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PHYSICS (537 journals)            First | 1 2 3 4 5 6 | Last

ECS Journal of Solid State Science and Technology     Full-text available via subscription  
Egyptian Journal of Remote Sensing and Space Science     Open Access   (Followers: 4)
EJNMMI Physics     Open Access  
Embedded Systems Letters, IEEE     Hybrid Journal   (Followers: 14)
Energy Procedia     Open Access   (Followers: 2)
Engineering Failure Analysis     Hybrid Journal   (Followers: 22)
Engineering Fracture Mechanics     Hybrid Journal   (Followers: 15)
Environmental Fluid Mechanics     Hybrid Journal   (Followers: 2)
EPJ Nonlinear Biomedical Physics     Open Access  
EPJ Quantum Technology     Open Access  
EPJ Techniques and Instrumentation     Full-text available via subscription  
EPJ Web of Conferences     Open Access  
European Journal of Physics     Full-text available via subscription   (Followers: 4)
European Journal of Physics Education     Open Access   (Followers: 5)
European Physical Journal - Applied Physics     Full-text available via subscription   (Followers: 4)
European Physical Journal C     Hybrid Journal  
Europhysics News     Open Access   (Followers: 1)
Experimental Mechanics     Hybrid Journal   (Followers: 14)
Experimental Methods in the Physical Sciences     Full-text available via subscription  
Experimental Techniques     Hybrid Journal   (Followers: 15)
Exploration Geophysics     Hybrid Journal   (Followers: 3)
Few-Body Systems     Hybrid Journal  
Fire and Materials     Hybrid Journal   (Followers: 4)
Flexible Services and Manufacturing Journal     Hybrid Journal   (Followers: 2)
Fluctuation and Noise Letters     Hybrid Journal   (Followers: 1)
Fluid Dynamics     Hybrid Journal   (Followers: 5)
Fortschritte der Physik/Progress of Physics     Hybrid Journal  
Frontiers in Physics     Open Access   (Followers: 2)
Frontiers of Materials Science     Hybrid Journal   (Followers: 4)
Frontiers of Physics     Hybrid Journal   (Followers: 1)
Fusion Engineering and Design     Hybrid Journal   (Followers: 2)
Geochemistry, Geophysics, Geosystems     Full-text available via subscription   (Followers: 21)
Geografiska Annaler, Series A: Physical Geography     Hybrid Journal   (Followers: 3)
Geophysical Research Letters     Full-text available via subscription   (Followers: 45)
Geoscience and Remote Sensing, IEEE Transactions on     Hybrid Journal   (Followers: 19)
Glass Physics and Chemistry     Hybrid Journal   (Followers: 1)
Granular Matter     Hybrid Journal   (Followers: 2)
Graphs and Combinatorics     Hybrid Journal   (Followers: 5)
Handbook of Geophysical Exploration: Seismic Exploration     Full-text available via subscription  
Handbook of Metal Physics     Full-text available via subscription  
Handbook of Surface Science     Full-text available via subscription   (Followers: 2)
Handbook of Thermal Analysis and Calorimetry     Full-text available via subscription  
Haptics, IEEE Transactions on     Hybrid Journal   (Followers: 4)
Heat Transfer - Asian Research     Hybrid Journal   (Followers: 6)
High Energy Density Physics     Hybrid Journal   (Followers: 1)
High Pressure Research: An International Journal     Hybrid Journal   (Followers: 1)
IEEE Journal of Quantum Electronics     Hybrid Journal   (Followers: 12)
IEEE Signal Processing Magazine     Full-text available via subscription   (Followers: 21)
IET Optoelectronics     Hybrid Journal   (Followers: 2)
Il Colle di Galileo     Open Access  
Indian Journal of Biochemistry and Biophysics (IJBB)     Open Access   (Followers: 4)
Indian Journal of Physics     Hybrid Journal   (Followers: 4)
Indian Journal of Pure & Applied Physics (IJPAP)     Open Access   (Followers: 8)
Indian Journal of Radio & Space Physics (IJRSP)     Open Access   (Followers: 4)
Industrial Electronics, IEEE Transactions on     Hybrid Journal   (Followers: 9)
Industry Applications, IEEE Transactions on     Hybrid Journal   (Followers: 5)
Infinite Dimensional Analysis, Quantum Probability and Related Topics     Hybrid Journal  
InfraMatics     Open Access  
Infrared Physics & Technology     Hybrid Journal  
Intelligent Transportation Systems Magazine, IEEE     Full-text available via subscription   (Followers: 1)
Intermetallics     Hybrid Journal   (Followers: 4)
International Applied Mechanics     Hybrid Journal   (Followers: 2)
International Geophysics     Full-text available via subscription   (Followers: 3)
International Journal for Computational Methods in Engineering Science and Mechanics     Hybrid Journal   (Followers: 8)
International Journal for Ion Mobility Spectrometry     Hybrid Journal   (Followers: 1)
International Journal for Simulation and Multidisciplinary Design Optimization     Full-text available via subscription   (Followers: 1)
International Journal of Abrasive Technology     Hybrid Journal   (Followers: 2)
International Journal of Aeroacoustics     Full-text available via subscription   (Followers: 6)
International Journal of Applied Electronics in Physics & Robotics     Open Access  
International Journal of Astronomy and Astrophysics     Open Access   (Followers: 3)
International Journal of Computational Materials Science and Surface Engineering     Hybrid Journal   (Followers: 7)
International Journal of Damage Mechanics     Hybrid Journal   (Followers: 5)
International Journal of Fatigue     Hybrid Journal   (Followers: 5)
International Journal of Fracture     Hybrid Journal   (Followers: 7)
International Journal of Geometric Methods in Modern Physics     Hybrid Journal   (Followers: 1)
International Journal of Geophysics     Open Access   (Followers: 3)
International Journal of Heat and Fluid Flow     Hybrid Journal   (Followers: 9)
International Journal of Low Radiation     Hybrid Journal  
International Journal of Low-Carbon Technologies     Open Access   (Followers: 1)
International Journal of Mass Spectrometry     Hybrid Journal   (Followers: 11)
International Journal of Material Forming     Hybrid Journal   (Followers: 2)
International Journal of Materials and Product Technology     Hybrid Journal   (Followers: 4)
International Journal of Mechanical Sciences     Hybrid Journal   (Followers: 5)
International Journal of Mechanics and Materials in Design     Hybrid Journal   (Followers: 5)
International Journal of Medical Physics, Clinical Engineering and Radiation Oncology     Open Access   (Followers: 4)
International Journal of Micro-Nano Scale Transport     Full-text available via subscription   (Followers: 2)
International Journal of Microstructure and Materials Properties     Hybrid Journal   (Followers: 7)
International Journal of Microwave Science and Technology     Open Access   (Followers: 2)
International Journal of Modeling, Simulation, and Scientific Computing     Hybrid Journal   (Followers: 1)
International Journal of Modern Physics A     Hybrid Journal   (Followers: 1)
International Journal of Modern Physics B     Hybrid Journal  
International Journal of Modern Physics C     Hybrid Journal  
International Journal of Modern Physics D     Hybrid Journal  
International Journal of Modern Physics E     Hybrid Journal   (Followers: 1)
International Journal of Nanomanufacturing     Hybrid Journal   (Followers: 1)
International Journal of Nanoscience     Hybrid Journal   (Followers: 1)
International Journal of Nanotechnology     Hybrid Journal   (Followers: 5)
International Journal of Non-Linear Mechanics     Hybrid Journal   (Followers: 4)
International Journal of Physical Sciences     Open Access  
International Journal of PIXE     Hybrid Journal   (Followers: 1)

  First | 1 2 3 4 5 6 | Last

Journal Cover Continuum Mechanics and Thermodynamics
   [5 followers]  Follow    
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
     ISSN (Print) 1432-0959 - ISSN (Online) 0935-1175
     Published by Springer-Verlag Homepage  [2210 journals]   [SJR: 0.749]   [H-I: 26]
  • Modeling thermally induced martensitic transformations in nickel titanium
           shape memory alloys
    • Abstract: During stress-free thermal analysis with differential scanning calorimetry (DSC), nickel titanium (NiTi) shape memory alloys show a thermal hysteresis which is affected by cooling/heating rates. Moreover, the Ni content of near equiatomic alloys governs the phase transition temperatures. This contribution aims at establishing a constitutive equation which can account for these effects, building on earlier work by Müller, Achenbach and Seelecke (MAS). To be specific, we discuss our new method with a focus on NiTi alloys. As in the original MAS model, our approach is rooted in a non-convex free energy representation and rate equations are utilized to incorporate history dependence during non-equilibrium processes. The relaxation times of these rate equations are determined by characteristic transformation probabilities which in turn are governed by the free energy landscape of our system. We show how the model can be parameterized to rationalize experimental DSC data observed for NiTi samples of variable composition and measured at variable cooling/heating rates. The good agreement between model predictions and experimental results suggests that thermal hystereses are not only related to interfacial strain energy effects but also affected by the transient character of the transformation process incorporating specific thermal relaxation times. Our analysis shows that we observe strong hysteretic effects when the cooling/heating rates exceed these characteristic relaxation rates.
      PubDate: 2014-08-15
  • Some research perspectives in galloping phenomena: critical conditions and
           post-critical behavior
    • Abstract: This paper gives an overview of wind-induced galloping phenomena, describing its manifold features and the many advances that have taken place in this field. Starting from a quasi-steady model of aeroelastic forces exerted by the wind on a rigid cylinder with three degree-of-freedom, two translations and a rotation in the plane of the model cross section, the fluid–structure interaction forces are described in simple terms, yet suitable with complexity of mechanical systems, both in the linear and in the nonlinear field, thus allowing investigation of a wide range of structural typologies and their dynamic behavior. The paper is driven by some key concerns. A great effort is made in underlying strengths and weaknesses of the classic quasi-steady theory as well as of the simplistic assumptions that are introduced in order to investigate such complex phenomena through simple engineering models. A second aspect, which is crucial to the authors’ approach, is to take into account and harmonize the engineering, physical and mathematical perspectives in an interdisciplinary way—something which does not happen often. The authors underline that the quasi-steady approach is an irreplaceable tool, tough approximate and simple, for performing engineering analyses; at the same time, the study of this phenomenon gives origin to numerous problems that make the application of high-level mathematical solutions particularly attractive. Finally, the paper discusses a wide range of features of the galloping theory and its practical use which deserve further attention and refinements, pointing to the great potential represented by new fields of application and advanced analysis tools.
      PubDate: 2014-08-14
  • Contact problems for a finitely deformed incompressible elastic halfspace
    • Abstract: This paper examines the class of problems related to the interaction between a finitely deformed incompressible elastic halfspace and contacting elements that include smooth, flat rigid indenters with elliptical and circular shapes and a thick plate of infinite extent. The contact between the finitely deformed elastic halfspace and the contacting elements is assumed to be bilateral. The interaction between both the rigid circular indenter and the finitely deformed halfspace is induced by a Mindlin force that acts at the interior of the halfspace regions and by exterior loads. Similar considerations apply for the contact between the flexible plate of infinite extent and the finitely deformed elastic halfspace. The theory of small deformations superposed on large deformations proposed by Green et al. (Proc R Soc Ser A 211:128–155, 1952) is used as the basis for the formulation of the problem, and results of potential theory and integral transform techniques are used to develop the analytical results. In particular, explicit results are presented for the displacement of the rigid elliptical indenter and the maximum deflection of the flexible plate induced by the Mindlin forces, when the finitely deformed halfspace region has a strain energy function of the Mooney–Rivlin form.
      PubDate: 2014-08-10
  • Gibbs free energy and integrability of continuum models for granular media
           at equilibrium
    • Abstract: In this letter, we address the problem of the integrability of a continuum model for granular media at equilibrium. By the means of a formal integrability analysis, we show that the equilibrium limit of such models can be cast into a gradient equation with zero right-hand side. In turn, this implies that the model of interest is inherently Frobenius integrable, in the absence of additional compatibility conditions. Moreover, the quantity inside the gradient is identified with the granular material’s Gibbs free energy. Consequently, the integrability for the model at hand is equivalent to setting the Gibbs free energy of the granular material constant throughout the domain. In other words, integrability is equivalent to the definition of equilibrium employed in statistical physics.
      PubDate: 2014-07-26
  • Group classification of one-dimensional nonisentropic equations of fluids
           with internal inertia II. General case
    • Abstract: The previous paper by the authors (Siriwat and Meleshko in Contin Mech Thermodyn 24:115–148, 2012) was devoted to group analysis of one-dimensional nonisentropic equations of fluids with internal inertia. A direct approach was employed for finding the admitted Lie group. This approach allowed to perform a partial group classification of the considered equations with respect to a potential function. The present paper completes this group classification by an efficient algebraic method.
      PubDate: 2014-07-25
  • State internal variables at different scales for the modeling of the
           behavior of granular materials
    • Abstract: The main difficulty in modeling the behavior of a granular material arises from the discrete nature of this material. The precision of the description of phenomena requires complex developments able to trace important changes within the material throughout complex loadings. The works by Darve have tried to answer this question and have provided valuable results. Nevertheless, constitutive models still encounter difficulties in providing a correct prediction of the behavior in any case because the state variables of the models are not actual measurements of the internal state of the material. Scaling may help to bridge the gap between the behavior at the sample scale and local phenomena. Studies performed at the scale of the contact between grains and the scale of several grains, the so-called meso-scale, have provided interesting results to understand how the internal structure evolves throughout a loading and what local variables are, either geometrical or static, capable of explaining phenomena at the sample scale.
      PubDate: 2014-07-22
  • A numerical study of the heat transfer through a rarefied gas confined in
           a microcavity
    • Abstract: Flow and heat transfer in a bottom-heated square cavity in a moderately rarefied gas is investigated using the R13 equations and the Navier–Stokes–Fourier equations. The results obtained are compared with those from the direct simulation Monte Carlo (DSMC) method with emphasis on understanding thermal flow characteristics from the slip flow to the early transition regime. The R13 theory gives satisfying results—including flow patterns in fair agreement with DSMC—in the transition regime, which the conventional Navier–Stokes–Fourier equations are not able to capture.
      PubDate: 2014-07-18
  • Fabric and connectivity as field descriptors for deformations in granular
    • Abstract: Granular materials involve microphysics across the various scales giving rise to distinct behaviours of geomaterials, such as steady states, plastic limit states, non-associativity of plastic and yield flow, as well as instability of homogeneous deformations through strain localization. Incorporating such micro-scale characteristics is one of the biggest challenges in the constitutive modelling of granular materials, especially when micro-variables may be interdependent. With this motivation, we use two micro-variables such as coordination number and fabric anisotropy computed from tessellation of the granular material to describe its state at the macroscopic level. In order to capture functional dependencies between micro-variables, the correlation between coordination number and fabric anisotropy limits is herein formulated at the particle level rather than on an average sense. This is the essence of the proposed work which investigates the evolutions of coordination number distribution (connectivity) and anisotropy (contact normal) distribution curves with deformation history and their inter-dependencies through discrete element modelling in two dimensions. These results enter as probability distribution functions into homogenization expressions during upscaling to a continuum constitutive model using tessellation as an abstract representation of the granular system. The end product is a micro-mechanically inspired continuum model with both coordination number and fabric anisotropy as underlying micro-variables incorporated into a plasticity flow rule. The derived plastic potential bears striking resemblance to cam–clay or stress–dilatancy-type yield surfaces used in soil mechanics.
      PubDate: 2014-07-15
  • Nonlinear vibrations of non-uniform beams by the MTS asymptotic expansion
    • Abstract: The frequency response curves of a non-uniform beam undergoing nonlinear oscillations are determined analytically by the multiple time scale method, which provides approximate, but accurate results. The axial inertia in neglected, and so the equations of motion are statically condensed on the transversal displacement only. The nonlinearity due to the stretching of the axis of the beam is considered. The effects of variable cross-section, of variable material properties and of the distributed axial loading are taken into account in the formulation. They have been illustrated by means of two examples and are also compared with existing results. The main result of this work is that the effects of any type of non-uniformity can be detected by simple formulas.
      PubDate: 2014-07-03
  • Analysis of steady combustion processes in a 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.
      PubDate: 2014-07-01
  • Analysis of the wave propagation processes in heat transfer problems of
           the hyperbolic type
    • 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.
      PubDate: 2014-07-01
  • Relevance of the time–quasi-polynomials in the classic linear
           thermodynamic theory of coupled transport processes
    • Abstract: A general description of the basic system of ordinary differential equations of coupled transport processes is given within framework of a linear approximation and treated by tools of matrix analysis and group representation theory. It is shown that the technique of hyperdyads directly generalizes the method of simple dyadic decomposition of operators used earlier in the classical linear irreversible thermodynamics and leads to possible new applications of the concept of quasi-polynomials at descriptions of coupled transport processes.
      PubDate: 2014-07-01
  • A model for high temperature creep of single crystal superalloys based on
           nonlocal damage and viscoplastic material behavior
    • 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.
      PubDate: 2014-07-01
  • On the modeling of equilibrium twin interfaces in a single-crystalline
           magnetic shape memory alloy sample. I: theoretical formulation
    • 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.
      PubDate: 2014-07-01
  • Capillary-driven flow analysis of a micro-grooved pipe
    • 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.
      PubDate: 2014-07-01
  • Conservation laws of an electro-active polymer
    • 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.
      PubDate: 2014-07-01
  • Unsteady heat and mass transfer in a rotating nanofluid layer
    • 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.
      PubDate: 2014-07-01
  • Bubbles in liquids with phase transition—part 2: on balance laws for
           mixture theories of disperse vapor bubbles in liquid with phase change
    • Abstract: We study averaging methods for the derivation of mixture equations for disperse vapor bubbles in liquids. The carrier liquid is modeled as a continuum, whereas simplified assumptions are made for the disperse bubble phase. An approach due to Petrov and Voinov is extended to derive mixture equations for the case that there is a phase transition between the carrier liquid and the vapor bubbles in water. We end up with a system of balance laws for a multi-phase mixture, which is completely in divergence form. Additional non-differential source terms describe the exchange of mass, momentum and energy between the phases. The sources depend explicitly on evolution laws for the total mass, the radius and the temperature of single bubbles. These evolution laws are derived in a prior article (Dreyer et al. in Cont Mech Thermodyn. doi:10.1007/s00161-0225-6, 2011) and are used to close the system. Finally, numerical examples are presented.
      PubDate: 2014-07-01
  • New trends and perspectives in nonlinear intracellular dynamics: one
           century from Michaelis–Menten paper
    • Abstract: One century after the seminal work by Leonor Michaelis and Maud Menten devoted to the theoretical study of the enzymatic reactions, in this paper, we give an overview of the most recent trends concerning the mathematical modeling of several enzymatic mechanisms, focusing on its asymptotic analysis, which needs the use of advanced mathematical tools, such as center manifold theory, normal forms, and bifurcation theory. Moreover, we present some perspectives, linking the models here presented with similar models, arising from different research fields.
      PubDate: 2014-06-28
  • Ordered rate constitutive theories for thermoviscoelastic solids without
           memory in Lagrangian description using Gibbs potential
    • Abstract: The paper presents rate constitutive theories for finite deformation of homogeneous, isotropic, compressible, and incompressible thermoviscoelastic solids without memory in Lagrangian description derived using the second law of thermodynamics expressed in terms of Gibbs potential Ψ. To ensure thermodynamic equilibrium during evolution, the rate constitutive theories must be derived using entropy inequality [as other three conservation and balance laws are do not provide a mechanism for deriving constitutive theories for the deforming matter (Surana in Advanced mechanics of continuua. in preparation, 2014)]. The two forms of the entropy inequality in Ψ derived using conjugate pairs \({\mathbf{\sigma}^*}\) , \({[\dot{J}]}\) : first Piola–Kirchhoff stress tensor and material derivative of the Jacobian of deformation and \({\mathbf{\sigma}^{[0]}}\) , \({\dot{\mathbf{\varepsilon}}_{[0]}}\) ; second Piola–Kirchhoff stress tensor and material derivative of Green’s strain tensor are precisely equivalent as the conjugate pairs \({\mathbf{\sigma}^*}\) , \({[\dot{J}]}\) and \({\mathbf{\sigma}^{[0]}}\) , \({\dot{\mathbf{\varepsilon}}_{[0]}}\) are transformable from each other. In the present work, we use \({\mathbf{\sigma}^{[0]}}\) , \({\dot{\mathbf{\varepsilon}}_{[0]}}\) as conjugate pair. Two possible choices of dependent variables in the constitutive theories: Ψ, η, \({\mathbf{\sigma}^{[0]}}\) , \({\mathbf{q}}\) and Ψ, η, \({\mathbf{\varepsilon}_{[0]}}\) , \({\mathbf{q}}\) (in which η is entropy density and \({\mathbf{q}}\) is heat vector) are explored based on conservation and balance laws. It is shown that the choice of Ψ, η, \({\mathbf{\varepsilon}_{[0]}}\) , \({\mathbf{q}}\) is essential when the entropy inequality is expressed in terms of Ψ. The arguments of these dependent variables are decided based on desired physics. Viscoelastic behavior requires considerations of at least \({\mathbf{\varepsilon}_{[0]}}\) and \({\dot{\mathbf{\varepsilon}}_{[0]}}\) (or \({\mathbf{\varepsilon}_{[1]}}\) ) in the constitutive theories. We generalize and consider strain rates \({\mathbf{\varepsilon}_{[i]}}\) ; i = 0, 1, …, n−1 as arguments of the dependent variables in the derivations of the ordered rate theories of up to orders n. At the onset, \({\mathbf{\sigma}^{[0]}}\) , ...
      PubDate: 2014-06-08
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