Macroscopic Instabilities Research Articles

Stability of magnetoactive composites with periodic microstructures undergoing finite strains in the presence of a magnetic field

Abstract We investigate the macroscopic magnetomechanical instabilities in magnetorheological elastomer (MRE) composites undergoing finite strains in the presence of a magnetic field. In particular, we identify the unstable domains for MRE composites with periodically distributed circular and elliptical inclusions embedded in a soft matrix. We use the isotropic Langevin model for magnetic behavior, to account for the initial (linear) susceptibility and saturation magnetization of the magnetoactive inclusions. We analyze the influence of the applied magnetic field and finite strains, as well as particle shape and material properties, on the stability of the MRE composites. We find that the stable and unstable domains can be significantly tuned by the applied magnetic field, depending on deformation, microstructure and magnetic properties of the inclusions such as initial susceptibility and saturation magnetization.

Electromechanical macroscopic instabilities in soft dielectric elastomer composites with periodic microstructures

Abstract We study electromechanical macroscopic instabilities in dielectric elastomer (DE) composites undergoing finite strains in the presence of an electric field. We identify the unstable domains for DE composites with periodically distributed circular and elliptical inclusions embedded in a soft matrix. We analyze the influence of the applied electric field and finite strains, as well as the microstructure geometrical parameters and material properties, on the stability of the DE composites. We find that the unstable domains can be significantly tuned by an electric field, depending on the electric field direction relative to pre-stretch and microstructure. More specifically, the electric field aligned with the stretch direction, promotes instabilities in the composites, and the electric field applied perpendicularly to the stretch direction, stabilizes the composites. Critical stretch decreases with an increase in the volume fraction of circular inclusions. An increase in the contrast between the dielectric properties of the constituents, magnifies the role of the electric field, while an increase in the shear modulus contrast results in a less stable DE composite. For periodic DE composites with elliptical inclusions, we find that the critical stretch depends on the inclination angle of the inclusion, and that the critical stretch reaches a unique maximum at an angle defined by the inclusion ellipticity aspect ratio. In the aligned case – when the longest side of the inclusion is aligned with the stretch direction – an increase in the ellipticity ratio results in an increase in critical stretch.

Role of Self-Organization of Dislocations in the Onset and Kinetics of Macroscopic Plastic Instability

The present paper examines two aspects of the problem of critical conditions of jerky flow in alloys, or the Portevin–Le Chatelier (PLC) effect. Recent development of dynamic strain aging (DSA) models proved their capacity to qualitatively reproduce complex non-monotonic behavior of the critical strain, providing that the parameters of theory are allowed to depend on strain. Experimental measurements of such strain dependences have been realized for the first time and used to revise the predictions of the critical strain and stress relaxation kinetics upon abrupt strain-rate changes. On the other hand, it is usually omitted from consideration that the PLC stress serrations can last very short time in comparison with the characteristic time of stress transients. The development of stress drops was studied with the aid of the acoustic emission (AE) technique. It is shown that such macroscopic instabilities are caused by clustering of AE events which otherwise occur all the time, including the periods of smooth plastic flow. The role of synchronization of dislocation avalanches in the development of abrupt stress serrations and its relationship with the predictions of the local DSA models is discussed.

Effect of an aggressive medium on discontinuous deformation of aluminum–magnesium alloy AlMg6

It is experimentally shown that the molecular (chemical) process of surface etching of deformed aluminum–magnesium alloy AlMg6 causes the development of a macroscopic plastic strain step with an amplitude of a few percent. Using numerical simulation of the polycrystalline solid etching process, it is shown that the corrosion front morphology varies during etching from Euclid (flat) to fractal (rough). The results obtained show the key role of the surface state on the development of macroscopic mechanical instability of a material exhibiting the Portevin–Le Chatelier effect.

Determining the prediction limits of models and classifiers with applications for disruption prediction in JET

Understanding the many aspects of tokamak physics requires the development of quite sophisticated models. Moreover, in the operation of the devices, prediction of the future evolution of discharges can be of crucial importance, particularly in the case of the prediction of disruptions, which can cause serious damage to various parts of the machine. The determination of the limits of predictability is therefore an important issue for modelling, classifying and forecasting. In all these cases, once a certain level of performance has been reached, the question typically arises as to whether all the information available in the data has been exploited, or whether there are still margins for improvement of the tools being developed. In this paper, a theoretical information approach is proposed to address this issue. The excellent properties of the developed indicator, called the prediction factor (PF), have been proved with the help of a series of numerical tests. Its application to some typical behaviour relating to macroscopic instabilities in tokamaks has shown very positive results. The prediction factor has also been used to assess the performance of disruption predictors running in real time in the JET system, including the one systematically deployed in the feedback loop for mitigation purposes. The main conclusion is that the most advanced predictors basically exploit all the information contained in the locked mode signal on which they are based. Therefore, qualitative improvements in disruption prediction performance in JET would need the processing of additional signals, probably profiles.

Microscopic and macroscopic instabilities in hyperelastic fiber composites

In this paper, we study the interplay between macroscopic and microscopic instabilities in 3D periodic fiber reinforced composites undergoing large deformations. We employ the Bloch-Floquet analysis to determine the onset of microscopic instabilities for composites with hyperelastic constituents. We show that the primary mode of buckling in the fiber composites is determined by the volume fraction of fibers and the contrast between elastic moduli of fiber and matrix phases. We find that for composites with volume fraction of fibers exceeding a threshold value, which depends on elastic modulus contrast, the primary buckling mode corresponds to the long wave or macroscopic instability. However, composites with a lower amount of fibers experience microscopic instabilities corresponding to wavy or helical buckling shapes. Buckling modes and critical wavelengths are shown to be highly tunable by material composition. A comparison between the instability behavior of 3D fiber composites and laminates, subjected to uniaxial compression, reveals the significant differences in critical strains, wavelengths, and transition points from macro- to microscopic instabilities in these composites.

Effects of microfracture and contact induced instabilities on the macroscopic response of finitely deformed elastic composites

Abstract An original non-linear analysis of the homogenized response of periodic elastic composites under large deformations, is here carried out by accounting for the coupled effects of micro-cracks in unilateral self-contact and of instabilities and bifurcation microstructural phenomena. The structure and properties of the composite macroscopic response are investigated by obtaining new analytical results able to distinguish the contributions of microstructural heterogeneities, including fractures and voids, crack self-contact and local constitutive behavior. In light of these results the relations between microstructural instability mechanisms and macroscopic instabilities detected by loss of ellipticity or softening behavior of the homogenized tangent moduli tensor related to conjugated stress and strain rate measures, are studied. Novel numerical applications of the theory, developed by means of coupled FE models of a 2D microcracked composite with circular inclusions driven along uniaxial and biaxial macro-deformation paths, are presented pointing out the sequence of bifurcation and instability load factors for different micro-geometries and the relations among the stability domains at both micro and the macro levels.

会切磁瓶探析—磁场位形为磁阱的新型磁约束装置

会切磁瓶是由布置在正多面体各顶点的磁体，构成的磁约束装置。其内部的磁场位形，是底部磁感应强度为零的理想磁阱，已达到了阱深定义的极限值。磁感应强度变化曲线显示，在相同容积下，正12面体会切磁瓶的磁感应强度落差，是垒球缝线圈的磁感应强度落差的20多倍，且会切磁瓶还有着极大的可扩展性。会切磁瓶对等离子体的约束原理是依靠磁阱，磁约束理论表明，只有磁阱位形磁场，才能真正做到等离子体的稳定约束。而Tokamak或磁镜，是依靠磁力线对电粒子的粘连，理论和实践都表明，其存在着各种宏观和微观不稳定性。而在会切磁瓶中，这些不稳定性都将不复存在。从会切磁瓶的构成看，无论是材料、运行、扩展性等方面，会切磁瓶都有着传统磁约束装置不可比拟优势。 The cusp magnetic bottle is a magnetic confinement device constituted by magnets on each vertex of the regular polyhedron. The internal magnetic field configuration is an ideal magnetic trap with the bottom magnetic induction intensity of zero, which could reach up to the limit value defined by the trap depth. The changing curve of magnetic induction intensity has indicated that, the magnetic induction intensity difference for cusp magnetic bottle of regular dodecahedron is over 20 times greater than that for softball seal coil of same volume and that the cusp magnetic bottle has a larger space to expand. The constraint theory of plasma by the cusp magnetic bottle is to rely on the magnetic trap and magnetic confinement theory indicates that, only magnetic trap configuration can truly achieve the stable confinement of plasma. Tokamak or magnetic mirror is to rely on the adhesion of particles of electricity on magnetic line of force. However, it has all kinds of macroscopic and microcosmic instabilities from both theoretically and practically. These instabilities would no long exist in the cusp magnetic bottle. From the constitution of cusp magnetic bottle, the materials, operation, structure, flexibility, expansibility and other aspects all indicate that the cusp magnetic bottle is far superior to traditional magnetic confinement devices.

Multiscale Stick-Slip Dynamics of Adhesive Tape Peeling.

Using a high-speed camera, we follow the propagation of the detachment front during the peeling of an adhesive tape from a flat surface. In a given range of peeling velocity, this front displays a multiscale unstable dynamics, entangling two well-separated spatiotemporal scales, which correspond to microscopic and macroscopic dynamical stick-slip instabilities. While the periodic release of the stretch energy of the whole peeled ribbon drives the classical macro-stick-slip, we show that the micro-stick-slip, due to the regular propagation of transverse dynamic fractures discovered by Thoroddsen et al. [Phys. Rev. E 82, 046107 (2010)], is related to a high-frequency periodic release of the elastic bending energy of the adhesive ribbon concentrated in the vicinity of the peeling front.

Statistical study of auroral fragmentation into patches

AbstractThe study of auroral dynamics is important when considering disturbances of the magnetosphere. Shiokawa et al. (2010, 2014) reported observations of finger‐like auroral structures that cause auroral fragmentation. Those structures are probably produced by macroscopic instabilities in the magnetosphere, mainly of the Rayleigh‐Taylor type. However, the statistical characteristics of these structures have not yet been investigated. Here based on observations by an all‐sky imager at Tromsø (magnetic latitude = 67.1°N), Norway, over three winter seasons, we statistically analyzed the occurrence conditions of 14 large‐scale finger‐like structures that developed from large‐scale auroral regions including arcs and 6 small‐scale finger‐like structures that developed in auroral patches. The large‐scale structures were seen from midnight to dawn local time and usually appeared at the beginning of the substorm recovery phase, near the low‐latitude boundary of the auroral region. The small‐scale structures were primarily seen at dawn and mainly occurred in the late recovery phase of substorms. The sizes of these large‐ and small‐scale structures mapped in the magnetospheric equatorial plane are usually larger than the gyroradius of 10 keV protons, indicating that the finger‐like structures could be caused by magnetohydrodynamic instabilities. However, the scale of small structures is only twice the gyroradius of 10 keV protons, suggesting that finite Larmor radius effects may contribute to the formation of small‐scale structures. The eastward propagation velocities of the structures are −40 to +200 m/s and are comparable with those of plasma drift velocities measured by the colocating Super Dual Auroral Radar Network radar.

Mechanical stability of Ni and Ir under hydrostatic and uniaxial loading

Two fcc crystals, Ni and Ir, are subjected to simulated isotropic and uniaxial tension along the direction. Their structural stability is assessed by analyzing phonon spectra that are calculated from first principles for different values of strain. A relevant analysis of elastic stability conditions is also performed. Predicted elastic instabilities correspond well to those associated with soft phonons with vanishing wavevectors. Although most of previous studies predicted that first instabilities in crystals correspond to macroscopic (elastic) instabilities, we found soft phonons of finite wavevectors at lower strains (and stresses) during both considered loadings in the crystal of Ir. Predicted instabilities were confirmed by our models of microscopic deformation.

Coupling extended magnetohydrodynamic fluid codes with radiofrequency ray tracing codes for fusion modeling

Neoclassical tearing modes are macroscopic (L∼1 m) instabilities in magnetic fusion experiments; if unchecked, these modes degrade plasma performance and may catastrophically destroy plasma confinement by inducing a disruption. Fortunately, the use of properly tuned and directed radiofrequency waves (λ∼1 mm) can eliminate these modes. Numerical modeling of this difficult multiscale problem requires the integration of separate mathematical models for each length and time scale (Jenkins and Kruger, 2012 [21]); the extended MHD model captures macroscopic plasma evolution while the RF model tracks the flow and deposition of injected RF power through the evolving plasma profiles. The scale separation enables use of the eikonal (ray-tracing) approximation to model the RF wave propagation. In this work we demonstrate a technique, based on methods of computational geometry, for mapping the ensuing RF data (associated with discrete ray trajectories) onto the finite-element/pseudospectral grid that is used to model the extended MHD physics. In the new representation, the RF data can then be used to construct source terms in the equations of the extended MHD model, enabling quantitative modeling of RF-induced tearing mode stabilization. Though our specific implementation uses the NIMROD extended MHD (Sovinec et al., 2004 [22]) and GENRAY RF (Smirnov et al., 1994 [23]) codes, the approach presented can be applied more generally to any code coupling requiring the mapping of ray tracing data onto Eulerian grids.

Vibrational and elastic properties as a pointer to stishovite to CaCl2 ferroelastic phase transition in RuO2

The high pressure behavior of RuO2 has been investigated using the first principles calculations based on the density functional theory. Here, we report the calculated properties on structure, electronic, elastic, phonon and electron–phonon coupling of rutile and CaCl2 type RuO2. Our calculated lattice constants and bulk modulus agree reasonably well with the available theoretical and experimental data. Results of our calculations of zone center phonon modes at ambient and high pressures are in good agreement with Raman scattering measurements. Elastic (shear) modulus and phonon analysis confirm the ferroelastic phase transition from rutile to CaCl2 phase in RuO2. It is clearly illustrated that the first transition is associated with macroscopic shear instability which arises from the strong coupling between elastic constants and softening of Raman active B1g mode. The observed pressure of phase transition in experimental measurements was reproduced more accurately than in previous calculations and the difference between observed and calculated transition pressure is only of the order of few percentage. We have also analyzed the rotation angle for O-R-O corresponding to B1g mode and found that the rotation of bond about 80 is required for transition from rutile to CaCl2 phase in RuO2. In addition, the mode Grüneisen parameter is discussed. The electron–phonon interaction in both rutile and CaCl2 type RuO2 at high pressure is also discussed.

Spreading of triboelectrically charged granular matter.

We report on the spreading of triboelectrically charged glass particles on an oppositely charged surface of a plastic cylindrical container in the presence of a constant mechanical agitation. The particles spread via sticking, as a monolayer on the cylinder's surface. Continued agitation initiates a sequence of instabilities of this monolayer, which first forms periodic wavy-stripe-shaped transverse density modulation in the monolayer and then ejects narrow and long particle-jets from the tips of these stripes. These jets finally coalesce laterally to form a homogeneous spreading front that is layered along the spreading direction. These remarkable growth patterns are related to a time evolving frictional drag between the moving charged glass particles and the countercharges on the plastic container. The results provide insight into the multiscale time-dependent tribolelectric processes and motivates further investigation into the microscopic causes of these macroscopic dynamical instabilities and spatial structures.

On the macroscopic response, microstructure evolution, and macroscopic stability of short-fiber-reinforced elastomers at finite strains: II – Representative examples

In Part I of this work, we presented a homogenization-based constitutive model for the overall behavior of reinforced elastomers consisting of aligned, spheroidal particles distributed randomly in an incompressible, hyperelastic matrix. In particular, we provided analytical estimates for the effective stored-energy functions of the composites, as well as for the associated average particle rotations under finite deformations. The rotation of the particles is found to be very sensitive to the specific loading conditions applied, and is such that the particles tend to align themselves with the largest tensile direction. In addition, we obtained corresponding formulae for the detection of macroscopic instabilities in these composites. With the objective of illustrating the key features of the analytical results presented in Part I, we conduct here a more detailed study of these results for several representative values of the microstructural and loading parameters, as well as matrix properties. More specifically, this study deals with neo-Hookean and Gent elastomers reinforced with spheroidal particles of prolate and oblate shapes with various aspect ratios and volume fractions, subjected to aligned and non-aligned macroscopic loading conditions. In addition, to assess the accuracy of the model, we compare our results with corresponding finite element results available from the literature for the special case of spherical particles, and good agreement is found. For non-spherical particles, the results indicate that the possible rotation of the particles has a major influence on the overall response of the elastomeric composites. Furthermore, it is found that the composite may develop macroscopic shear localization instabilities, as a consequence of the geometric softening induced by the sudden rotation – or flopping – of the particles, when a sufficiently large amount of compression is applied along the long axes of the particles.

Multiscale instabilities in soft heterogeneous dielectric elastomers

The development of instabilities in soft heterogeneous dielectric elastomers is investigated. Motivated by experiments and possible applications, we use in our analysis the physically relevant referential electric field instead of electric displacement. In terms of this variable, a closed form solution is derived for the class of layered neo-Hookean dielectrics. A criterion for the onset of electromechanical multiscale instabilities for the layered composites with anisotropic phases is formulated. A general condition for the onset of the macroscopic instability in soft multiphase dielectrics is introduced. In the example of the layered dielectrics, the essential influence of the microstructure on the onset of instabilities is revealed. We found that: (i)macroscopic instabilities dominate at moderate volume fractions of the stiffer phase, (ii) interface instabilities appear at small volume fractions of the stiffer phase and (iii) instabilities of a finite scale, comparable to the microstructure size, occur at large volume fractions of the stiffer phase. The latest new type of instabilities does not appear in the purely mechanical case and dominates in the region of large volume fractions of the stiff phase.

Nonlinear Evolution of the Travelling Waves in Roll Coating Flows of Thin Viscoelastic Polymer Falling Films

Roll coating is widely used to apply a thin liquid film to a continuous, flexible substrate. It is known that macroscopic instabilities of the film system can result in a non-homogenous film growth to fluid flow. The influence of the Rossby number, the viscoelastic parameter, and the roller radius on the nonlinear hydrodynamic stability of a thin viscoelastic polymer fluid film coating flow down a rotating vertical roller is investigated. In contrast to most previous studies, the solution scheme employed in this study is based on a numerical approximation approach rather than an analytical method. The size of the explosive supercritical instability region increases significantly as the roller rotates. It is shown that the stability of the liquid film is enhanced by reducing the viscoelastic effect or decreasing the speed of the rotating roller. At higher values of the Reynolds number, the tendency of the rotation effect to prompt thin-film instability increases with an increasing roller radius.

Crossover from quasi-static to dense flow regime in compressed frictional granular media

Being ubiquitous in a large variety of geomaterials, granular assemblies play a crucial role in the mechanical stability of engineering and geophysical structures. For these applications, an accurate knowledge of the processes at the origin of shear localization, i.e. faulting, in frictional granular assemblies submitted to compressive loading is needed. Here we tackle this problem by performing discrete-element numerical simulations. A thorough analysis of the evolution of multi-scale mechanical properties as approaching sample macroscopic instability is performed. Spatial correlations operating within the shear stress and strain fields are analyzed by means of a coarse-graining analysis. The divergence of correlation lengths is reported on both shear stress and strain fields as approaching the transition to sample instability. We thus show that the crossover from a quasi-static regime where the sample deforms infinitely slowly to a dense flow regime, where inertial forces play a significant role, can be interpreted as a critical phase transition. At this transition, no shear band of characteristic thickness can be defined.

A two‐scale failure model for heterogeneous materials: numerical implementation based on the finite element method

SUMMARYIn the first part of this contribution, a brief theoretical revision of the mechanical and variational foundations of a Failure‐Oriented Multiscale Formulation devised for modeling failure in heterogeneous materials is described.The proposed model considers two well separated physical length scales, namely: (i) the macroscale where nucleation and evolution of a cohesive surface is considered as a medium to characterize the degradation phenomenon occurring at the lower length scale, and (ii) the microscale where some mechanical processes that lead to the material failure are taking place, such as strain localization, damage, shear band formation, and so on. These processes are modeled using the concept of Representative Volume Element (RVE). On the macroscale, the traction separation response, characterizing the mechanical behavior of the cohesive interface, is a result of the failure processes simulated in the microscale. The traction separation response is obtained by a particular homogenization technique applied on specific RVE sub‐domains. Standard, as well as, Non‐Standard boundary conditions are consistently derived in order to preserve objectivity of the homogenized response with respect to the micro‐cell size.In the second part of the paper, and as an original contribution, the detailed numerical implementation of the two‐scale model based on the finite element method is presented. Special attention is devoted to the topics, which are distinctive of the Failure‐Oriented Multiscale Formulation, such as: (i) the finite element technologies adopted in each scale along with their corresponding algorithmic expressions, (ii) the generalized treatment given to the kinematical boundary conditions in the RVE, and (iii) how these kinematical restrictions affect the capturing of macroscopic material instability modes and the posterior evolution of failure at the RVE level.Finally, a set of numerical simulations is performed in order to show the potentialities of the proposed methodology, as well as, to compare and validate the numerical solutions furnished by the two‐scale model with respect to a direct numerical simulation approach. Copyright © 2013 John Wiley & Sons, Ltd.

New developments, plasma physics regimes and issues for the Ignitor experiment

The scientific goal of the Ignitor experiment is to approach, for the first time, the ignition conditions of a magnetically confined D–T plasma. The IGNIR collaboration between Italy and Russia is centred on the construction of the core of the Ignitor machine in Italy and its installation and operation within the Triniti site (Troitsk). A parallel initiative has developed that integrates this programme, involving the study of plasmas in which high-energy populations are present, with ongoing research in high-energy astrophysics, with a theory effort involving the National Institute for High Mathematics, and with INFN and the University of Pisa for the development of relevant nuclear and optical diagnostics. The construction of the main components of the machine core has been fully funded by the Italian Government. Therefore, considerable attention has been devoted towards identifying the industrial groups having the facilities necessary to build these components. An important step for the Ignitor programme is the adoption of the superconducting MgB2 material for the largest poloidal field coils (P14) that is compatible with the He-gas cooling system designed for the entire machine. The progress made in the construction of these coils is described. An important advance has been made in the reconfiguration of the cooling channels of the toroidal magnet that can double the machine duty cycle. A facility has been constructed to test the most important components of the ICRH system at full scale, and the main results of the tests carried out are presented. The main physics issues that the Ignitor experiment is expected to face are analysed considering the most recent developments in both experimental observations and theory for weakly collisional plasma regimes. Of special interest is the I-regime that has been investigated in depth only recently and combines advanced confinement properties with a high degree of plasma purity. This is a promising alternative to the high-density L-regime that had been observed by the Alcator experiment and whose features motivated the Ignitor project. The provisions that are incorporated in the machine design, and in that of the plasma chamber in particular, in order to withstand or prevent the development of macroscopic instabilities with deleterious amplitudes are presented together with relevant analyses.