Mechanical Dissipation Rate Research Articles

Thermodynamically consistent strain hardening variable/driving force, inelastic stored energy and self-heating in dynamic plasticity

Accounting for self-heating and subsequent thermal softening in dynamic plasticity requires an accurate estimation of the mechanical dissipation rate which is by definition the difference between the plastic work rate and the inelastic stored energy rate. Yet, in constitutive modeling, the evaluation of the inelastic stored energy strongly depends on the adopted approach, viz. irreversible thermodynamics vs microstructure-motivated approach, and, whatever the approach, does not yet lead to realistic results in terms of self-heating. The aim of the present study is to attempt to conciliate both above mentioned approaches by building constitutive models that relate strain hardening, inelastic stored energy and self-heating in a consistent way. The models in question are developed in agreement with experimental results obtained on five high-strength steels.

Sympathetic feedback cooling in the optomechanical system consisting of two coupled cantilevers

We present sympathetic cooling in an optomechanical system consisting of two coupled cantilevers. The hybridization of the cantilevers creates a symmetric mode, which is feedback cooled, and an anti-symmetric mode not directly controllable by the feedback. The scheme of sympathetic cooling is adopted to cool the anti-symmetric mode indirectly by parametrically coupling to the feedback-cooled symmetric mode, from which the cooling power can be transferred. Experiment shows that the realization of coherent dynamics plays an essential role in sympathetic cooling, in which optimal cooling is achieved when the mechanical dissipation rate and the strength of coupling become comparable. The sympathetic cooling is improved by increasing the strength of mode coupling to enhance the transfer of cooling power. Also, the limit of sympathetic cooling imposed by the capacity of feedback cooling is reached as the effective temperatures of the two modes approach the strong coherent coupling condition. Our research provides the prospect of extending the cooling techniques to coupled mechanical resonators for a broad application in sensing and information processing.

Effect of viscous shearing stresses on optimal material designs for flow of fluids through porous media

Topology optimization offers optimal material layouts, enabling automation in the design of devices. Given the recent advances in computer technology and additive manufacturing, topology optimization is increasingly being used to design complex porous structures, for example, microfluidic devices. For the flow of fluids in such miniature-sized porous structures, viscous shearing stresses will be significant. However, the Darcy model—the most popular mathematical model describing the flow of a single-phase incompressible fluid in rigid porous media—neglects the internal friction arising from viscous shearing stresses. We, therefore, develop a material design framework under the topology optimization based on the Darcy–Brinkman model—a mathematical model for the flow of fluids through porous media that accounts for internal friction besides the drag considered in the Darcy model. The proposed framework uses the total rate of mechanical dissipation—a physical quantity—for the objective function. To understand the effect of viscous shearing stresses on the design, we compare the optimal material layouts provided by the Darcy and Darcy–Brinkman models under topology optimization. In particular, we show, using analytical solutions corroborated by numerical simulations, that the optimal material layouts are alike for the class of problems exhibiting axisymmetry, for which viscous shearing stresses vanish. These analytical solutions will be valuable to check the veracity of numerical simulators. For those problems with dominant viscous shearing stresses (e.g., flow in a backward-facing step domain), we show, using numerical solutions, the optimal material layouts under the Darcy and Darcy–Brinkman models are very different. Also, the associated solution fields (i.e., velocity and pressure) are qualitatively different under their respective optimal layouts for these two models.

On Optimal Designs Using Topology Optimization for Flow Through Porous Media Applications

Topology optimization (TopOpt) is a mathematical-driven design procedure to realize optimal material architectures. This procedure is often used to automate the design of devices involving flow through porous media, such as micro-fluidic devices. TopOpt offers material layouts that control the flow of fluids through porous materials, providing desired functionalities. Many prior studies in this application area have used Darcy equations for primal analysis and the minimum power theorem (MPT) to drive the optimization problem. But both these choices (Darcy equations and MPT) are restrictive and not valid for general working conditions of modern devices. Being simple and linear, Darcy equations are often used to model flow of fluids through porous media. However, two inherent assumptions of the Darcy model are: the viscosity of a fluid is a constant, and inertial effects are negligible. There is irrefutable experimental evidence that viscosity of a fluid, especially organic liquids, depends on the pressure. Given the typical small pore-sizes, inertial effects are dominant in micro-fluidic devices. Next, MPT is not a general principle and is not valid for (nonlinear) models that relax the assumptions of the Darcy model. This paper aims to overcome the mentioned deficiencies by presenting a general strategy for using TopOpt. First, we will consider nonlinear models that take into account the pressure-dependent viscosity and inertial effects, and study the effect of these nonlinearities on the optimal material layouts under TopOpt. Second, we will explore the rate of mechanical dissipation, valid even for nonlinear models, as an alternative for the objective function. Third, we will present analytical solutions of optimal designs for canonical problems; these solutions not only possess research and pedagogical values but also facilitate verification of computer implementations.

Processing light with an optically tunable mechanical memory

Mechanical systems are one of the promising platforms for classical and quantum information processing and are already widely-used in electronics and photonics. Cavity optomechanics offers many new possibilities for information processing using mechanical degrees of freedom; one of them is storing optical signals in long-lived mechanical vibrations by means of optomechanically induced transparency. However, the memory storage time is limited by intrinsic mechanical dissipation. More over, in-situ control and manipulation of the stored signals processing has not been demonstrated. Here, we address both of these limitations using a multi-mode cavity optomechanical memory. An additional optical field coupled to the memory modifies its dynamics through time-varying parametric feedback. We demonstrate that this can extend the memory decay time by an order of magnitude, decrease its effective mechanical dissipation rate by two orders of magnitude, and deterministically shift the phase of a stored field by over 2π. This further expands the information processing toolkit provided by cavity optomechanics.

Multi-scale analysis on coal permeability using the lattice Boltzmann method

As a mesoscopic kinetic approach, the lattice Boltzmann method (LBM) has been widely applied to characterize the flows in porous medium. However, for larger scale flows, upscaling microscale technique is the key and difficult point. Based on the X-ray computed tomography (X-CT) images of actual coal samples, numerical simulations were carried out using the LBM at the pore scale. The velocity/pressure distribution and coal permeability were obtained. The local rate of mechanical dissipation is applied to determine an appropriate representative elementary volume (REV) scale. Then based on a gray lattice Boltzmann model, numerical simulations were carried at the REV scale and the pressure distribution is almost identical with the solution of the LBM simulations at the pore scale. The simulation results of REV with different sizes indicate that the size of REV determined in this paper is reasonable. The relative errors between the pore scale and REV scale simulation for permeability prediction are less than 6%. In addition, the REV scale simulation can greatly improve the computational efficiency and provides an effective approach for large-scale flow simulation.

Determining the up-down-up response through tension tests of a pre-twisted shape memory alloy tube

In this paper, the stress-induced phase transitions in a shape memory alloy (SMA) tube under torsion and pre-twisted tension are studied analytically. A constitutive model with the specific forms of Helmholtz free energy and mechanical dissipation rate is employed to formulate the governing system. Exact solution of the tube under pure torsion is first derived and the shear stress–shear strain response is determined, which reveals the hardening effect. For the pre-twisted tube under uniaxial tension, the one-dimensional asymptotic tensile stress–tensile strain relations for the austenite, the phase transition and the martensite regions are derived by using the asymptotic expansion method. By properly defining an elastic energy potential, the present system can be viewed as an elastic problem, which can be related to the problem of Ericksen's bar. The analytical formulas for the nucleation and propagation stresses in terms of the pre-shear strain (caused by the pre-twist) are obtained. Tension tests with fixed pre-twists on SMA thin-walled tube are conducted, with a focus on the stress–strain response. The measured values and the analytical formula for the propagation stress are used to determine the material parameters, which, in turn, yields the up-down-up response of a shape memory alloy tube under pure tension. The tendency and turning point of the phase transformation in the pre-twisted tube from localization to homogeneous deformation are also determined, which suggests a plausible way to avoid the instability in actuation applications.

Negative nonlinear damping of a multilayer graphene mechanical resonator

We experimentally investigate the nonlinear response of a multilayer graphene resonator using a superconducting microwave cavity to detect its motion. The radiation pressure force is used to drive the mechanical resonator in an optomechanically induced transparency configuration. By varying the amplitudes of drive and probe tones, the mechanical resonator can be brought into a nonlinear limit. Using the calibration of the optomechanical coupling, we quantify the mechanical Duffing nonlinearity. By increasing the drive force, we observe a decrease in the mechanical dissipation rate at large amplitudes, suggesting a negative nonlinear damping mechanism in the graphene resonator. Increasing the optomechanical backaction further, we observe instabilities in the mechanical response.

Cascaded optical transparency in multimode-cavity optomechanical systems.

Electromagnetically induced transparency has great theoretical and experimental importance in many areas of physics, such as atomic physics, quantum optics and, more recent, cavity optomechanics. Optical delay is the most prominent feature of electromagnetically induced transparency, and in cavity optomechanics, the optical delay is limited by the mechanical dissipation rate of sideband-resolved mechanical modes. Here we demonstrate a cascaded optical transparency scheme by leveraging the parametric phonon-phonon coupling in a multimode optomechanical system, where a low damping mechanical mode in the unresolved-sideband regime is made to couple to an intermediate, high-frequency mechanical mode in the resolved-sideband regime of an optical cavity. Extended optical delay and higher transmission as well as optical advancing are demonstrated. These results provide a route to realize ultra-long optical delay, indicating a significant step towards integrated classical and quantum information storage devices.

Propagation stresses in phase transitions of an SMA wire: New analytical formulas based on an internal-variable model

In this paper, we study the stress-induced isothermal phase transitions of a shape memory alloy wire, with a focus on homogeneous or piecewise homogeneous deformations. Based on the constitutive model in the literature with the specific Helmholz free energy and rate of mechanical dissipation, the three-dimensional model is formulated. Identifying the characteristic axial strain as the small parameter, we arrive at the asymptotic one-dimensional equation which involves the stress, the axial strain and the phase state variable. By considering the evolution law of the phase state variable, the stress–strain relations corresponding to austenite, martensite and phase transition (phase mixture) regions are obtained. Although we take the dissipation into consideration, we find that each of the pure loading and unloading processes is equivalent to the Ericksen’s bar problem with three branches in the stress–strain curve. As a result, we successfully deduce the analytical formulas for the nucleation stresses and propagation stresses. The analytical results reveal explicitly how such important quantities depend on the material constants and the temperature. We also demonstrate that they capture a number of features observed in experiments. As an important application, we show that these formulas can be used for calibration of the material constants (such as the difference of the thermal free energies of two phases) by comparing with the measured nominal stress–strain curves. Three examples are also provided.

An internal-variable rod model for stress-induced phase transitions in a slender SMA layer. I: Asymptotic equations and a two-phase solution

In part I of this series of two papers, an internal-variable rod model is proposed to study the stress-induced phase transitions in a slender shape memory alloy (SMA) layer. To study the mechanical responses of SMAs, two independent energy functions are adopted: the Helmholtz free energy and the rate of mechanical dissipation. A phase state variable is introduced to describe the phase transition process. Starting from the 2-D governing system and by using the coupled series-asymptotic expansion method, one single equilibrium equation is derived, which involves the leading order term of the axial strain and the phase state functions. Further by using the phase transition criteria, the evolution laws of the phase state functions corresponding to the outer loop of the stress–strain response are derived. As a result, the governing ODEs for the purely loading and purely unloading processes are obtained, which are called the asymptotic rod equations. The two-phase solution of the asymptotic rod equations in an infinitely long layer is then constructed. An explicit solution for the phase volume fraction of the corresponding inhomogeneous deformation is deduced, which appears to be the first analytical expression for this important quantity in stress-induced phase transitions. The key parameters in terms of original material constants for the phase transitions and deformations are also identified.

Quantifying mixing in viscously unstable porous media flows

Viscous fingering is a well-known hydrodynamic instability that sets in when a less viscous fluid displaces a more viscous fluid. When the two fluids are miscible, viscous fingering introduces disorder in the velocity field and exerts a fundamental control on the rate at which the fluids mix. Here we analyze the characteristic signature of the mixing process in viscously unstable flows, by means of high-resolution numerical simulations using a computational strategy that is stable for arbitrary viscosity ratios. We propose a reduced-order model of mixing, which, in the spirit of turbulence modeling and in contrast with previous approaches, recognizes the fundamental role played by the mechanical dissipation rate. The proposed model captures the nontrivial interplay between channeling and creation of interfacial area as a result of viscous fingering.

A thermodynamically self-consistent damage equation for grain size evolution during dynamic recrystallization

We employ basic non-equilibrium thermodynamics to propose a general equation for the mean grain size evolution in a deforming medium, under the assumption that the whole grain size distribution remains self-similar. We show that the grain size reduction is controlled by the rate of mechanical dissipation in agreement with recent findings. Our formalism is self consistent with mass and energy conservation laws and allows a mixed rheology. As an example, we consider the case where the grain size distribution is lognormal, as is often experimentally observed. This distribution can be used to compute both the kinetics of diffusion between grains and of dynamic recrystallization. The experimentally deduced kinetics of grain size coarsening indicates that large grains grow faster than what is assumed in classical normal grain growth theory. We discuss the implications of this model for a mineral that can be deformed under both dislocation creep and grain size sensitive diffusion creep using experimental data of olivine. Our predictions of the piezometric equilibrium in the dislocation-creep regime are in very good agreement with the observations for this major mantle-forming mineral. We show that grain size reduction occurs even when the average grain size is in diffusion creep, because the largest grains of the grain size distribution can still undergo recrystallization. The resulting rheology that we predict for olivine is time-dependent and more non-linear than in dislocation creep. As the deformation rate remains an increasing function of the deviatoric stress, this rheology is not localizing.

Mechanical dissipation versus thermo-mechanical exergy destruction for plane shockwaves in an inviscid perfect gas

In this paper, the physical exergy destruction caused by a shockwave, as an overall measure of the thermo-mechanical dissipation, is compared to the evaluation of mechanical dissipation alone. Travelling and stationary compression shockwaves are considered assuming an inviscid perfect gas with constant specific heats. Although quantities such as the change in exergy are not frame-indifferent, it is shown that mechanical dissipation and exergy destruction are both frame-indifferent. The results of this work reveal that, in many cases, the exergy destruction rate is a small fraction of the mechanical energy dissipation rate typically used to determine losses in gas dynamics. This is particularly true when the initial temperature of the fluid is high relative to the environment temperature. In contrast, the results show that, for very low initial temperatures that are below the environment temperature, the thermo-mechanical dissipation rate can be much greater than mechanical dissipation rate.

Elastic shadow flow and its theoretical implications for inelastic solids

Microstructural considerations have led to a constitutive format for the modeling of inelastic solids which does not make use of a fixed material reference in the usual sense. A principal motivation for this Eulerian-type' theoretical structure stems from a belief that large deformation inelastic flow phenomena (such as that encountered in certain metal forming processes) will one day prove amenable to numerical techniques of the sort common to the field of fluid mechanics. Unfortunately, virtually all established theoretical results of a general nature have been developed in a Lagrangian or referential context, and are not readily adapted to this new format. Here, this difficulty is partially overcome through the introduction of an instantaneous local reference corresponding to a material element's so called 'shadow' (elastically unstretched) configuration. A related state variable transformation and the definition of a shadow frame time derivative (analogous to the corotational time derivative) are then shown to facilitate a far more tractable theoretical reformulation. Throughout, three equivalent variants of this general theory are presented, one expressed in terms of a gradient type 'cell placement tensor', a second involving symmetric elastic stretch and orthogonal cell orientation tensors, and a third in which the aforementioned elastic stretch is replaced by the elastic (natural) log-strain tensor. In each case, the theoretical simplifications appropriate for various types of materials are enumerated. It is noteworthy that the latter two forms are instantly specialized for the most common class of structurally isotropic materials by merely dropping dependence on the cell orientation tensor. In all forms, basic thermodynamic considerations (second law) result in general expressions for true stress response in terms of energy derivatives, the rate of mechanical dissipation, and to necessary conditions (in the form of constitutive inequalities) for Il'iushin stability. Finally, the specific circumstances under which these inequalities reduce to the familiar Drucker-like' forms are identified.

On the thermomechanics of shape memory wires

The thermomechanical behavior of a shape memory wire is modeled based on a theory that takes cognizance of the fact that the body can possess multiple natural configurations [1]. The constitutive equations are developed by first constructing the form of the Helmholtz potential (based on different modes of energy storage), and dissipation mechanisms. The internal energy includes contributions from the strain energy, the latent energy, the interfacial energy and thermal energy. The entropy of the system includes the"entropy jump" associated with the phase transition.¶The role of the rate of mechanical dissipation as a mechanism for entropy generation and its importance in describing the hysteretic behavior is brought out by considering the difference between hysteretic and non-hysteretic (dissipation-less) behavior.¶Finally, simple linear or quadratic forms are assumed for the various constitutive functions and the full shape memory response is modeled. A procedure for the determination of the constants is also indicated and the constants for two systems (CuZnAl and NiTi) are calculated from published experimental data (see [2, 3]). The predictions of the theory show remarkable agreement with the experimental data. However, some of the results predicted by the theory are different from the experimental results reported in Huo and Muller [2] We discuss some of the issues regarding this discrepancy and show that there appears to be some internal inconsistency between the experimental data reported in Figure 6 and Figure 9 of Huo and Muller [2] (provided they represent the same sample).

Dissipative behaviour of viscoelastic fluids derived from rheological constitutive equations

The dissipative source term in the temperature equation is investigated for non-isothermal flows of viscoelastic fluids. Two special cases are considered. These are the pure entropic and (internal) energy elasticity, respectively. The mechanical dissipation rate (entropy production in the system) is derived from rheological constitutive equations of the rate type. This dissipation rate is equivalent to the dissipative source term (heat production) in the temperature equation in the case of energy elasticity.

Acoustic dissipation and H/-/ radiation in the solar chromosphere. II

view Abstract Citations (10) References (16) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Acoustic dissipation and H- radiation in the solar chromosphere. II. Kalkofen, W. ; Ulmschneider, P. Abstract The relation between mechanical heating and radiative cooling in the solar chromosphere is investigated, and the dependence of the temperature rise on the mechanical dissipation rate and on the microscopic state of H(-) ions at the foot of the chromosphere is studied. It is found that H(-) is very nearly in local thermodynamic equilibrium (LTE) at the temperature minimum; but near the upper end of the range where H(-) dominates the opacity, deviations from LTE should be taken into account in estimating the mechanical energy input from the empirical temperature distribution. The use of empirical models for calculating the mechanical energy input into the chromosphere is considered. The estimate of mechanical heating implied by the recent work of Pradeire and Thomas (1976) is found to be too low by about an order of magnitude. Publication: The Astrophysical Journal Pub Date: January 1979 DOI: 10.1086/156776 Bibcode: 1979ApJ...227..655K Keywords: Acoustic Attenuation; Chromosphere; H Lines; Hydrogen Ions; Solar Temperature; Atmospheric Attenuation; Atmospheric Heating; Radiative Heat Transfer; Stellar Models; Temperature Distribution; Thermodynamic Equilibrium; Solar Physics; Opacities:Solar Chromosphere; Solar Chromosphere:Energy Transport full text sources ADS |