Energetic Scales Research Articles

Thermo-mechanical strain gradient plasticity with energetic and dissipative length scales

Plasticity in heterogeneous metallic materials of small volumes is governed by the interactions of the dislocations in the bulk and at the interfaces. The temperature distribution and accumulated heat in the medium, due to the high rate of loading, can also strongly affect the mechanical properties in micro and nanosystems. In this paper, the framework of higher-order strain gradient plasticity with interfacial energy effect is used to investigate the coupling of thermal and mechanical responses of materials in small scales and fast transient process. In order to accurately describe the size effect exhibited in micro/nano structured materials and to address the strengthening and hardening mechanisms, the theory is developed based on the decomposition of the mechanical state variables into energetic and dissipative counterparts. This, in turn, endowed the constitutive equations to have both energetic and dissipative gradient length scales ℓen and ℓdis respectively. The effect of the material microstructural interface between two materials is also incorporated into the proposed formulation. Hence four material length scales are introduced: two for the bulk and the other two for the interface. In addition, the temperature distribution in the system due to conversion of plastic work into heat and the partial dissipation of heat due to fast transient time, is included into the model using a generalized heat equation. The microstructural interactions (i.e. photon–electron coupling) and the effect of fast transients is considered by incorporating two time scales into the heat equation. The developed framework is solved numerically by using a thin film on an elastic substrate under biaxial straining. Furthermore, the obtained results are compared with experimental data.

Spectral analysis of mean flow and turbulence forced by waves in a horizontally homogeneous zone of the Iroise sea

The 1D version of the Model for Applications at Regional Scale is used to parameterize the effects of sea surface waves in 2D in a horizontally homogeneous offshore zone of the Iroise sea. Here we present the first simulation of the Iroise sea including sea surface waves forcing, and more generally, the first study of a boundary layer including the Hasselmann force with a tidal wave. We use a single equation turbulence closure based on a non-local diagnosis for energetic and dissipation length scales. The turbulent energy flux at the surface due to whitecaps and the Hasselmann force induced by Stokes drift are assessed using the whole sea surface waves spectrum given by the Wave Watch Third generation model. The ability of the parameterization to reproduce surface currents over a period of 1 year (2007) is tested with high frequency radar using spectral and time-frequency analysis. One problem with 1D modelling, corresponding to overestimation of current oscillating at inertial frequency is illustrated by comparing 1D and 3D simulations. We found an overall improvement by including the Hasselmann force mainly within the bandwidth of less than one cycle per day to one cycle per day for surface currents. Turbulence is induced by whitecaps decaying rapidly below the ocean surface but the mixed layer below 40 m is deeper due to waves breaking on the sea surface.

Chemical bonding in complexes with high coordination numbers: a charge density study

The topological analysis of an experimental charge-density distribution in crystalline tris(pyridine)bis(o-hydroxybenzoato)cadmium(ii) revealed that the metal–ligand bonds occupy nearly the same place in the energetic scale as the hydrogen bonds do, thus being extremely sensitive to steric and crystal-packing effects.

Bauschinger and size effects in thin-film plasticity due to defect-energy of geometrical necessary dislocations

The Bauschinger and size effects in the thin-film plasticity theory arising from the defect-energy of geometrically necessary dislocations (GNDs) are analytically investigated in this paper. Firstly, this defect-energy is deduced based on the elastic interactions of coupling dislocations (or pile-ups) moving on the closed neighboring slip plane. This energy is a quadratic function of the GNDs density, and includes an elastic interaction coefficient and an energetic length scale L. By incorporating it into the workconjugate strain gradient plasticity theory of Gurtin, an energetic stress associated with this defect energy is obtained, which just plays the role of back stress in the kinematic hardening model. Then this back-stress hardening model is used to investigate the Bauschinger and size effects in the tension problem of single crystal Al films with passivation layers. The tension stress in the film shows a reverse dependence on the film thickness h. By comparing it with discrete-dislocation simulation results, the length scale L is determined, which is just several slip plane spacing, and accords well with our physical interpretation for the defectenergy. The Bauschinger effect after unloading is analyzed by combining this back-stress hardening model with a friction model. The effects of film thickness and pre-strain on the reversed plastic strain after unloading are quantified and qualitatively compared with experiment results.

Persistence of turbulent flow in microchannels at very low Reynolds numbers

A fully resolved numerical simulation of a turbulent microchannel flow, with uniformly spaced two-dimensional obstruction elements mounted at the wall and normal to the flow direction, was carried out at a very low Reynolds number of Re ≃ 970 based on the centerline velocity and the microchannel height. Employing the lattice Boltzmann numerical technique, all energetic scales of turbulence were resolved with about 19 × 106 grid points (1261 × 129 × 128 in the x 1, x 2, and x 3 directions). The simulated results confirm the self-maintenance of turbulence at such a low Reynolds number. Turbulence persisted over more than 1,000 turnover times, which was sufficiently long to prove its self-maintenance. These findings support the conjecture that turbulence developing in microchannels having rough walls can not only be initiated but also maintained at very low Reynolds numbers.

Dimensional analysis of the earthquake-induced pounding between inelastic structures

In this paper the seismic response of inelastic structures with unilateral contact is revisited with dimensional analysis. All physically realizable contact types are captured via a non-smooth complementarity approach. The implementation of formal dimensional analysis leads to a condensed presentation of the response and unveils remarkable order even though two different types of non-linearity coexist in the response: the boundary non-linearity of unilateral contact and the inelastic behaviour of the structure itself. It is shown that regardless the intensity and frequency content of the excitation, all response spectra become self-similar when expressed in the appropriate dimensionless terms. The proposed approach hinges upon the notion of the energetic length scale of an excitation which measures the persistence of ground shaking to impose deformation demands. Using the concept of persistency which is defined for excitations with or without distinct pulses, the response is scaled via meaningful novel intensity measures: the dimensionless gap and the dimensionless yield displacement. The study confirms that contact may have a different effect on the response displacements of inelastic structures depending on the spectral region. In adjacent inelastic structures, such as colliding buildings or interacting bridge segments, contact is likely to alter drastically the excitation frequencies’ at which the system is most vulnerable. Finally, it is shown that the proposed approach yields maximum response displacements which correlate very well with the persistency of real earthquakes for a bridge system with considerably complex behaviour.

Second-order structure function in fully developed turbulence

We relate the second-order structure function of a time series with the power spectrum of the original variable, taking an assumption of statistical stationarity. With this approach, we find that the structure function is strongly influenced by the large scales. The large-scale contribution and the contribution range are, respectively, 79% and 1.4 decades for a Kolmogorov -5/3 power spectrum. We show numerically that a single scale influence range, over smaller scales is about 2 decades. We argue that the structure function is not a good method to extract the scaling exponents when the data possess large energetic scales. An alternative methodology, the arbitrary order Hilbert spectral analysis which may constrain this influence within 0.3 decade, is proposed to characterize the scaling property directly in an amplitude-frequency space. An analysis of passive scalar (temperature) turbulence time series is presented to show the influence of large-scale structures in real turbulence and the efficiency of the Hilbert-based methodology. The corresponding scaling exponents ζ(θ)(q) provided by the Hilbert-based approach indicate that the passive scalar turbulence field may be less intermittent than what was previously believed.

Self-Sustained Process at Large Scales in Turbulent Channel Flow

Large-scale motions, important in turbulent shear flows, are frequently attributed to the interaction of structures at smaller scales. Here we show that, in a turbulent channel at Re{τ}≈550, large-scale motions can self-sustain even when smaller-scale structures populating the near-wall and logarithmic regions are artificially quenched. This large-scale self-sustained mechanism is not active in periodic boxes of width smaller than L{z}≈1.5h or length shorter than L{x}≈3h which correspond well to the most energetic large scales observed in the turbulent channel.

Turbulent mixing in an accelerated nozzle flow

To analyze the procedure of gasdynamically generating nanoparticles, the turbulent mixing of the heavy gas tetraethoxysilane (TEOS - Si ( C 2 H 5 0 ) 4 ) in a hot accelerated transonic air co-flow is numerically investigated. The precursor gas TEOS is premixed with nitrogen and then ejected through circular holes in the base of an injector into the subsonic region of a nozzle flow at a co-flow Mach number of Ma co - flow ≈ 0.66 and a temperature of T co - flow ≈ 1200 K . A multi-species large-eddy simulation (LES) capturing the most energetic turbulent scales is used to simulate the mixing process. Close behind the blunt trailing edge of the injector the results show the mixing to be dominated by pronounced free shear layers. Downstream of the injector the flow field is accelerated to supersonic speed and dominated by trailing vortices, which transport the partially mixed precursor gas but do not enhance further mixing. The analysis of the simulation results indicates that no further mixing occurs approximately 16 trailing edge thicknesses downstream of the trailing edge.

Formation and Rheology of Viscoelastic “Double Networks” in Wormlike Micelle−Nanoparticle Mixtures

We present a systematic study of thermodynamics, structure, and rheology of mixtures of cationic wormlike micelles and like-charged nanoparticles. Structural and thermodynamic measurements in dilute surfactant-nanoparticle mixtures show the formation of micelle-nanoparticle junctions that act as physical cross-links between micelles. The presence of these junctions is shown to build significant viscosity and viscoelasticity in dilute and semidilute WLMs, even in cases where the fluid is Newtonian in the absence of nanoparticles. Increases in viscosity, shear modulus, and relaxation time, as well as decreases in entanglement concentration, are observed with increasing particle concentration. As such, nanoparticle addition gives rise to a so-called "double network" comprised of micellar entanglements and particle junctions. A simple model for such networks is proposed, where the elasticity can be tuned through two energetic scales, the micellar end-cap energy and micelle-nanoparticle adsorption energy. As a practical application, the results demonstrate that nanoparticle addition provides formulators a unique method to tailor surfactant solution rheology over a wide range of conditions.

Dimensional Analysis of the Earthquake Response of a Pounding Oscillator

In this paper, the dynamic response of a pounding oscillator subjected to pulse type excitations is revisited with dimensional analysis. The study adopts the concept of the energetic length scale which is a measure of the persistence of the distinguishable pulse of strong ground motions and subsequently presents the dimensionless Π products that govern the response of the pounding oscillator. The introduction of Buckingham’s Π theorem reduces the number of variables that govern the response of the system from 7 to 5. The proposed dimensionless Π products are liberated from the response of an oscillator without impact and most importantly reveal remarkable order in the response. It is shown that, regardless the acceleration level and duration of the pulse, all response spectra become self-similar and, when expressed in the dimensionless Π products, follow a single master curve. This is true despite the realization of contacts with increasing durations as the excitation level increases. All physically reali...

Molecular Mobility and Interfacial Dynamics in Organic Nano-electromechanical Systems (NEMS)

The underpinnings of material properties in nanoscopic polymer systems are reviewed in light of the relaxation modes available for molecular motion. When motion is altered due to the presence of constraints, a rich variety of material and transport behaviors become apparent. On the one hand, external constraints imposed by interfaces and system boundaries generate structural and dynamical anisotropies that can propagate over device-relevant length scales. On the other hand, the ability to cater relaxation behavior through molecularly-engineered internal constraints offers a path to optimize material properties in nanoscopic systems. These two aspects are highlighted throughout the review, and their technological implications are discussed for MEMS/NEMS operations, including frictional and mechanical loading of polymer thin films. In this regard, material performance attributes and feedback for molecular designs are drawn from perturbation techniques that provide access to the energetic signatures and characteristic scales of molecular relaxation. In particular, the importance of the operating time scale in nanoscopic devices is emphasized with examples of both quasi-static and dynamic operations. Material responses have been found to change significantly when the drive velocity or loading rate was either comparable to or in excess of the characteristic molecular frequencies. Correspondingly, intrinsic molecular modes were found to either couple with the external mechanical disturbance, thus establishing channels for energy transport, or to remain passive, leading to apparent material stiffening. Findings such as these suggest that comprehensive investigations of the spatial distribution of molecular relaxation spectra in confined systems are necessary in order to match (or mismatch) molecular response times with system operating times. Along this line, this review provides examples for cognitive engineering of functional materials, with molecular structures that are tailored to system constraints and employed in nanoscale device technologies.

Comparison of large-scale amplitude modulation in turbulent boundary layers, pipes, and channel flows

Recent investigations by Monty et al. [J. Fluid Mech. 632, 431 (2009)] showed that important modal differences exist between channels/pipes and boundary layers, mainly in the largest energetic scales. In addition, Mathis et al. [J. Fluid Mech. 628, 311 (2009)] recently reported and quantified a nonlinear scale interaction in zero-pressure gradient turbulent boundary layers, whereby the large-scale motion amplitude modulates the small-scale motions. In this study, a comparison of this modulation effect of the streamwise velocity component is undertaken for all three flows for matched Reynolds number and measurement conditions. Despite the different large-scale phenomena in these internal and external wall-bounded flows, the results show that their amplitude modulation influence remains invariant in the inner region with some differences appearing in the outer region.

Hot-wire spatial resolution issues in wall-bounded turbulence

Careful reassessment of new and pre-existing data shows that recorded scatter in the hot-wire-measured near-wall peak in viscous-scaled streamwise turbulence intensity is due in large part to the simultaneous competing effects of the Reynolds number and viscous-scaled wire length l+. An empirical expression is given to account for these effects. These competing factors can explain much of the disparity in existing literature, in particular explaining how previous studies have incorrectly concluded that the inner-scaled near-wall peak is independent of the Reynolds number. We also investigate the appearance of the so-called outer peak in the broadband streamwise intensity, found by some researchers to occur within the log region of high-Reynolds-number boundary layers. We show that the ‘outer peak’ is consistent with the attenuation of small scales due to large l+. For turbulent boundary layers, in the absence of spatial resolution problems, there is no outer peak up to the Reynolds numbers investigated here (Reτ = 18830). Beyond these Reynolds numbers – and for internal geometries – the existence of such peaks remains open to debate. Fully mapped energy spectra, obtained with a range of l+, are used to demonstrate this phenomenon. We also establish the basis for a ‘maximum flow frequency’, a minimum time scale that the full experimental system must be capable of resolving, in order to ensure that the energetic scales are not attenuated. It is shown that where this criterion is not met (in this instance due to insufficient anemometer/probe response), an outer peak can be reproduced in the streamwise intensity even in the absence of spatial resolution problems. It is also shown that attenuation due to wire length can erode the region of the streamwise energy spectra in which we would normally expect to see kx−1 scaling. In doing so, we are able to rationalize much of the disparity in pre-existing literature over the kx−1 region of self-similarity. Not surprisingly, the attenuated spectra also indicate that Kolmogorov-scaled spectra are subject to substantial errors due to wire spatial resolution issues. These errors persist to wavelengths far beyond those which we might otherwise assume from simple isotropic assumptions of small-scale motions. The effects of hot-wire length-to-diameter ratio (l/d) are also briefly investigated. For the moderate wire Reynolds numbers investigated here, reducing l/d from 200 to 100 has a detrimental effect on measured turbulent fluctuations at a wide range of energetic scales, affecting both the broadband intensity and the energy spectra.

Large eddy simulation modelling of combustion for propulsion applications

Predictive modelling of turbulent combustion is important for the development of air-breathing engines, internal combustion engines, furnaces and for power generation. Significant advances in modelling non-reactive turbulent flows are now possible with the development of large eddy simulation (LES), in which the large energetic scales of the flow are resolved on the grid while modelling the effects of the small scales. Here, we discuss the use of combustion LES in predictive modelling of propulsion applications such as gas turbine, ramjet and scramjet engines. The LES models used are described in some detail and are validated against laboratory data-of which results from two cases are presented. These validated LES models are then applied to an annular multi-burner gas turbine combustor and a simplified scramjet combustor, for which some additional experimental data are available. For these cases, good agreement with the available reference data is obtained, and the LES predictions are used to elucidate the flow physics in such devices to further enhance our knowledge of these propulsion systems. Particular attention is focused on the influence of the combustion chemistry, turbulence-chemistry interaction, self-ignition, flame holding burner-to-burner interactions and combustion oscillations.

Mechanics of strain gradient plasticity with particular reference to decomposition of the state variables into energetic and dissipative components

The results of recent studies on strengthening and hardening mechanisms for micro/nano structured materials indicate that the use of only one type of energetic or dissipative description may be insufficient to accurately describe the size effects exhibited in metallic components. Therefore, it is important to incorporate more than one description of the thermodynamic processes into the modeling in order to have a better understanding of the hardening and strengthening mechanisms for micro/nano structured materials. The research presented here is based on this deficiency and the goal is to develop a strain gradient theory based on the decomposition of the state variables into energetic and dissipative components. This, in turn, endowed the constitutive equations to have both energetic and dissipative gradient length scales ℓ en and ℓ dis , respectively. The effect of the material microstructural interface between two materials is also incorporated into the proposed formulation. Hence four material length scales are introduced: two for the bulk and the other two for the interface. The resulting formulation exhibits the following important physical phenomena: (i) standard energetic hardening associated with plastic strain and nonlocal energetic hardening associated with plastic strain gradients; (ii) size dependent increase in yield strength which is characterized by the dissipative strengthening associated with plastic strain gradient rate; (iii) the effect of interfacial yield strength and hardening; (iv) description of the boundary layer; and (v) the effect of the different boundary conditions. The problem is solved analytically by using for example, a thin film on elastic substrate under uniaxial uniform tension or a single phase bicrystal under uniform tension where the interface represents the grain boundary. The interface model here describes the internal boundary of the plastic region and characterizes the physical understanding of the dislocation mechanics at the interface between two phases. The results of the analytical results indicate that the proposed theory qualitatively captures the overall physical behavior. However there is strong debate in the literature on the choice of accurate physical boundary conditions at the elastic plastic boundaries. Therefore, more elaborate studies are needed for better assessment of the boundary conditions of the higher-order strain gradient plasticity theories.

Statistical analysis of seismic processes on the basis of the diffusion approach

On the basis of the diffusion approach, statistical analysis of seismicity is carried out in order to reveal the peculiarities characteristic of random walk processes. In accordance with the hypothesis on connectivity of earthquakes and energetic criterion, the expansion of the seismic process into a set of sequences is made; each sequence is a Brownian process with specific spatial, temporal, and energetic scales. The statistical distributions of sequences by the number of links, total energies, distances, time, and flight velocities between events are built.

A comparison of in situ bottom pressure array measurements with GRACE estimates in the Kuroshio Extension

Ocean bottom pressure estimates from Gravity Recovery and Climate Experiment (GRACE) have been validated by comparisons with an array of in situ bottom pressure measurements. The 600 km by 600 km array comprised 46 bottom pressure sensors that were part of the Kuroshio Extension System Study (KESS). Validations in other ocean regions have been limited by available data to pointwise bottom pressure measurements. Spatially‐averaged monthly‐mean bottom pressure over the KESS array is highly correlated with GRACE bottom pressure estimated at the center of the array. The correlations are nearly equally high for three standard choices of spatial smoothing radius applied to GRACE estimates, 300, 500, and 750 km. In contrast, pointwise comparisons between GRACE and individual bottom pressures are high or low in sub‐regions of KESS, depending partially upon the local variance of deep mesoscale eddies whose energetic length scales are shorter than 300 km. KESS is a suitable validation experiment for the GRACE estimates at monthly scales with 300 to 750 km spatial radius of smoothing.

Influence of material parameters and crystallography on the size effects describable by means of strain gradient plasticity

In the context of single-crystal strain gradient plasticity, we focus on the simple shear of a constrained strip in order to study the effects of the material parameters possibly involved in the modelling. The model consists of a deformation theory suggested and left undeveloped by Bardella [(2007). Some remarks on the strain gradient crystal plasticity modelling, with particular reference to the material length scales involved. Int. J. Plasticity 23, 296–322] in which, for each glide, three dissipative length scales are considered; they enter the model through the definition of an effective slip which brings into the isotropic hardening function the relevant plastic strain gradients, averaged by means of a p-norm. By means of the defect energy (i.e., a function of Nye's dislocation density tensor added to the free energy; see, e.g., Gurtin [2002. A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations. J. Mech. Phys. Solids 50, 5–32]), the model further involves an energetic material length scale. The application suggests that two dissipative length scales may be enough to qualitatively describe the size effect of metals at the microscale, and they are chosen in such a way that the higher-order state variables of the model be the dislocation densities. Moreover, we show that, depending on the crystallography, the size effect governed by the defect energy may be different from what expected (based on the findings of [Bardella, L., 2006. A deformation theory of strain gradient crystal plasticity that accounts for geometrically necessary dislocations. J. Mech. Phys. Solids 54, 128–160] and [Gurtin et al. 2007. Gradient single-crystal plasticity with free energy dependent on dislocation densities. J. Mech. Phys. Solids 55, 1853–1878]), leading mostly to some strengthening. In order to investigate the model capability, we also exploit a Γ -convergence technique to find closed-form solutions in the “isotropic limit”. Finally, we analytically show that in the “perfect plasticity” case, should the dissipative length scales be set to zero, the presence of the sole energetic length scale may lead, as in standard plasticity, to non-uniqueness of solutions.

Localized dynamic kinetic-energy-based models for stochastic coherent adaptive large eddy simulation

Stochastic coherent adaptive large eddy simulation (SCALES) is an extension of the large eddy simulation approach in which a wavelet filter-based dynamic grid adaptation strategy is employed to solve for the most “energetic” coherent structures in a turbulent field while modeling the effect of the less energetic background flow. In order to take full advantage of the ability of the method in simulating complex flows, the use of localized subgrid-scale models is required. In this paper, new local dynamic one-equation subgrid-scale models based on both eddy-viscosity and non-eddy-viscosity assumptions are proposed for SCALES. The models involve the definition of an additional field variable that represents the kinetic energy associated with the unresolved motions. This way, the energy transfer between resolved and residual flow structures is explicitly taken into account by the modeling procedure without an equilibrium assumption, as in the classical Smagorinsky approach. The wavelet-filtered incompressible Navier–Stokes equations for the velocity field, along with the additional evolution equation for the subgrid-scale kinetic energy variable, are numerically solved by means of the dynamically adaptive wavelet collocation solver. The proposed models are tested for freely decaying homogeneous turbulence at Reλ=72. It is shown that the SCALES results, obtained with less than 0.5% of the total nonadaptive computational nodes, closely match reference data from direct numerical simulation. In contrast to classical large eddy simulation, where the energetic small scales are poorly simulated, the agreement holds not only in terms of global statistical quantities but also in terms of spectral distribution of energy and, more importantly, enstrophy all the way down to the dissipative scales.