Authors:Ioannis Tsagrakis; Elias C. Aifantis Pages: 1181 - 1194 Abstract: In the electrode materials of lithium ion batteries, the large variations of Li concentration during the charge and discharge processes are often accompanied by phase separations to lithium-rich and lithium-poor states. In particular, when the composition of the material moves into the spinodal region (linearly unstable uniform compositions) or into the miscibility gap (metastable uniform compositions), it tends to decompose spontaneously under composition fluctuations. If the lattice mismatch of the two phases is not negligible, coherency strains arise affecting the decomposition process. Furthermore, when the dimensions of a specimen or a grain reduce down to the nanometer level, the phase transition mechanisms are also substantially influenced by the domain size. This size effect is interpreted in the present article by developing a thermodynamically consistent model of gradient elastodiffusion. The proposed formulation is based on the coupling of the standard Cahn–Hilliard type of diffusion and a simple gradient elasticity model that includes the gradient of volumetric strain in the expression of the Helmholtz free energy density. An initial boundary value problem is derived in terms of concentration and displacement fields, and linear stability analysis is employed to determine the contribution of concentration and strain gradient terms on the instability leading to spinodal decomposition. It is shown that the theoretical predictions are in accordance with the experimental trends, i.e., the spinodal concentration range shrinks (i.e., the tendency for phase separation is reduced) as the crystal size decreases. Moreover, depending on the interplay between the strain and the concentration gradient coefficients, the spinodal region can be completely suppressed below a critical crystal size. Spinodal characteristic length and time are also evaluated by considering the dominant instability mode during the primary stages of the decomposition process, and it is found that they are increasing functions of the strain gradient coefficient. PubDate: 2017-11-01 DOI: 10.1007/s00161-017-0565-y Issue No:Vol. 29, No. 6 (2017)

Authors:Artur V. Dmitrenko Pages: 1197 - 1205 Abstract: The stochastic equations of continuum are used for determining the heat transfer coefficients. As a result, the formulas for Nusselt (Nu) number dependent on the turbulence intensity and scale instead of only on the Reynolds (Peclet) number are proposed for the classic flows of a nonisothermal fluid in a round smooth tube. It is shown that the new expressions for the classical heat transfer coefficient Nu, which depend only on the Reynolds number, should be obtained from these new general formulas if to use the well-known experimental data for the initial turbulence. It is found that the limitations of classical empirical and semiempirical formulas for heat transfer coefficients and their deviation from the experimental data depend on different parameters of initial fluctuations in the flow for different experiments in a wide range of Reynolds or Peclet numbers. Based on these new dependences, it is possible to explain that the differences between the experimental results for the fixed Reynolds or Peclet numbers are caused by the difference in values of flow fluctuations for each experiment instead of only due to the systematic error in the experiment processing. Accordingly, the obtained general dependences of Nu for a smooth round tube can serve as the basis for clarifying the experimental results and empirical formulas used for continuum flows in various power devices. Obtained results show that both for isothermal and for nonisothermal flows, the reason for the process of transition from a deterministic state into a turbulent one is determined by the physical law of equivalence of measures between them. Also the theory of stochastic equations and the law of equivalence of measures could determine mechanics which is basis in different phenomena of self-organization and chaos theory. PubDate: 2017-11-01 DOI: 10.1007/s00161-017-0566-x Issue No:Vol. 29, No. 6 (2017)

Authors:Fadi Aldakheel Pages: 1207 - 1217 Abstract: The coupled thermo-mechanical strain gradient plasticity theory that accounts for microstructure-based size effects is outlined within this work. It extends the recent work of Miehe et al. (Comput Methods Appl Mech Eng 268:704–734, 2014) to account for thermal effects at finite strains. From the computational viewpoint, the finite element design of the coupled problem is not straightforward and requires additional strategies due to the difficulties near the elastic–plastic boundaries. To simplify the finite element formulation, we extend it toward the micromorphic approach to gradient thermo-plasticity model in the logarithmic strain space. The key point is the introduction of dual local–global field variables via a penalty method, where only the global fields are restricted by boundary conditions. Hence, the problem of restricting the gradient variable to the plastic domain is relaxed, which makes the formulation very attractive for finite element implementation as discussed in Forest (J Eng Mech 135:117–131, 2009) and Miehe et al. (Philos Trans R Soc A Math Phys Eng Sci 374:20150170, 2016). PubDate: 2017-11-01 DOI: 10.1007/s00161-017-0571-0 Issue No:Vol. 29, No. 6 (2017)

Authors:Evgeniy Yu. Vitokhin; Elena A. Ivanova Pages: 1219 - 1240 Abstract: The Maxwell–Cattaneo heat conduction theory, the Lord–Shulman theory of thermoelasticity and a hyperbolic theory of thermoviscoelasticity are studied. The dispersion relations are analyzed in the case when a solution is represented in the form of an exponential function decreasing in time. Simple formulas that quite accurately approximate the dispersion curves are obtained. Based on the results of analysis of the dispersion relations, an experimental method of determination of the heat flux relaxation time is suggested. PubDate: 2017-11-01 DOI: 10.1007/s00161-017-0574-x Issue No:Vol. 29, No. 6 (2017)

Authors:Paolo Maria Mariano Pages: 1241 - 1248 Abstract: We show how a general description of microstructural changes in a macroscopically rigid conductor implies finite-speed propagation of temperature variations. In this way, we interpret once again Fourier’s paradox as a result of an insufficient representation of the structure of matter. The result is independent of the type of the material microstructure, provided that its changes are influenced by temperature variations. With the present treatment, we indicate a possible view on an old problem, already analyzed from different perspectives. PubDate: 2017-11-01 DOI: 10.1007/s00161-017-0577-7 Issue No:Vol. 29, No. 6 (2017)

Authors:K. S. Surana; A. D. Joy; J. N. Reddy Pages: 1249 - 1289 Abstract: This paper presents a non-classical continuum theory for fluent continua in which the conservation and balance laws are derived by incorporating both internal rotation rates arising from the velocity gradient tensor and the rotation rates of the Cosserats. Specifically, in this non-classical continuum theory we have (1) the usual velocities ( \(\bar{ \pmb {\varvec{v }}}\) ), (2) the three internal rotation rates ( \({}_i^t\bar{ \pmb {\varvec{\Theta }}}\) ) about the axes of a fixed triad whose axes are parallel to the x-frame arising from the velocity gradient tensor \((\bar{ \pmb {\varvec{L }}})\) that are completely defined by the antisymmetric part of the velocity gradient tensor, and (3) three additional rotation rates ( \({}_e^t\bar{ \pmb {\varvec{\Theta }}}\) ) about the axes of the same triad located at each material point as additional three unknown degrees of freedom, referred to as Cosserat rotation rates. This gives rise to \(\bar{ \pmb {\varvec{v }}}\) and \({}_e^t\bar{ \pmb {\varvec{\Theta }}}\) as six degrees of freedom at a material point. The internal rotation rates \({}_i^t\bar{ \pmb {\varvec{\Theta }}}\) , often neglected in classical fluid mechanics, exist in all deforming fluent continua as these are due to velocity gradient tensor. When the internal rotation rates \({}_i^t\bar{ \pmb {\varvec{\Theta }}}\) are resisted by deforming fluent continua, conjugate moment tensor arises that together with \({}_i^t\bar{ \pmb {\varvec{\Theta }}}\) may result in energy storage and/or dissipation, which must be considered in the conservation and balance laws. The Cosserat rotation rations \({}_e^t\bar{ \pmb {\varvec{\Theta }}}\) also result in conjugate moment tensor that together with \({}_e^t\bar{ \pmb {\varvec{\Theta }}}\) may also result in energy storage and/or dissipation. The main focus of this paper is a consistent derivation of conservation and balance laws for fluent continua that incorporate the aforementioned physics and associated constitutive theories for thermofluids using the conditions resulting from the entropy inequality. The material coefficients derived in the constitutive theories are clearly defined and discussed. PubDate: 2017-11-01 DOI: 10.1007/s00161-017-0579-5 Issue No:Vol. 29, No. 6 (2017)

Authors:Vamshi Krishna Chillara Pages: 1291 - 1311 Abstract: We develop a thermodynamic framework for modeling nonlinear ultrasonic damage sensing and prognosis in materials undergoing progressive damage. The framework is based on the internal variable approach and relies on the construction of a pseudo-elastic strain energy function that captures the energetics associated with the damage progression. The pseudo-elastic strain energy function is composed of two energy functions—one that describes how a material stores energy in an elastic fashion and the other describes how material dissipates energy or stores it in an inelastic fashion. Experimental motivation for the choice of the above two functionals is discussed and some specific choices pertaining to damage progression during fatigue and creep are presented. The thermodynamic framework is employed to model the nonlinear response of material undergoing stress relaxation and creep-like degradation. For each of the above cases, evolution of the nonlinearity parameter with damage as well as with macroscopic measurables like accumulated plastic strain is obtained. PubDate: 2017-11-01 DOI: 10.1007/s00161-017-0575-9 Issue No:Vol. 29, No. 6 (2017)

Authors:Sebastian Glane; Felix A. Reich; Wolfgang H. Müller Pages: 1313 - 1333 Abstract: This study is dedicated to continuum-scale material modeling of isotropic permanent magnets. An affine-linear extension to the commonly used ideal hard model for permanent magnets is proposed, motivated, and detailed. In order to demonstrate the differences between these models, bar and horseshoe magnets are considered. The structure of the boundary value problem for the magnetic field and related solution techniques are discussed. For the ideal model, closed-form analytical solutions were obtained for both geometries. Magnetic fields of the boundary value problems for both models and differently shaped magnets were computed numerically by using the boundary element method. The results show that the character of the magnetic field is strongly influenced by the model that is used. Furthermore, it can be observed that the shape of an affine-linear magnet influences the near-field significantly. Qualitative comparisons with experiments suggest that both the ideal and the affine-linear models are relevant in practice, depending on the magnetic material employed. Mathematically speaking, the ideal magnetic model is a special case of the affine-linear one. Therefore, in applications where knowledge of the near-field is important, the affine-linear model can yield more accurate results—depending on the magnetic material. PubDate: 2017-11-01 DOI: 10.1007/s00161-017-0578-6 Issue No:Vol. 29, No. 6 (2017)

Authors:L. F. R. Espath; A. F. Sarmiento; L. Dalcin; V. M. Calo Pages: 1335 - 1345 Abstract: We present the microbalance including the microforces, the first- and second-order microstresses for the Swift–Hohenberg equation concomitantly with their constitutive equations, which are consistent with the free-energy imbalance. We provide an explicit form for the microstress structure for a free-energy functional endowed with second-order spatial derivatives. Additionally, we generalize the Swift–Hohenberg theory via a proper constitutive process. Finally, we present one highly resolved three-dimensional numerical simulation to demonstrate the particular form of the resulting microstresses and their interactions in the evolution of the Swift–Hohenberg equation. PubDate: 2017-11-01 DOI: 10.1007/s00161-017-0581-y Issue No:Vol. 29, No. 6 (2017)

Authors:C. S. K. Raju; P. Sanjeevi; M. C. Raju; S. M. Ibrahim; G. Lorenzini; E. Lorenzini Pages: 1347 - 1363 Abstract: A theoretical analysis is performed for studying the flow and heat and mass transfer characteristics of Maxwell fluid over a cylinder with Cattaneo–Christov and non-uniform heat source/sink. The Brownian motion and thermophoresis parameters also considered into account. Numerical solutions are carried out by using Runge–Kutta-based shooting technique. The effects of various governing parameters on the flow and temperature profiles are demonstrated graphically. We also computed the friction factor coefficient, local Nusselt and Sherwood numbers for the permeable and impermeable flow over a cylinder cases. It is found that the rising values of Biot number, non-uniform heat source/sink and thermophoresis parameters reduce the rate of heat transfer. It is also found that the friction factor coefficient is high in impermeable flow over a cylinder case when compared with the permeable flow over a cylinder case. PubDate: 2017-11-01 DOI: 10.1007/s00161-017-0580-z Issue No:Vol. 29, No. 6 (2017)

Authors:Marin Marin; Andreas Öchsner Pages: 1365 - 1374 Abstract: This study is concerned with the mixed initial boundary value problem for a dipolar body in the context of the thermoelastic theory proposed by Green and Naghdi. For the solutions of this problem we prove a result of Hölder’s-type stability on the supply terms. We impose middle restrictions on the thermoelastic coefficients, which are common in continuum mechanics. For the same conditions we propose a continuous dependence result with regard to the initial data. PubDate: 2017-11-01 DOI: 10.1007/s00161-017-0585-7 Issue No:Vol. 29, No. 6 (2017)

Authors:Ivan Argatov; Alexei Iantchenko; Vitaly Kocherbitov Pages: 1375 - 1387 Abstract: A large amplitude oscillatory shear (LAOS) is considered in the strain-controlled regime, and the interrelation between the Fourier transform and the stress decomposition approaches is established. Several definitions of the generalized storage and loss moduli are examined in a unified conceptual scheme based on the Lissajous–Bowditch plots. An illustrative example of evaluating the generalized moduli from a LAOS flow is given. PubDate: 2017-11-01 DOI: 10.1007/s00161-017-0584-8 Issue No:Vol. 29, No. 6 (2017)

Authors:Habib Pouriayevali; Bai-Xiang Xu Pages: 1389 - 1412 Abstract: A comprehensive study on a finite-deformation gradient crystal-plasticity model which has been derived based on Gurtin’s framework (Int J Plast 24:702–725, 2008) is carried out here. This systematic investigation on the different roles of governing components of the model represents the strength of this framework in the prediction of a wide range of hardening behaviors as well as rate-dependent and scale-variation responses in a single crystal. The model is represented in the reference configuration for the purpose of numerical implementation and then implemented in the FEM software ABAQUS via a user-defined subroutine (UEL). Furthermore, a function of accumulation rates of dislocations is employed and viewed as a measure of formation of short-range interactions. Our simulation results reveal that the dissipative gradient strengthening can be identified as a source of isotropic-hardening behavior, which may represent the effect of irrecoverable work introduced by Gurtin and Ohno (J Mech Phys Solids 59:320–343, 2011). Here, the variation of size dependency at different magnitude of a rate-sensitivity parameter is also discussed. Moreover, an observation of effect of a distinctive feature in the model which explains the effect of distortion of crystal lattice in the reference configuration is reported in this study for the first time. In addition, plastic flows in predefined slip systems and expansion of accumulation of GNDs are distinctly observed in varying scales and under different loading conditions. PubDate: 2017-11-01 DOI: 10.1007/s00161-017-0589-3 Issue No:Vol. 29, No. 6 (2017)

Authors:C. S. K. Raju; K. R. Sekhar; S. M. Ibrahim; G. Lorenzini; G. Viswanatha Reddy; E. Lorenzini Pages: 1417 - 1417 PubDate: 2017-11-01 DOI: 10.1007/s00161-017-0576-8 Issue No:Vol. 29, No. 6 (2017)

Authors:Michal Beneš; Igor Pažanin Abstract: This paper reports an analytical investigation of non-isothermal fluid flow in a thin (or long) vertical pipe filled with porous medium via asymptotic analysis. We assume that the fluid inside the pipe is cooled (or heated) by the surrounding medium and that the flow is governed by the prescribed pressure drop between pipe’s ends. Starting from the dimensionless Darcy–Brinkman–Boussinesq system, we formally derive a macroscopic model describing the effective flow at small Brinkman–Darcy number. The asymptotic approximation is given by the explicit formulae for the velocity, pressure and temperature clearly acknowledging the effects of the cooling (heating) and porous structure. The theoretical error analysis is carried out to indicate the order of accuracy and to provide a rigorous justification of the effective model. PubDate: 2017-11-11 DOI: 10.1007/s00161-017-0603-9

Authors:Tijani A. Apalara Abstract: In this paper, we consider a linear thermoelastic Timoshenko system with memory effects where the thermoelastic coupling is acting on shear force under Neumann–Dirichlet–Dirichlet boundary conditions. The same system with fully Dirichlet boundary conditions was considered by Messaoudi and Fareh (Nonlinear Anal TMA 74(18):6895–6906, 2011, Acta Math Sci 33(1):23–40, 2013), but they obtained a general stability result which depends on the speeds of wave propagation. In our case, we obtained a general stability result irrespective of the wave speeds of the system. PubDate: 2017-11-10 DOI: 10.1007/s00161-017-0601-y

Authors:Sarah Welzenbach; Tim Fischer; Felix Meier; Ewald Werner; Sonun Ulan kyzy; Oliver Munz Abstract: In gas turbines, high combustion efficiency as well as operational safety are required. Thus, labyrinth seal systems with honeycomb liners are commonly used. In the case of rubbing events in the seal system, the components can be damaged due to cyclic thermal and mechanical loads. Temperature differences occurring at labyrinth seal fins during rubbing events can be determined by considering a single heat source acting periodically on the surface of a rotating cylinder. Existing literature analysing the temperature distribution on rotating cylindrical bodies due to a stationary heat source is reviewed. The temperature distribution on the circumference of a simplified labyrinth seal fin is calculated using an available and easy to implement analytical approach. A finite element model of the simplified labyrinth seal fin is created and the numerical results are compared to the analytical results. The temperature distributions calculated by the analytical and the numerical approaches coincide for low sliding velocities, while there are discrepancies of the calculated maximum temperatures for higher sliding velocities. The use of the analytical approach allows the conservative estimation of the maximum temperatures arising in labyrinth seal fins during rubbing events. At the same time, high calculation costs can be avoided. PubDate: 2017-11-02 DOI: 10.1007/s00161-017-0600-z