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 Continuum Mechanics and Thermodynamics   [SJR: 0.681]   [H-I: 29]   [5 followers]  Follow         Hybrid journal (It can contain Open Access articles)    ISSN (Print) 1432-0959 - ISSN (Online) 0935-1175    Published by Springer-Verlag  [2335 journals]
• Thermodynamical properties of triangular quantum wires: entropy, specific
heat, and internal energy
• Abstract: Abstract In the present work, thermodynamical properties of a GaAs quantum wire with equilateral triangle cross section are studied. First, the energy levels of the system are obtained by solving the Schrödinger equation. Second, the Tsallis formalism is applied to obtain entropy, internal energy, and specific heat of the system. We have found that the specific heat and entropy have certain physically meaningful values, which mean thermodynamic properties cannot take any continuous value, unlike classical thermodynamics in which they are considered as continuous quantities. Maximum of entropy increases with increasing the wire size. The specific heat is zero at special temperatures. Specific heat decreases with increasing temperature. There are several peaks in specific heat, and these are dependent on quantum wire size.
PubDate: 2016-07-01

• Quadratic and rate-independent limits for a large-deviations functional
• Abstract: Abstract We construct a stochastic model showing the relationship between noise, gradient flows and rate-independent systems. The model consists of a one-dimensional birth–death process on a lattice, with rates derived from Kramers’ law as an approximation of a Brownian motion on a wiggly energy landscape. Taking various limits, we show how to obtain a whole family of generalized gradient flows, ranging from quadratic to rate-independent ones, connected via ‘L log L’ gradient flows. This is achieved via Mosco-convergence of the renormalized large-deviations rate functional of the stochastic process.
PubDate: 2016-07-01

• A k – $${\varepsilon}$$ ε turbulence closure model of an
isothermal dry granular dense matter
• Abstract: Abstract The turbulent flow characteristics of an isothermal dry granular dense matter with incompressible grains are investigated by the proposed first-order k– $${\varepsilon}$$ turbulence closure model. Reynolds-filter process is applied to obtain the balance equations of the mean fields with two kinematic equations describing the time evolutions of the turbulent kinetic energy and dissipation. The first and second laws of thermodynamics are used to derive the equilibrium closure relations satisfying turbulence realizability conditions, with the dynamic responses postulated by a quasi-linear theory. The established closure model is applied to analyses of a gravity-driven stationary flow down an inclined moving plane. While the mean velocity decreases monotonically from its value on the moving plane toward the free surface, the mean porosity increases exponentially; the turbulent kinetic energy and dissipation evolve, respectively, from their minimum and maximum values on the plane toward their maximum and minimum values on the free surface. The evaluated mean velocity and porosity correspond to the experimental outcomes, while the turbulent dissipation distribution demonstrates a similarity to that of Newtonian fluids in turbulent shear flows. When compared to the zero-order model, the turbulent eddy evolution tends to enhance the transfer of the turbulent kinetic energy and plane shearing across the flow layer, resulting in more intensive turbulent fluctuation in the upper part of the flow. Solid boundary as energy source and sink of the turbulent kinetic energy becomes more apparent in the established first-order model.
PubDate: 2016-07-01

• Dissipative heating of elastomers: a new modelling approach based on
finite and coupled thermomechanics
• Abstract: Abstract Especially in the automotive industries, elastomers take an important role. They are used in different types of bearings, where they inhibit vibration propagation and thereby significantly enhance driving performance and comfort. That is why several models have already been developed to simulate the material’s mechanical response to stresses and strains. In many cases, these models are developed under isothermal conditions. Others include the temperature-dependent mechanical behaviour to represent lower stiffness’s for higher temperatures. In this contribution it is shown by some exemplary experiments that viscoelastic material heats up under dynamic deformations. Hence, the material’s properties change due to the influence of the temperature without changing the surrounding conditions. With some of these experiments, it is shown that a fully coupled material model is necessary to predict the behaviour of bearings under dynamic loads. The focus of this contribution lies on the modelling of the thermoviscoelastic behaviour of elastomers. In a first step, a twofold multiplicative split of the deformation gradient is performed to be able to describe both mechanical and thermal deformations. This concept introduces different configurations. The stress tensors existing on these configurations are used to formulate the stress power in the first law of thermodynamics which allows to simulate the material’s self-heating. To formulate the temperature dependency of the mechanical behaviour, the non-equilibrium part of the Helmholtz free energy function is formulated as a function of the temperature and the deformation history. With the introduced model, some FE calculations are carried out to show the model’s capability to represent the thermoviscoelastic behaviour including the coupling in both directions.
PubDate: 2016-07-01

• Improved bounds on the energy-minimizing strains in martensitic
polycrystals
• Abstract: Abstract This paper is concerned with the theoretical prediction of the energy-minimizing (or recoverable) strains in martensitic polycrystals, considering a nonlinear elasticity model of phase transformation at finite strains. The main results are some rigorous upper bounds on the set of energy-minimizing strains. Those bounds depend on the polycrystalline texture through the volume fractions of the different orientations. The simplest form of the bounds presented is obtained by combining recent results for single crystals with a homogenization approach proposed previously for martensitic polycrystals. However, the polycrystalline bound delivered by that procedure may fail to recover the monocrystalline bound in the homogeneous limit, as is demonstrated in this paper by considering an example related to tetragonal martensite. This motivates the development of a more detailed analysis, leading to improved polycrystalline bounds that are notably consistent with results for single crystals in the homogeneous limit. A two-orientation polycrystal of tetragonal martensite is studied as an illustration. In that case, analytical expressions of the upper bounds are derived and the results are compared with lower bounds obtained by considering laminate textures.
PubDate: 2016-07-01

• Constitutive equations for an electroactive polymer
• Abstract: Abstract Ionic electroactive polymers can be used as sensors or actuators. For this purpose, a thin film of polyelectrolyte is saturated with a solvent and sandwiched between two platinum electrodes. The solvent causes a complete dissociation of the polymer and the release of small cations. The application of an electric field across the thickness results in the bending of the strip and vice versa. The material is modeled by a two-phase continuous medium. The solid phase, constituted by the polymer backbone inlaid with anions, is depicted as a deformable porous media. The liquid phase is composed of the free cations and the solvent (usually water). We used a coarse grain model. The conservation laws of this system have been established in a previous work. The entropy balance law and the thermodynamic relations are first written for each phase and then for the complete material using a statistical average technique and the material derivative concept. One deduces the entropy production. Identifying generalized forces and fluxes provides the constitutive equations of the whole system: the stress–strain relations which satisfy a Kelvin–Voigt model, generalized Fourier’s and Darcy’s laws and the Nernst–Planck equation.
PubDate: 2016-07-01

• A thermomechanical model accounting for the behavior of shape memory
alloys in finite deformations
• Abstract: Abstract Shape memory alloys (SMA) comport an interesting behavior. They can undertake large strains and then recover their undeformed shape by heating. In this context, one of the aspects that challenged many researchers was the development of a mathematical model to predict the behavior of a known SMA under real-life conditions, or finite strain. This paper is aimed at working out a finite strain mathematical model for a Ni–Ti SMA, under the superelastic experiment conditions and under uniaxial mechanical loading, based on the Zaki–Moumni 3D mathematical model developed under the small perturbations assumption. Within the current article, a comparison between experimental findings and calculated results is also investigated. The proposed finite strain mathematical model shows good agreement with experimental data.
PubDate: 2016-07-01

• Closure conditions for non-equilibrium multi-component models
• Abstract: Abstract A class of non-equilibrium models for compressible multi-component fluids in multi-dimensions is investigated taking into account viscosity and heat conduction. These models are subject to the choice of interfacial pressures and interfacial velocity as well as relaxation terms for velocity, pressure, temperature and chemical potentials. Sufficient conditions are derived for these quantities that ensure meaningful physical properties such as a non-negative entropy production, thermodynamical stability, Galilean invariance and mathematical properties such as hyperbolicity, subcharacteristic property and existence of an entropy–entropy flux pair. For the relaxation of chemical potentials, a two-component and a three-component models for vapor–water and gas–water–vapor, respectively, are considered.
PubDate: 2016-07-01

• A numerical method for determining the strain rate intensity factor under
plane strain conditions
• Abstract: Abstract Using the classical model of rigid perfectly plastic solids, the strain rate intensity factor has been previously introduced as the coefficient of the leading singular term in a series expansion of the equivalent strain rate in the vicinity of maximum friction surfaces. Since then, many strain rate intensity factors have been determined by means of analytical and semi-analytical solutions. However, no attempt has been made to develop a numerical method for calculating the strain rate intensity factor. This paper presents such a method for planar flow. The method is based on the theory of characteristics. First, the strain rate intensity factor is derived in characteristic coordinates. Then, a standard numerical slip-line technique is supplemented with a procedure to calculate the strain rate intensity factor. The distribution of the strain rate intensity factor along the friction surface in compression of a layer between two parallel plates is determined. A high accuracy of this numerical solution for the strain rate intensity factor is confirmed by comparison with an analytic solution. It is shown that the distribution of the strain rate intensity factor is in general discontinuous.
PubDate: 2016-07-01

• Constitutive model for flake graphite cast iron automotive brake discs:
from macroscopic multiscale models to a 1D rheological description
• Abstract: Abstract One of the critical points of the thermomechanical fatigue design process is the correct description of the cyclic behavior of the material. This work focuses on the material of automotive brake discs, namely flake graphite cast iron. The specificity of this material is its asymmetric behavior under tensile and compressive loadings, which is due to the shape of graphite that acts as small cracks. Multiscale models inspired from the literature are first presented. They lead to a good description of the material behavior under cyclic loadings. An elastoviscoplastic constitutive model is then proposed in a one-dimensional setting in order to accurately describe cyclic tests from room temperature up to $${600^{\circ}{C}}$$ .
PubDate: 2016-07-01

• Transformation-induced plasticity in high-temperature shape memory alloys:
a one-dimensional continuum model
• Abstract: Abstract A constitutive model based on isotropic plasticity consideration is presented in this work to model the thermo-mechanical behavior of high-temperature shape memory alloys. In high-temperature shape memory alloys (HTSMAs), both martensitic transformation and rate-dependent plasticity (creep) occur simultaneously at high temperatures. Furthermore, transformation-induced plasticity is another deformation mechanism during martensitic transformation. All these phenomena are considered as dissipative processes to model the mechanical behavior of HTSMAs in this study. The constitutive model was implemented for one-dimensional cases, and the results have been compared with experimental data from thermal cycling test for actuator applications.
PubDate: 2016-07-01

• Microinertia and internal variables
• Abstract: Abstract The description of microinertia in micromorphic continua is discussed from the point of view of non-equilibrium thermodynamics. In the framework of dual internal variables, the microinertia stems from a thermodynamic equation of state related to the internal variable, which has the properties similar to mechanical momentum.
PubDate: 2016-07-01

• A thermo-mechanically coupled finite strain model considering inelastic
heat generation
• Abstract: Abstract The procedure for reuse of finite element method (FEM) programs for heat transfer and structure analysis to solve advanced thermo-mechanical problems is presented as powerful algorithm applicable for coupling of other physical fields (magnetic, fluid flow, etc.). In this case, nonlinear Block-Gauss–Seidel partitioned algorithm strongly couples the heat transfer and structural FEM programs by a component-based software engineering. Component template library provides possibility to exchange the data between the components which solve the corresponding subproblems. The structural component evaluates the dissipative energy induced by inelastic strain. The heat transfer component computes the temperature change due to the dissipation. The convergence is guaranteed by posing the global convergence criterion on the previously locally converged coupled variables. This enables reuse of software and allows the numerical simulation of thermo-sensitive problems.
PubDate: 2016-07-01

• On configurational weak phase transitions in graphene
• Abstract: Abstract We report a study on configurational weak phase transitions for a freestanding monolayer graphene. Firstly, we characterize weak transformation neighborhoods by suitably bounding the metric components. Then, we distinguish between structural and configurational phase changes and elaborate on the second class of them. We evaluate the irreducible invariant subspaces corresponding to these phase changes and lay down symmetry-breaking as well as symmetry-preserving stretches. In the reduced bifurcation diagram, symmetry-preserving stretches are related to a turning point with a change of stability but not of symmetry. Symmetry-breaking stretches are related to a first-order weak phase transition. We evaluate symmetry-breaking stretches as well as their generating cosets. The reduced bifurcation diagram consists of three transcritical bifurcating curves which are all unstable but can be stabilized producing a subcritical bifurcation. We, also, shortly comment on the hysteretical behavior that might appear in this case.
PubDate: 2016-07-01

• Homogenization of rectangular cross-section fibre-reinforced materials:
bending–torsion effects
• Abstract: Abstract We study the homogenization of an elastic material in contact with periodic parallel elastic rectangular cross-section fibres of higher rigidity. The interactions between the matrix and the fibres are described by a local adhesion contact law with interfacial adhesive stiffness parameter depending on the period. Assuming that the Lamé constants in the fibres and the stiffness parameter have appropriate orders of magnitude, we derive a class of energy functionals involving extension, flexure and torsion terms.
PubDate: 2016-07-01

• A microstructure continuum approach to electromagneto-elastic conductors
• Abstract: Abstract A micromorphic continuum model of a deformable electromagnetic conductor is established introducing microdensities of bound and free charges. The conductive part of electric current consists of contributions due to free charges and microdeformation. Beside the conservation of charge, we derive suitable evolution equations for electric multipoles which are exploited to obtain the macroscopic form of Maxwell’s equations. A constitutive model for electromagneto-elastic conductors is considered which allows for a natural characterization of perfect conductors independently on the form of the constitutive equation for the conduction current. A generalized Ohm’s law is also derived for not ideal conductors which accounts for relaxation effects. The consequences of the linearized Ohm’s law on the classic magnetic transport equation are shown.
PubDate: 2016-06-23

• Nonextensive thermodynamic relations based on the assumption of
temperature duality
• Abstract: Abstract The nonextensive thermodynamic relations are expressed under the assumption of temperature duality, endowing the “physical temperature” and the “Lagrange temperature” in different physical senses. Based on this assumption, two sets of parallel Legendre transform structures are given. One is called “physical” set, and the other is called “Lagrange” set. In these two formalisms, the thermodynamic quantities and the thermodynamic relations are both liked through the Tsallis factor. Application of the two sets of the thermodynamic relations to the self-gravitating system shows that the heat capacity defined in the classical thermodynamics has no relevance to the stability of the system. Instead, the newly defined heat capacity can determine the stability of the system.
PubDate: 2016-06-18

• Modeling and research of temperature distribution in surface layer of
titanium alloy workpiece during AEDG and conventional grinding
• Abstract: Abstract Titanium and its alloys are widely recognized as the hardly machinable materials, especially due to their relatively high hardness, low thermal conductivity and possible subcritical superplasticity. Then, a thorough control of the machining process parameters shall be maintained. In this paper, we have concentrated on the grinding of the Ti6Al4V titanium alloy using cBN (boron nitride) grinding wheel combined with the AEDG (abrasive electrodischarge grinding) process. The mathematical model we have dealt with has been based mainly on Jaeger model of the heat taking over between sliding bodies with substantial upgrades related to: estimation of the frictional heat generating based on friction forces distribution, spatial, not only planar, shape of the contact area, generated heat partition between different parties of the grinding process, heat transfer in the multilayered environment. The experimental verification of the theoretical predictions has been carried out. Fundamental difficulty in such a research is placing temperature probes sufficiently close to the ground surface with possibly low space devoted for probes due to the temperature field deformation with relation to the real conditions of grinding. The temperature field in the machined workpiece has been investigated using electronic data logging and DSP methods. Obtained results exhibit clearly that distribution of heat generation in the contact zone could be of the relatively complicated shape due to the external cooling and the very specific heat transfer and accumulation in the titanium workpiece surface layer.
PubDate: 2016-06-04

• Micropolar continuum in spatial description
• Abstract: Abstract Within the spatial description, it is customary to refer thermodynamic state quantities to an elementary volume fixed in space containing an ensemble of particles. During its evolution, the elementary volume is occupied by different particles, each having its own mass, tensor of inertia, angular and linear velocities. The aim of the present paper is to answer the question of how to determine the inertial and kinematic characteristics of the elementary volume. In order to model structural transformations due to the consolidation or defragmentation of particles or anisotropic changes, one should consider the fact that the tensor of inertia of the elementary volume may change. This means that an additional constitutive equation must be formulated. The paper suggests kinetic equations for the tensor of inertia of the elementary volume. It also discusses the specificity of the inelastic polar continuum description within the framework of the spatial description.
PubDate: 2016-06-01

• Viscoelasticity behavior for finite deformations, using a consistent
hypoelastic model based on Rivlin materials
• Abstract: Abstract When constructing viscoelastic models, rate-form relations appear naturally to relate strain and stress tensors. One has to ensure that these tensors and their rates are indifferent with respect to the change of observers and to the superposition with rigid body motions. Objective transports are commonly accepted to ensure this invariance. However, the large number of transport operators developed makes the choice often difficult for the user and may lead to physically inconsistent formulation of hypoelasticity. In this paper, a methodology based on the use of the Lie derivative is proposed to model consistent hypoelasticity as an equivalent incremental formulation of hyperelasticity. Both models are shown to be reversible and completely equivalent. Extension to viscoelasticity is then proposed from this consistent model by associating consistent hypoelastic models with viscous behavior. As an illustration, Mooney–Rivlin nonlinear elasticity is coupled with Newton viscosity and a Maxwell-like material is investigated. Numerical solutions are then presented to illustrate a viscoelastic material subjected to finite deformations for a large range of strain rates.
PubDate: 2016-05-24

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