Abstract: 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

Abstract: 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

Abstract: 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

Abstract: 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

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

Abstract: 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

Abstract: 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

Abstract: 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

Abstract: 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

Abstract: 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

Abstract: 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

Abstract: 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

Abstract: 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

Abstract: 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

Abstract: 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

Abstract: 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

Abstract: 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

Abstract: Abstract
A semi-analytic solution for the elastic/plastic distribution of stress and strain in a spherical shell subject to pressure over its inner and outer radii and subsequent unloading is presented. The Bauschinger effect is taken into account. The flow theory of plasticity is adopted in conjunction with quite an arbitrary yield criterion and its associated flow rule. The yield stress is an arbitrary function of the equivalent strain. It is shown that the boundary value problem is significantly simplified if the equivalent strain is used as an independent variable instead of the radial coordinate. In particular, numerical methods are only necessary to evaluate ordinary integrals and solve simple transcendental equations. An illustrative example is provided to demonstrate the distribution of residual stresses and strains. PubDate: 2014-06-03

Abstract: Abstract
A model of linear, internally constrained shell with single, constant curvature is used to describe the behaviour of existing structures, such as barrel shells. A linear, elastic, isotropic material is considered. Observing that in the shell two families of mono-dimensional interacting beams can be recognized: straight longitudinal beams and transversal arches, a non-conventional semi-analytical approximate solution, which uses the method of separation of variables, is proposed. By using an integral procedure, reduced differential, ordinary equations, capable of describing the behaviour of the shell, are obtained. Both linear static behaviour and longitudinal buckling of the shell are investigated. The approximate solution proposed leads to results that match those of a finite element model and permits to give a description of shells similar to that of beams on elastic soil. With regard to the linear static behaviour of the shell, a “short” and a “long” characterization is proposed and original graphical abaci are obtained with the purpose of facilitating the classification. An extensive study is then performed in order to analyse the buckling of the shells. PubDate: 2014-06-01

Abstract: Abstract
The destabilization effect of damping on a class of general dynamical systems is discussed. The phenomenon of jump in the critical value of the bifurcation parameter, in passing from undamped to damped system, is view in a new perspective, according to which no discontinuities manifest themselves. By using asymptotic analysis, it is proved that all subcritically loaded undamped systems are candidate to become unstable, provided a suitable damping matrix is added. The mechanism of instability is explained by introducing the concept of modal dampings, as the components of the damping forces along the unit vectors of a non-orthogonal eigenvector basis. Such quantities can change sign while the load changes the eigenvectors of the basis, thus triggering instability. A paradigmatic, non-physical, minimal system has been built up, admitting closed-form solutions able to explain the essence of the destabilizing phenomenon. Series expansions carried out on the exact solution give information on how to deal more complex systems by perturbation methods. PubDate: 2014-05-25