Showing papers in "Continuum Mechanics and Thermodynamics in 2014"
TL;DR: In this article, a relaxed linear elastic micromorphic continuum model with symmetric Cauchy force stresses and curvature contribution depending only on the micro-dislocation tensor is proposed.
Abstract: We formulate a relaxed linear elastic micromorphic continuum model with symmetric Cauchy force stresses and curvature contribution depending only on the micro-dislocation tensor. Our relaxed model is still able to fully describe rotation of the microstructure and to predict nonpolar size effects. It is intended for the homogenized description of highly heterogeneous, but nonpolar materials with microstructure liable to slip and fracture. In contrast to classical linear micromorphic models, our free energy is not uniformly pointwise positive definite in the control of the independent constitutive variables. The new relaxed micromorphic model supports well-posedness results for the dynamic and static case. There, decisive use is made of new coercive inequalities recently proved by Neff, Pauly and Witsch and by Bauer, Neff, Pauly and Starke. The new relaxed micromorphic formulation can be related to dislocation dynamics, gradient plasticity and seismic processes of earthquakes. It unifies and simplifies the understanding of the linear micromorphic models.
247 citations
TL;DR: The lattice Boltzmann method for simulating fluid phases was coupled with the discrete element method for studying solid phases to formulate a novel solver for fast discrete particle simulation (DPS) of particle–fluid flows that was found to yield results faster than its FVM–DEM counterpart.
Abstract: The lattice Boltzmann method (LBM) for simulating fluid phases was coupled with the discrete element method (DEM) for studying solid phases to formulate a novel solver for fast discrete particle simulation (DPS) of particle–fluid flows. The fluid hydrodynamics was obtained by solving LBM equations instead of solving the Navier–Stokes equation by the finite volume method (FVM). Interparticle and particle–wall collisions were determined by DEM. The new DPS solver was validated by simulating a three-dimensional gas–solid bubbling fluidized bed. The new solver was found to yield results faster than its FVM–DEM counterpart, with the increase in the domain-averaged gas volume fraction. Additionally, the scalability of the LBM–DEM DPS solver was superior to that of the FVM–DEM DPS solver in parallel computing. Thus, the LBM–DEM DPS solver is highly suitable for use in simulating dilute and large-scale particle–fluid flows.
44 citations
TL;DR: In this paper, a simple model for phonon interaction with crystal boundaries, similar to the Maxwell boundary conditions in classical kinetic theory, is proposed, and a macroscopic transport equation for an arbitrary set of moments is developed and closed by means of Grad's moment method.
Abstract: Heat transfer in solids is modeled in the framework of kinetic theory of the phonon gas. The microscopic description of the phonon gas relies on the phonon Boltzmann equation and the Callaway model for phonon–phonon interaction. A simple model for phonon interaction with crystal boundaries, similar to the Maxwell boundary conditions in classical kinetic theory, is proposed. Macroscopic transport equation for an arbitrary set of moments is developed and closed by means of Grad’s moment method. Boundary conditions for the macroscopic equations are derived from the microscopic model and the Grad closure. As example, sets with 4, 9, 16, and 25 moments are considered and solved analytically for one-dimensional heat transfer and Poiseuille flow of phonons. The results show the influence of Knudsen number on phonon drag at solid boundaries. The appearance of Knudsen layers reduces the net heat conductivity of solids in rarefied phonon regimes.
36 citations
TL;DR: In this article, a potential-based approach for non-isothermal inelastic processes is presented, which is based on the principle of the minimum of the dissipation potential which was used previously only in the isothermal context.
Abstract: In this paper, we contribute to the methodology of material modeling by presenting a potential-based approach for non-isothermal inelastic processes. It is based on the principle of the minimum of the dissipation potential which was used previously only in the isothermal context. In contrast to the principle of maximum dissipation, the presented procedure results in mathematically simplified equations. Due to its variational character, the inclusion of constraints is very simple. After derivation of our method, we use the examples of non-isothermal perfect plasticity and shape memory alloys for demonstration of the validity and performance of the concept.
35 citations
TL;DR: In this paper, the Piola-Kirchhoff framework was used to derive the generalized generalized solid mechanics (GGSM) over the isotropic small-strain case.
Abstract: Governing equations of dissipative generalized solid mechanics are derived by thermodynamic methods in the Piola–Kirchhoff framework using the Liu procedure. The isotropic small-strain case is investigated in more detail. The connection to the Ginzburg–Landau type evolution, dual internal variables, and a thermodynamic generalization of the standard linear solid model of rheology is demonstrated. Specific examples are chosen to emphasize experimental confirmations and predictions beyond less general approaches.
33 citations
TL;DR: In this article, a thermomechanical framework for the modelling of gradient plasticity is developed within the range of linear strains, and special focus is given to the restrictions imposed by the Clausius-Duhem inequality.
Abstract: A thermomechanical framework for the modelling of gradient plasticity is developed within the range of linear strains. Full anisotropy is considered. Special focus is given to the restrictions imposed by the Clausius-Duhem inequality. A rather general example gives a complete anisotropic model and shows its ther- modynamic consistency. This is finally particularized for the isotropic case by using isotropic tensor-function representations.
33 citations
TL;DR: In this article, a model for polycrystalline shape memory alloys which takes full thermo-mechanical coupling into account is presented, which allows to model the experimentally well-documented transformation fronts in tension tests by a finite element scheme without further assumptions.
Abstract: The impressive properties of shape memory alloys are produced by means of solid-to-solid phase transformations where thermal effects play an important role. In this paper, we present a model for polycrystalline shape memory alloys which takes full thermo-mechanical coupling into account. Starting from the equations of the first and the second law of thermodynamics, we derive evolution equations for the volume fractions of the different martensitic variants and a related equation for heat conduction. A thermodynamic analysis allows to formulate a complete expression for the dissipation caused by phase transformation and heat flux. This allows to model the experimentally well-documented transformation fronts in tension tests by a finite element scheme without further assumptions. Additionally, the number of required model parameters is very small in comparison with phenomenological approaches. Numerical examples are presented which show a good agreement with experimental observations.
27 citations
TL;DR: A continuum theory of rubber elasticity from a discrete model by variational convergence is derived and physically motivate this model and complete the analysis by numerical simulations.
Abstract: Since the pioneering work by Treloar, many models based on polymer chain statistics have been proposed to describe rubber elasticity. Recently, Alicandro, Cicalese, and the first author rigorously derived a continuum theory of rubber elasticity from a discrete model by variational convergence. The aim of this paper is twofold. First, we further physically motivate this model and complete the analysis by numerical simulations. Second, in order to compare this model to the literature, we present in a common language two other representative types of models, specify their underlying assumptions, check their mathematical properties, and compare them to Treloar’s experiments.
26 citations
TL;DR: In this paper, the authors proposed a correlated relation that expresses normalized mass flow rate increment due to thermal creep as a function of flow rarefaction, normalized wall temperature gradient and pressure ratio over a wide range of Knudsen number.
Abstract: In this paper, we study mass flow rate of rarefied gas flow through micro/nanoscale channels under simultaneous thermal and pressure gradients using the direct simulation Monte Carlo (DSMC) method. We first compare our DSMC solutions for mass flow rate of pure temperature-driven flow with those of Boltzmann-Krook-Walender equation and Bhatnagar-Gross-Krook solutions. Then, we focus on pressure–temperature-driven flows. The effects of different parameters such as flow rarefaction, channel pressure ratio, wall temperature gradient and flow bulk temperature on the thermal mass flow rate of the pressure–temperature-driven flow are examined. Based on our analysis, we propose a correlated relation that expresses normalized mass flow rate increment due to thermal creep as a function of flow rarefaction, normalized wall temperature gradient and pressure ratio over a wide range of Knudsen number. We examine our predictive relation by simulation of pressure-driven flows under uniform wall heat flux (UWH) boundary condition. Walls under UWH condition have non-uniform temperature distribution, that is, thermal creep effects exist. Our investigation shows that developed analytical relation could predict mass flow rate of rarefied pressure-driven gas flows under UWH condition at early transition regime, that is, up to Knudsen numbers of 0.5.
25 citations
TL;DR: In this article, a continuum model for a graphene sheet undergoing infinitesimal in-plane deformations is derived by applying the arguments of homogenization theory, which turns out to coincide with that found by various authors with different methods, but it avoids anticipations on the validity of any properly adjusted or generalized Cauchy-Born rule.
Abstract: A continuum model for a graphene sheet undergoing infinitesimal in-plane deformations is derived by applying the arguments of homogenization theory. The model turns out to coincide with that found by various authors with different methods, but it avoids anticipations on the validity of any properly adjusted or generalized Cauchy–Born rule. The constitutive equation for stress and the effective Young’s modulus and Poisson ratio are explicitly given in terms of the bond constants.
25 citations
TL;DR: In this paper, a number of problems for the interaction of laser radiation with a heat-conducting half-space and a layer are considered, and the obtained solutions are compared with each other and with the solutions of the classic heat equation and the wave equation.
Abstract: A number of problems for the interaction of laser radiation with a heat-conducting half-space and a layer are considered. The obtained solutions are compared with each other and with the solutions of the classic heat equation and the wave equation. A laser impulse is modelled by defining the heat flux at the boundary for the opaque medium, or by defining the distribution of heat sources in the volume for the semitransparent medium. The power of the laser pulse depends on time as the Dirac delta function or as the Heaviside function do. It allows for the simulation of instant and continuous laser exposure on the medium. Temperature distributions are obtained by using Green’s functions for a half-space and a layer with the Dirichlet and Neumann boundary conditions.
TL;DR: In this paper, a phenomenological model for the coupled thermo-electro-magneto-mechanical and phase-transformation behavior of magnetic shape-memory alloys is advanced in small strains and eddy current approximation.
Abstract: A phenomenological model for the coupled thermo-electro-magneto-mechanical and phase-transformation behaviour of magnetic shape-memory alloys is advanced in small strains and eddy current approximation. The corresponding system of strongly nonlinear relations is tackled via a suitable enthalpy-like transformation. A fully implicit regularized time-discretization scheme is devised and proved to be stable and convergent. In particular, the convergence proof for discrete solutions entails that a suitably weak, energy-conserving solution to the continuous nonlinear system exists. Moreover, several particular models as e.g. ferro/paramagnetic transformation in ferromagnetic materials, martensitic transformation in shape memory allows, or just a simple thermistor problem are covered just as special cases.
TL;DR: In this article, the effect of rotation on the thermal instability in a horizontal layer of a Newtonian nanofluid was studied and the results showed that rotation delays the rate of heat and mass transferred, representing a delay in the onset on convection.
Abstract: The present paper studies the effect of rotation on the thermal instability in a horizontal layer of a Newtonian nanofluid which incorporates the effect of Brownian motion along with thermophoresis. In order to find the concentration and the thermal Nusselt numbers for unsteady state, a nonlinear analysis, using a minimal representation of the truncated Fourier series of two terms, has been performed. The results obtained are then presented graphically. It is observed that rotation delays the rate of heat and mass transferred, representing a delay in the onset on convection. This shows a stabilizing effect for a rotating system against a nonrotating system.
TL;DR: In this paper, the authors developed rate constitutive theories for compressible and incompressible ordered thermoviscoelastic fluids in Eulerian description, where the convected time derivative of the Cauchy stress tensor and the heat vector were derived for a desired order.
Abstract: This paper presents development of rate constitutive theories for compressible as well as in incompressible ordered thermoviscoelastic fluids, i.e., polymeric fluids in Eulerian description. The polymeric fluids in this paper are considered as ordered thermoviscoelastic fluids in which the stress rate of a desired order, i.e., the convected time derivative of a desired order ‘m’ of the chosen deviatoric Cauchy stress tensor, and the heat vector are functions of density, temperature, temperature gradient, convected time derivatives of the chosen strain tensor up to any desired order ‘n’ and the convected time derivative of up to orders ‘m−1’ of the chosen deviatoric Cauchy stress tensor. The development of the constitutive theories is presented in contravariant and covariant bases, as well as using Jaumann rates. The polymeric fluids described by these constitutive theories will be referred to as ordered thermoviscoelastic fluids due to the fact that the constitutive theories are dependent on the orders ‘m’ and ‘n’ of the convected time derivatives of the deviatoric Cauchy stress and conjugate strain tensors. The highest orders of the convected time derivative of the deviatoric Cauchy stress and strain tensors define the orders of the polymeric fluid. The admissibility requirement necessitates that the constitutive theories for the stress tensor and heat vector satisfy conservation laws, hence, in addition to conservation of mass, balance of momenta, and conservation of energy, the second law of thermodynamics, i.e., Clausius–Duhem inequality must also be satisfied by the constitutive theories or be used in their derivations. If we decompose the total Cauchy stress tensor into equilibrium and deviatoric components, then Clausius–Duhem inequality and Helmholtz free-energy density can be used to determine the equilibrium stress in terms of thermodynamic pressure for compressible fluids and in terms of mechanical pressure for incompressible fluids, but the second law of thermodynamics provides no mechanism for deriving the constitutive theories for the deviatoric Cauchy stress tensor. In the development of the constitutive theories in Eulerian description, the covariant and contravariant convected coordinate systems and Jaumann measures are natural choices. Furthermore, the mathematical models for fluids require Eulerian description in which material point displacements are not measurable. This precludes the use of displacement gradients, i.e., strain measures, in the development of the constitutive theories. It is shown that compatible conjugate pairs of convected time derivatives of the deviatoric Cauchy stress and strain measures in co-, contravariant and Jaumann bases in conjunction with the theory of generators and invariants provide a general mathematical framework for the development of constitutive theories for ordered thermofluids in Eulerian description. This framework has a foundation based on the basic principles and axioms of continuum mechanics, but the resulting constitutive theories for the deviatoric Cauchy stress tensor must satisfy the condition of positive work expanded, a requirement resulting from the entropy inequality. The paper presents a general theory of constitutive equations for ordered thermoviscoelastic fluids which is then specialized to obtain commonly used constitutive equations for Maxwell, Giesekus and Oldroyd-B constitutive models in contra- and covariant bases and using Jaumann rates.
TL;DR: In this article, the thermodynamics of an electrically charged, multicomponent continuous medium with intrinsic rotation was analyzed in the presence of electromagnetic fields with a weak linear magnetoelectric coupling in the non-relativistic limit.
Abstract: The thermodynamics of an electrically charged, multicomponent continuous medium with intrinsic rotation is analysed in the presence of electromagnetic fields with a weak linear magnetoelectric coupling in the non-relativistic limit. Taking into account the chemical composition of the current densities and stress tensors yields scalar dissipation terms accounting for chemical reactivities and vectorial dissipation terms accounting for transport. Three equations characterising the continuous medium are derived: a thermostatic equilibrium equation, a reversible and an irreversible thermodynamic evolution equation. Explicit expressions for the temperature and the chemical potentials are derived in terms of the electromagnetic fields and the magnetoelectric coupling. The transport equations contain electromagnetic terms normally not included in a standard thermodynamic phenomenology.
TL;DR: In this paper, non-equilibrium electron transport in silicon nanowires has been tackled with a hydrodynamic model by taking the moments of the multisubband Boltzmann equation coupled to the Schrodinger-Poisson system.
Abstract: Non-equilibrium electron transport in silicon nanowires has been tackled with a hydrodynamic model This model has been formulated by taking the moments of the multisubband Boltzmann equation, coupled to the Schrodinger–Poisson system Closure relations are obtained by means of the maximum entropy principle (MEP) of extended thermodynamics, including scattering of electrons with acoustic and nonpolar optical phonons Simulation results for a quantum n+ − n − n+ silicon diode are shown
TL;DR: In this article, the covariance principle of differential geometry within a four-dimensional space-time ensures the validity of any equations and physical relations through any changes of frame of reference, due to the definition of the 4D space time and the use of 4D tensors, operations and operators.
Abstract: The covariance principle of differential geometry within a four-dimensional (4D) space-time ensures the validity of any equations and physical relations through any changes of frame of reference, due to the definition of the 4D space-time and the use of 4D tensors, operations and operators. This enables to separate covariance (i.e. frame-indifference) and material objectivity (i.e. material-indifference). We propose here a method to build a constitutive relation for thermo-elastic materials using such a 4D formalism. A 4D generalization of the classical variational approach is assumed leading to a model for a general thermo-elastic material. The isotropy of the relation can be ensured by the use of the invariants of variables, which offers new possibilities for the construction of constitutive relations. It is then possible to build a general frame-indifferent but not necessarily material-indifferent constitutive relation. It encompasses both the 3D Eulerian and Lagrangian thermo-elastic isotropic relations for finite transformations.
TL;DR: In this paper, a variational approach is proposed to study the response of a single-crystalline magnetic shape memory alloy (MSMA) sample subject to external forces and magnetic fields.
Abstract: In this paper, a variational approach is proposed to study the response of a single-crystalline magnetic shape memory alloy (MSMA) sample subject to external forces and magnetic fields. Especially, some criteria are derived to model the (quasi-static) movements of twin interfaces in the sample. By considering the compatibility condition, twin interfaces between two martensite variants are found to be flat planes with given normal vectors. To adopt the variational method, a total energy functional for the whole magneto-mechanical system is proposed. By calculating the variations of the total energy functional with respect to the independent variables, the equilibrium equations and the evolution laws for the internal variables can be derived. By further considering the variation of the total energy functional with respect to the variant distribution, some criteria for twin interface movements can be derived. The governing system of the current model is then formulated by composing the equilibrium equations, the evolution laws for the internal variables and the twin interface movement criteria. To show the validity of the governing system, some analytical results are constructed under certain simplified conditions, which can be used to simulate the magneto-mechanical response of the MSMA sample.
TL;DR: In this paper, a multi-axial elastic potential for incompressible, isotropic rubber-like materials was obtained directly from two one-dimensional elastic potentials for uniaxial case and simple shear case, in a sense of exactly matching finite strain data for four benchmark tests.
Abstract: With a novel approach based on certain logarithmic invariants, we demonstrate that a multi-axial elastic potential for incompressible, isotropic rubber-like materials may be obtained directly from two one-dimensional elastic potentials for uniaxial case and simple shear case, in a sense of exactly matching finite strain data for four benchmark tests, including uniaxial extension, simple shear, bi-axial extension, and plane-strain extension. As such, determination of multi-axial elastic potentials may be reduced to that of two one-dimensional elastic potentials. We further demonstrate that the latter two may be obtained by means of rational interpolating procedures for uniaxial data and shear data displaying strain-stiffening effects. Numerical examples are presented in fitting Treloar’s data and other data.
TL;DR: In this paper, a constitutive model for polycrystalline ice, which contains delayed-elastic and viscous deformations, and a damage variable is coupled to the delayedelastic deformation by a fiber bundle ansatz.
Abstract: We consider a constitutive model for polycrystalline ice, which contains delayed-elastic and viscous deformations, and a damage variable. The damage variable is coupled to the delayed-elastic deformation by a fiber bundle ansatz. We construct an isotropic theory, which can be calibrated with experimental data. Furthermore, we generalize the theory to a damage model in terms of rank-four tensors. This general model allows the evolution of anisotropic damage.
TL;DR: In this paper, the authors developed an elastic-viscoplastic, three-dimensional, finite-deformation constitutive model to describe the large deformation behavior of bulk metallic glass (BMG) composite.
Abstract: The focus of this study is the development of an elastic-viscoplastic, three-dimensional, finite-deformation constitutive model to describe the large deformation behavior of bulk metallic glass (BMG) composite. A macroscopic theoretical formulation is proposed based on thermodynamic considerations to describe the response at ambient temperature and pressure, as well as at different strain rates. A constitutive equation is derived using the principle of thermodynamics and the augmenting of free energy. This is done by assuming that deformation within the constituent phases of the composite is affine; kinetic equations defining plastic shear and evolution of free volume concentration are then derived. The constitutive model is subsequently implemented in a finite-element program (Abaqus/Explicit) via a user-defined material subroutine. Numerical predictions are compared with experimental results from tests on La-based in situ BMG composite (La–Al–Cu–Ni) specimens cast in-house; this demonstrates that the model is able to describe the material behavior observed.
TL;DR: In this paper, a material model which takes into account the internal structure of an adhesive is introduced, where an interphase zone is introduced to model the change in mechanical properties due to ageing.
Abstract: With the increasing number of requirements on joinings, it gets more and more important to understand and predict an assemblies properties. Nowadays, in industrial applications, combinations of different materials get more common. In most of those cases, it is, besides other advantages, useful to connect such parts with adhesives to avoid local cells. Thus, the knowledge about the mechanical behaviour of adhesives over the whole time of utilisation is an essential element of engineering. As it is well known, ageing due to environmental influences such as oxygen, radiation, ozone and others plays a major role in polymers properties. So, for the prediction of applicability over the whole lifetime of a technical component, the change in mechanical properties due to ageing is necessary. In this contribution, we introduce a material model which takes into account the internal structure of an adhesive. Therefore, an interphase zone is introduced. In the interphase, which is developed due to the contact of an adhesive with an adherent, the materials properties change continuously from the surface to the centre of the joint, where the polymer is in a bulky state. Built up on this geometry dependency, the materials ageing as a function of the position is described. To model the change of the polymers state, we use a parameter representing chain scission processes and another one for the reformation of a new network. In a last step, the model is transferred into a finite element code for exemplary calculations.
TL;DR: In this paper, a model for high temperature creep of single crystal superalloys is developed, which includes constitutive laws for nonlocal damage and viscoplasticity, based on a variational formulation, employing potentials for free energy and dissipation originating from plasticity and damage.
Abstract: A model for high temperature creep of single crystal superalloys is developed, which includes constitutive laws for nonlocal damage and viscoplasticity. It is based on a variational formulation, employing potentials for free energy, and dissipation originating from plasticity and damage. Evolution equations for plastic strain and damage variables are derived from the well-established minimum principle for the dissipation potential. The model is capable of describing the different stages of creep in a unified way. Plastic deformation in superalloys incorporates the evolution of dislocation densities of the different phases present. It results in a time dependence of the creep rate in primary and secondary creep. Tertiary creep is taken into account by introducing local and nonlocal damage. Herein, the nonlocal one is included in order to model strain localization as well as to remove mesh dependence of finite element calculations. Numerical results and comparisons with experimental data of the single crystal superalloy LEK94 are shown.
TL;DR: In this article, the authors used a continuous medium approach to model an ionic polyelectrolyte with two phases, where the deformable solid phase is the polymer backbone with fixed anions, and the electrolyte phase is made of a solvent (usually water) with free cations.
Abstract: Ionic electro-active polymer is an active material consisting in a polyelectrolyte (for example Nafion). Such material is usually used as thin film sandwiched between two platinum electrodes. The polymer undergoes large bending motions when an electric field is applied across the thickness. Conversely, a voltage can be detected between both electrodes when the polymer is suddenly bent. The solvent-saturated polymer is fully dissociated, releasing cations of small size. We used a continuous medium approach. The material is modelled by the coexistence of two phases; it can be considered as a porous medium where the deformable solid phase is the polymer backbone with fixed anions; the electrolyte phase is made of a solvent (usually water) with free cations. The microscale conservation laws of mass, linear momentum and energy and the Maxwell’s equations are first written for each phase. The physical quantities linked to the interfaces are deduced. The use of an average technique applied to the two-phase medium finally leads to an Eulerian formulation of the conservation laws of the complete material. Macroscale equations relative to each phase provide exchanges through the interfaces. An analysis of the balance equations of kinetic, potential and internal energy highlights the phenomena responsible of the conversion of one kind of energy into another, especially the dissipative ones : viscous frictions and Joule effect.
TL;DR: In this article, the combustion processes represented by steady deflagration or detonation waves are studied for a set of balance laws in the framework of Navier-Stokes reactive equations related to a diatomic recombination reaction.
Abstract: In the present paper, the combustion processes, represented by steady deflagration or detonation waves, are studied for a set of balance laws in the framework of Navier–Stokes reactive equations related to a diatomic recombination reaction. Moreover, a systematic analysis of the combustion solutions is carried out, investigating the influence of all the physical parameters present in the hydrodynamical equations: the Mach number of the gas mixture in the unburned state, the chemical link energy of the diatomic molecule and the activation energy of the reaction. Results are discussed according to several numerical experiments.
TL;DR: In this article, a new method of describing the liquid-gas phase transition is presented, based on a special form of the internal energy and a source term in the particle balance equation, which allows to model continua which have different specific heat capacities in liquid and in gas state.
Abstract: A new method of describing the liquid-gas phase transition is presented. It is assumed that the phase transition is characterized by a significant change of the particle density distribution as a result of energy supply at the boiling point that leads to structural changes but not to heating. Structural changes are described by an additional state characteristics of the system—the distribution density of the particles which is presented by an independent balance equation. The mathematical treatment is based on a special form of the internal energy and a source term in the particle balance equation. The presented method allows to model continua which have different specific heat capacities in liquid and in gas state.
TL;DR: In this article, the authors developed a capillary-driven two-phase flow model to examine the influences caused by different micro-grooves, fluids, temperatures, radiuses and widths of groove and concluded that triangular-micro-groove has better influence of the liquid front position than semicircular-micro groove.
Abstract: Solar energy provides significant opportunities to the power needs. The pipes with micro-grooves etched in the inner wall have been widely taken on the absorber receiver in the parabolic trough and cooling systems for solar thermal absorbers because this sort of pipes improves heat transfer. To support parabolic trough design in solar energy application systems, this study developed a capillary-driven two-phase flow model. The study further examines the influences caused by different micro-grooves, fluids, temperatures, radiuses and widths of groove. Our study concludes that (1) the triangular-microgroove has better influence of the liquid front position than semicircular-microgroove. (2) Water has better influence of liquid front position than ethanol and benzene. (3) The saturated temperature is indirectly proportional to the liquid front position. (4) The length of liquid front position is longer if value of radius is higher. (5) The width of groove does not significantly affect on the liquid front position and velocity. In addition, the proposed mathematical modeling is solved more correctly as compared to previous research. From our results, a good design of the micro-groove pipe can be achieved.
TL;DR: In this paper, an energetic framework for the study of the macroscopic evolution of shape memory alloys (SMA) with softening behavior is presented. But this framework is restricted to a class of standard rate-independent materials with an internal variable derived from the Drucker-Ilyushin work property.
Abstract: This paper presents an energetic framework for the study of the macroscopic evolution of shape memory alloys (SMA) with softening behavior. It is written for a class of standard rate-independent materials with an internal variable derived from the Drucker–Ilyushin work property. This one-dimensional model is defined by three material functions of the internal variable and one material parameter. The quasi-static evolution is formulated for a one-dimensional bar under traction and is based on two physical principles: a stability criterion which consists in selecting the local minima of the total energy and an energy balance condition which requires the absolute continuity of the total energy. The stability criterion aims to overcome the non-uniqueness issue associated with the intrinsic softening character of SMA while the energy balance condition accounts for evolutions even with possible time discontinuities. While being consistent with the classical Kuhn–Tucker formulation of the phase transformations, such energetic formulation proved to be more suitable than this latter for the study of stress-softening SMA. Both homogeneous and non-homogenous solutions are investigated with respect to this variational evolution problem. Specifically, we show the instability of the homogeneous states for softening materials and construct, in this latter case, a non-homogeneous stable evolution that follows a transformation stress line which corresponds to the Maxwell line of the softening intrinsic behavior.
TL;DR: In this article, a new version of rate-independent generalized plasticity, suitable for the derivation of general thermomechanical constitutive laws for materials undergoing phase transformations, is proposed within a finite deformation framework.
Abstract: A new version of rate-independent generalized plasticity, suitable for the derivation of general thermomechanical constitutive laws for materials undergoing phase transformations, is proposed within a finite deformation framework. More specifically, by assuming an additive decomposition of the finite strain tensor into elastic and inelastic (transformation induced) parts and by considering the fractions of the various material phases as internal variables, a multi-phase formulation of the theory is developed. The concepts presented are applied for the derivation of a three-dimensional thermomechanical model for shape memory alloy materials. The ability of the model in simulating several patterns of the extremely complex behavior of these materials, under both monotonic and cyclic loadings, is assessed by representative numerical examples.
TL;DR: In this paper, two new formulations of Maxwell's equations are provided that avoid the paradoxes of earlier formulations and thus describe the physics clearly and without self-contradiction, and demonstrate that the perplexity arises from a misunderstanding of the limitations of material frame descriptions, and the failure to appreciate the centrality of relativity theory to the formulation of electrodynamic equations in the vicinity of mechanical motion.
Abstract: Despite the importance of electromagnetomechanical physics to processes ranging from piezoelectricity to the dynamics of electron beams, confusion abounds in the continuum mechanics literature as to how Maxwell’s equations of electrodynamics should be formulated in the material frame of continuum mechanics. Current formulations in the literature conflict as to the manner in which the authors define fields, derive constitutive relations, and interpret contradictory formulations. The difficulties persist even when the phenomena described are electrostatic. This paper will demonstrate that the perplexity arises from two sources: a misunderstanding of the limitations of material frame descriptions, and the failure to appreciate the centrality of relativity theory to the formulation of electrodynamic equations in the vicinity of mechanical motion. Two new formulations of Maxwell’s equations are provided that avoid the paradoxes of earlier formulations and thus describe the physics clearly and without self-contradiction.