007) , and even a simplified version of Chaboche (1991)’s model accounting for complex cyclic effects. Numerical micromechanical simulations of a hollow sphere made of elastic–plastic materials obeying the various hardening laws considered, and subjected to cyclic loadings at high triaxiality, fully confirm the predictions of the model developed, provided elasticity is made negligible by using an artificially high value of Young’s modulus. When a realistic value is employed, however, the agreement between theoretical predictions and numerical results is degraded, thus emphasizing again the importance of the effect of elasticity in cyclic ductile rupture. To deal with this effect we derive, apparently for the first time, an evolution equation of the porosity accounting for (compressible) elasticity. However, numerical micromechanical simulations reveal that simply using this new evolution law, while keeping all other aspects of the model unchanged, remains insufficient to get a good match of theoretical and numerical results. Such a match is achieved by introducing the ad hoc hypothesis that the yield criterion and flow rule derived from sequential analysis still apply in the presence of elasticity, but with some “effective porosity” slightly differing from the true one through some heuristic, adjustable factor.

Impact of thermodynamical rotational flow of cerebrospinal fluid in the presence of elasticity

ObjectiveTo explore the experimental justification of cerebrospinal fluid (CSF) amplitude and elastic fluctuations of ventricles, we extend our previous computational study to models with rotational flow and suitable boundary conditions. In the present study, we include an elastic effect due to the interaction with the thermal solutal model which accounts for CSF motion which flows rotationally due to hydrocephalus flows within the spinal canal.MethodsUsing an analytical pertubation method, we have attempted a new model to justify CSF flow movement using the influences of wall temperature difference.ResultsThis paper presents results from a computational study of the biomechanics of hydrocephalus, with special emphasis on a reassessment of the parenchymal elastic module. CSF amplitude in hydrocephalus patients is 2.7 times greater than that of normal subjects.ConclusionsThis finding suggests a non-linear mechanical system to present the hydrocephalic condition using a numerical model. The results can be useful to relieve the complexities in the mechanism of hydrocephalus and can shed light to support clinically for a convincing simulation.

BULK FILL COMPOSITE RESIN RESTORATION TECHNIQUES REPLACE INCREMENTAL TECHNIQUES

Introduction: Shrinkage during the polymerization process is the main disadvantage of using composite resins because it creates pressure between the tooth and the restoration which causes failure of the adhesion of the composite resin to the tooth, micro-fissures, and cuspid deflection. Review: To reduce shrinkage that occurs, it is known that conventional composite resins must be inserted into the cavity incrementally or in layers with a maximum thickness of 2 mm per layer. However, the incremental insertion method has several disadvantages, namely that it requires a longer clinical time for restoration. To overcome the shortcomings of these conventional composites, Bulk-fill composite resin was introduced. Composite bulk fill is a sophisticated technology that allows composites to be directly placed on the restoration, has a low polymerization shrinkage to reduce micro-leakage, reduces stress in the presence of elasticity, increases the depth of at least 4 mm translucent at the time of application, is very conducive to light transmission, is more flowable to allow adaptation to the cavity, including cervical margins, it is easy to apply with minimal handling and is resistant to large stresses. Conclusion: With the characteristics possessed by the Bulk-fill composite resin, it is known that the bulk-fill technique in addition to reducing the clinical application time, can also improve the edge adaptation between the restoration and the tooth compared to the incremental technique, without reducing its physical strength.

Flow regimes of a single pulse of inelastic and elastic liquids from a round capillary tube

The ejection of liquids through round nozzles is a commonplace process in many industrial applications, from inkjet printing to bottling of consumer products. In this work, a Computational Fluid Dynamics model of the ejection of inelastic and elastic liquids through a round capillary tube has been developed to assess the influence of the ejection’s duration and velocity on the regimes of jet/droplet formation. Simulations have been performed at different Weissenberg and Ohnesorge numbers to further assess the impact of the fluid’s physical properties on the observed flow regimes. Several regimes have been identified: no fluid detachment, single droplet formation, and breakup into several droplets. The presence of elasticity has been observed to delay the breakup of droplets from the nozzle. More importantly, the results show that the injection time has an impact on the dynamics of droplet formation, having a crucial role on the process design of various industrial applications.

TEKNIK RESTORASI RESIN KOMPOSIT BULK FILL MENGGANTIKAN TEKNIK INKREMENTAL

Introduction. Shrinkage during the polymerization process is the main disadvantage of using composite resins because it creates pressure between the tooth and the restoration which causes failure of the adhesion of the composite resin to the tooth, micro-fissures, and cuspid deflection. Review. To reduce shrinkage that occurs, it is known that conventional composite resins must be inserted into the cavity incrementally or in layers with a maximum thickness of 2 mm per layer. However, the incremental insertion method has several disadvantages, namely that it requires a longer clinical time for restoration. To overcome the shortcomings of these conventional composites, Bulk-fill composite resin was introduced. Composite bulk fill is a sophisticated technology that allows composites to be directly placed on the restoration, has a low polymerization shrinkage to reduce micro-leakage, reduces stress in the presence of elasticity, increases the depth of at least 4 mm translucent at the time of application, is very conducive to light transmission, is more flowable to allow adaptation to the cavity, including cervical margins, it is easy to apply with minimal handling and is resistant to large stresses. Conclusion. With the characteristics possessed by the Bulk-fill composite resin, it is known that the bulk-fill technique in addition to reducing the clinical application time, can also improve the edge adaptation between the restoration and the tooth compared to the incremental technique, without reducing its physical strength

Exact Solution of the Startup Electroosmotic Flow of Generalized Maxwell Fluids in Triangular Microducts

Abstract The unsteady electroosmotic flow of generalized Maxwell fluids in triangular microducts is investigated. The governing equation is formulated with Caputo–Fabrizio time-fractional derivatives whose orders are distributed in the interval [0, 1). The linear momentum and the Poisson–Boltzmann equations are solved analytically in tandem in the triangular region with the help of the Helmholtz eigenvalue problem and Laplace transforms. The analytical solution developed is exact. The solution technique used is new, leads to exact solutions, is completely different from those available in the literature, and applies to other similar problems. The new expression for the velocity field displays experimentally observed ‘velocity overshoot’ as opposed to existing analytical studies none of which can predict the overshoot phenomenon. We show that when Caputo–Fabrizio time-fractional derivatives approach unity the exact solution for the classical upper convected Maxwell fluid is obtained. The presence of elasticity in the constitutive structure alters the Newtonian velocity profiles drastically. The influence of pertinent parameters on the flow field is explored.

Temporal instability of a viscoelastic liquid thread surrounded by another viscoelastic fluid in presence of insoluble surfactant and inertia

In recent years, there has been controversy in the literature regarding the role of viscoelasticity in determining the onset of stability for a viscoelastic thread surrounded by another viscoelastic fluid. Whereas a number of authors have found that viscoelasticity serves to destabilize the system, Patrascu and Balan (2018) obtained very different results. They considered a very simple canonical system subject to axisymmetric perturbations that neglected inertia and did not include the effect of surfactant. Their analysis provided two genuinely startling results: firstly, when both fluids have similar elastic properties, the dispersion relation reduces to the Newtonian limit; and secondly, the presence of elasticity in the external medium decreases the value of the unstable growth rate. In this paper, we investigate the axisymmetric temporal stability of an infinitely long viscoelastic thread surrounded by another immiscible viscoelastic fluid in presence of small amount of insoluble surfactant. Our analysis also includes the effects of inertia. The dispersion relations for cases with and without inertia are carefully derived. For the case of zero inertia and no surfactant, our results directly contradict those of Patrascu and Balan. We show that when both fluids have similar elastic properties that the dispersion relation does not reduce to the Newtonian case. We also show that, when one of the fluids is viscoelastic or both fluids are viscoelastic, the system is more unstable than the case in which both fluids are Newtonian. Moreover, our results also reveal that the system with inertia is less unstable than the system without inertia, and when the inner–outer density ratio becomes larger, the system becomes less unstable. We also carry out a parametric study of the effects of surfactant. Our results show that adding surfactant can decrease the growth rate of the instability and increase the wavenumber of the most unstable mode. We also show that the reduction of the unstable growth rate induced by the surfactant is more significant for larger internal–external total viscosity ratios. Finally, an energy budget analysis is performed to investigate the contribution of each physical factor towards the instability. This reveals the roles that the various physical mechanisms play in determining the temporal growth rate. The energy analysis further confirms that the elasticity in either inner or outer fluid increases the growth rate. • Address the controversy regarding the stability of viscoelastic threads. • Dispersion relation for fluids with same elasticity differs from Newtonian case. • Elasticity in the external medium does not decreases the growth rate. • We examine the role played by inertia and surfactant in determining the instability.

Flow due to an infinite flat plate suddenly set into motion in a viscoelastic fluid: first Stokes problem

The problem of flow and heat transfer due to an infinite flat surface suddenly set into motion in an unbounded mass of viscoelastic fluid is investigated under the consideration of time-dependent temperature distribution along the plate surface. A new type of similarity solution is devised that converts the governing partial differential equations into a set of non-linear ordinary differential equations with four physical parameters, viz., viscoelastic parameter k, unsteadiness parameter $$\beta $$ , Eckert number E and Prandtl number Pr. These equations are then solved numerically by finite-difference method after using the perturbation technique owing to the inherent unavailability of the necessary boundary conditions for solving this type of flow problem. The influences of these parameters on this flow dynamics are graphically analysed. The present analysis discloses that both the velocity and temperature at a given location decrease with the increase of the elasticity in the fluid as well as the unsteadiness of the flow field. The analysis reveals that the elastic property of the fluids causes the back-flow inside the boundary layer after a certain value of the unsteadiness parameter depending upon the presence of elasticity in the fluids. Another important result of this study that comes from the heat transfer analysis is that the elasticity of the fluids reduces the severity of the unwanted effect of the viscous heating.

Temporal instability of a viscoelastic liquid thread in the presence of a surrounding viscoelastic fluid

This paper is concerned with the temporal stability analysis of an infinitely long thread of a viscoelastic fluid surrounded by another immiscible viscoelastic fluid. The study provides an extension of the dispersion relation derived by Tomotika that captures the effects of elasticity on the fastest growing mode. The general case of two Jeffreys fluids is presented first, from which limiting cases, such as the Maxwell model or the Newtonian model, are discussed. We show that the presence of elasticity in the constitutive equation of the external medium decreases the value of the growth rate correspondent to the fastest growing mode. This implies a more stable fluid thread, thus longer breakup lengths. When both fluids have similar elastic properties, the dispersion relation reduces to the Newtonian limit and the interface behaves as if the fluids were purely viscous.

Localized instabilities and spinodal decomposition in driven systems in the presence of elasticity.

We study numerically and analytically the instabilities associated with phase separation in a solid layer on which an external material flux is imposed. The first instability is localized within a boundary layer at the exposed free surface by a process akin to spinodal decomposition. In the limiting static case, when there is no material flux, the coherent spinodal decomposition is recovered. In the present problem, stability analysis of the time-dependent and nonuniform base states as well as numerical simulations of the full governing equations are used to establish the dependence of the wavelength and onset of the instability on parameter settings and its transient nature as the patterns eventually coarsen into a flat moving front. The second instability is related to the Mullins-Sekerka instability in the presence of elasticity and arises at the moving front between the two phases when the flux is reversed. Stability analyses of the full model and the corresponding sharp-interface model are carried out and compared. Our results demonstrate how interface and bulk instabilities can be analyzed within the same framework which allows us to identify and distinguish each of them clearly. The relevance for a detailed understanding of both instabilities and their interconnections in a realistic setting is demonstrated for a system of equations modeling the lithiation and delithiation processes within the context of lithium ion batteries.

The Influence of Grooved Surface and Liquid Properties on Vortices Formation in Vicinity of Immersed Cylinders

The paper is dedicated to the experimental and numerical investigations of the viscous and viscoelastic flows around immersed cylinders with smooth and grooved surfaces. The study analyses the influences of the cylinders surface quality on the vortical structures and the wake developed downstream in a 2D open channel. The analyzed flow is in the domain of the free surface weakly turbulence regime under subcritical conditions. Numerical simulations are performed with turbulent solvers implemented in Ansys Fluent, using the VOF code for the calculation of the free surface geometry. The numerical results and visualizations are corroborated to determine the effect of the grooved surface on the drag coefficient and the location of the boundary layer separation points. The investigations emphasize also the qualitative changes of the flow spectrum induced by the Reynolds number magnitude and the presence of elasticity within the viscous fluid.

Local hydrodynamic parameters of bubble column reactors operating with non‐Newtonian liquids: Experiments and models development

The effects of liquid phase rheology on the local hydrodynamics of bubble column reactors operating with non‐Newtonian liquids are investigated. Local bubble properties, including bubble frequency, bubble chord length, and bubble rise velocity, are measured by placing two in‐house made optical fiber probes at various locations within a bubble column reactor operating with different non‐Newtonian liquids. It was found that the presence of elasticity can noticeably increase the bubble frequency but decreases the bubble chord length and its rise velocity. The radial profiles of bubble frequency, bubble chord length, and bubble rise velocity are shown to be relatively flat at low superficial gas velocity while they become parabolic at high superficial gas velocity. Moreover, the bubble size and gas holdup are correlated with respect to dimensionless groups by considering the ratio between dynamic moduli of viscoelastic liquids. The novel proposed correlations are capable of predicting the experimental data of bubble size and gas holdup within a mean absolute percentage error of 9.3% and 10%, respectively. © 2015 American Institute of Chemical Engineers AIChE J, 62: 1382–1396, 2016

Effect of the Temperature on the Non-Newtonian Behavior of Heavy Oils

The rheological behavior of heavy oils is critical for oil exploitation in different stages, such as extraction, transportation, and refining; during this process, the oil undergoes temperature changes that directly affect the viscosity. For light oils, the viscosity decreases around 1 order of magnitude when the temperature increases 100 K, whereas for heavy oils, this change could be of more than 3 orders of magnitude for the same temperature increment. Furthermore, the heavy oils exhibit a viscoelastic behavior, usually characterized by a viscosity reduction with the increment in the shear rate, the presence of elasticity, and time-dependent rheological behavior. As the temperature increases, the oils acquire a Newtonian behavior. This change is illustrated with the rheological characterization of five heavy oils with an American Petroleum Institute (API) gravity around 12°, different compositions, and zero-shear viscosity that varies up to 2 orders of magnitude among oils. The measurements were carried out in a controlled stress rheometer using a 40 mm parallel plate geometry with a gap of 1 mm. The fluids were tested in rotational and oscillatory modes at temperatures from 5 to 100 °C. In the oscillatory experiments, the loss and storage moduli, associated with viscosity and elasticity, respectively, are presented. Above a transition temperature, not only does the viscosity decrease but also the normal force and the elastic modulus tend to vanish, suggesting that the non-Newtonian behavior is also strongly related to the temperature. Furthermore, the departure from linearity of the logarithm of zero-shear viscosity versus the inverse of the temperature appears to correlate with the transition from non-Newtonian to Newtonian behavior.

Evolution of elastic thin films with curvature regularization via minimizing movements

The evolution equation with curvature regularization that models the motion of a two-dimensional thin film by evaporation-condensation on a rigid substrate is considered. The film is strained due to the mismatch between the crystalline lattices of the two materials. Here, short time existence, uniqueness and regularity of the solution are established using De Giorgi’s minimizing movements to exploit the $$L^{2}$$ -gradient flow structure of the equation. This seems to be the first analytical result for the evaporation-condensation case in the presence of elasticity.

Investigations of vortex formation in microbifurcations

The paper is dedicated to experimental studies and numerical simulations of viscous and viscoelastic flows in microchannels. The present work investigates separation phenomena and the formation of vortical structures in two microbifurcations with one closed branch: (1) Y-bifurcation with a square cross section and (2) T-bifurcation with trapezoidal sections and small aspect ratios depth/width. The main goal of the study is to characterize the dynamics of the vortex from the vicinity of Y-bifurcation and to emphasize the changes induced by the presence of elasticity on the local path lines. Velocity measurements and flow pattern visualizations of Newtonian fluid (deionized water) and weakly elastic polymer solution (low concentration of polyacrylamide in water) are obtained using a μPIV system. Numerical computations are performed in 2D and 3D flow configurations with the commercial FLUENT code. The Newtonian simulations offer very precise descriptions of the vortical structures for all flow regimes. In the case of polymer solution, the comparison between experimental data and numerical solutions for generalized Newtonian models prove the dominant role of elasticity in modifications induced on the vortical patterns in the analyzed microgeometries. The present topic is of great interest in developing novel microfluidic applications which require precise control of the hydrodynamics of viscoelastic fluids in the vicinity of complex geometries and patterned surfaces.

Motion of Elastic Thin Films by Anisotropic Surface Diffusion with Curvature Regularization

In this paper, we prove short time existence, uniqueness, and regularity for a surface diffusion evolution equation with curvature regularization in the context of epitaxially strained two-dimensional films. This is achieved by using the H −1-gradient flow structure of the evolution law, via De Giorgi’s minimizing movements. This seems to be the first short time existence result for a surface diffusion type geometric evolution equation in the presence of elasticity.

Expansion of source equation of elastic line

SUMMARYThe paper is concerned with the relationship between the equation of elastic line motion, the “Euler-Bernoulli approach” (EBA), and equation of motion at the point of elastic line tip, the “Lumped-mass approach” (LMA). The Euler–Bernoulli equations (which have for a long time been used in the literature) should be expanded according to the requirements of the motion complexity of elastic robotic systems. The Euler–Bernoulli equation (based on the known laws of dynamics) should be supplemented with all the forces that are participating in the formation of the bending moment of the considered mode. This yields the difference in the structure of Euler–Bernoulli equations for each mode. The stiffness matrix is a full matrix. Mathematical model of the actuators also comprises coupling between elasticity forces. Particular integral of Daniel Bernoulli should be supplemented with the stationary character of elastic deformation of any point of the considered mode, caused by the present forces. General form of the elastic line is a direct outcome of the system motion dynamics, and can not be described by one scalar equation but by three equations for position and three equations for orientation of every point on that elastic line. Simulation results are shown for a selected robotic example involving the simultaneous presence of elasticity of the joint and of the link (two modes), as well the environment force dynamics.