Authors:C. S. K. Raju; K. R. Sekhar; S. M. Ibrahim; G. Lorenzini; G. Viswanatha Reddy; E. Lorenzini Pages: 699 - 713 Abstract: In this study, we proposed a theoretical investigation on the temperature-dependent viscosity effect on magnetohydrodynamic dissipative nanofluid over a truncated cone with heat source/sink. The involving set of nonlinear partial differential equations is transforming to set of nonlinear ordinary differential equations by using self-similarity solutions. The transformed governing equations are solved numerically using Runge–Kutta-based Newton’s technique. The effects of various dimensionless parameters on the skin friction coefficient and the local Nusselt number profiles are discussed and presented with the support of graphs. We also obtained the validation of the current solutions with existing solution under some special cases. The water-based titanium alloy has a lesser friction factor coefficient as compared with kerosene-based titanium alloy, whereas the rate of heat transfer is higher in water-based titanium alloy compared with kerosene-based titanium alloy. From this we can highlight that depending on the industrial needs cooling/heating chooses the water- or kerosene-based titanium alloys. PubDate: 2017-05-01 DOI: 10.1007/s00161-016-0552-8 Issue No:Vol. 29, No. 3 (2017)

Authors:Valeriy A. Ryabov Pages: 715 - 729 Abstract: Theory of particle and continuous mechanics is developed which allows a treatment of pure deformation in terms of the set of variables “coordinate-momentum–force” instead of the standard treatment in terms of tensor-valued variables “strain–stress.” This approach is quite natural for a microscopic description of atomic system, according to which only pointwise forces caused by the stress act to atoms making a body deform. The new concept starts from affine transformation of spatial to material coordinates in terms of the stretch tensor or its analogs. Thus, three principal stretches and three angles related to their orientation form a set of six scalar variables to describe deformation. Instead of volume-dependent potential used in the standard theory, which requires conditions of equilibrium for surface and body forces acting to a volume element, a potential dependent on scalar variables is introduced. A consistent introduction of generalized force associated with this potential becomes possible if a deformed body is considered to be confined on the surface of torus having six genuine dimensions. Strain, constitutive equations and other fundamental laws of the continuum and particle mechanics may be neatly rewritten in terms of scalar variables. Giving a new presentation for finite deformation new approach provides a full treatment of hyperelasticity including anisotropic case. Derived equations of motion generate a new kind of thermodynamical ensemble in terms of constant tension forces. In this ensemble, six internal deformation forces proportional to the components of Irving–Kirkwood stress are controlled by applied external forces. In thermodynamical limit, instead of the pressure and volume as state variables, this ensemble employs deformation force measured in kelvin unit and stretch ratio. PubDate: 2017-05-01 DOI: 10.1007/s00161-017-0555-0 Issue No:Vol. 29, No. 3 (2017)

Authors:Wenjun Liu; Miaomiao Chen Pages: 731 - 746 Abstract: In this paper, we study the well-posedness and exponential decay for the porous thermoelastic system with the heat conduction given by Cattaneo’s law and a time-varying delay term, the coefficient of which is not necessarily positive. Using the semigroup arguments and variable norm technique of Kato, we first prove that the system is well-posed under a certain condition on the weight of the delay term, the weight of the elastic damping term and the speed of the delay function. By introducing a suitable energy and an appropriate Lyapunov functional, we then establish an exponential decay rate result. PubDate: 2017-05-01 DOI: 10.1007/s00161-017-0556-z Issue No:Vol. 29, No. 3 (2017)

Authors:Q. Yang; Q. C. Lv; Y. R. Liu Pages: 747 - 756 Abstract: This paper is concerned with Hamilton’s principle for inelastic bodies with conservative external forces. Inelasticity is described by internal variable theory by Rice (J Mech Phys Solids 19:433–455, 1971), and the influence of strain change on the temperature field is ignored. Unlike Hamilton’s principle for elastic bodies which has an explicit Lagrangian, Hamilton’s principle for inelastic bodies generally has no an explicit Lagrangian. Based on the entropy inequality, a quasi Hamilton’s principle for inelastic bodies is established in the form of inequality and with an explicit Lagrangian, which is just the Lagrangian for elastic bodies by replacing the strain energy with free energy. The quasi Hamilton’s principle for inelastic bodies states that the actual motion is distinguished by making the action an maximum. The evolution equations of internal variables can not be recovered from the quasi Hamilton’s principle. PubDate: 2017-05-01 DOI: 10.1007/s00161-017-0557-y Issue No:Vol. 29, No. 3 (2017)

Authors:Hans-Dieter Alber Pages: 757 - 803 Abstract: We study how the propagation speed of interfaces in the Allen–Cahn phase field model for phase transformations in solids consisting of the elasticity equations and the Allen–Cahn equation depends on two parameters of the model. The two parameters control the interface energy and the interface width, but change also the interface speed. To this end, we derive an asymptotic expansion of second order for the interface speed, called the kinetic relation, and prove that it is uniformly valid in both parameters. As a consequence, we show that the model error is proportional to the interface width divided by the interface energy. We conclude that simulations of interfaces with low interface energy based on this model require a very small interface width, implying a large numerical effort. Effective simulations thus need adaptive mesh refinement or other advanced techniques. PubDate: 2017-05-01 DOI: 10.1007/s00161-017-0558-x Issue No:Vol. 29, No. 3 (2017)

Authors:Evgeniy Yu. Vitokhin; Elena A. Ivanova 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: 2017-05-20 DOI: 10.1007/s00161-017-0574-x

Authors:Leif Kari Abstract: The dynamic stiffness of a chemically and physically ageing rubber vibration isolator in the audible frequency range is modelled as a function of ageing temperature, ageing time, actual temperature, time, frequency and isolator dimension. In particular, the dynamic stiffness for an axially symmetric, homogeneously aged rubber vibration isolator is derived by waveguides where the eigenmodes given by the dispersion relation for an infinite cylinder satisfying traction free radial surface boundary condition are matched to satisfy the displacement boundary conditions at the lateral surface ends of the finite rubber cylinder. The constitutive equations are derived in a companion paper (Part 1). The dynamic stiffness is calculated over the whole audible frequency range 20–20,000 Hz at several physical ageing times for a temperature history starting at thermodynamic equilibrium at \(+25\,^{\circ }\hbox {C}\) and exposed by a sudden temperature step down to \(-60\,^{\circ }\hbox {C}\) and at several chemical ageing times at temperature \(+25\,^{\circ }\hbox {C}\) with simultaneous molecular network scission and reformation. The dynamic stiffness results are displaying a strong frequency dependence at a short physical ageing time, showing stiffness magnitude peaks and troughs, and a strong physical ageing time dependence, showing a large stiffness magnitude increase with the increased physical ageing time, while the peaks and troughs are smoothed out. Likewise, stiffness magnitude peaks and troughs are frequency-shifted with increased chemical ageing time. The developed model is possible to apply for dynamic stiffness prediction of rubber vibration isolator over a broad audible frequency range under realistic environmental condition of chemical ageing, mainly attributed to oxygen exposure from outside and of physical ageing, primarily perceived at low-temperature steps. PubDate: 2017-05-16 DOI: 10.1007/s00161-017-0573-y

Authors:Thomas Glanowski; Vincent Le Saux; Cédric Doudard; Yann Marco; Clément Champy; Pierre Charrier Abstract: A methodology is proposed to define an equivalent geometry allowing the use of an uncoupled algorithm to solve thermomechanical problems when cyclic large strain occurs. This methodology is set up on the case of a simple bar and is then challenged on a structural sample for cyclic loadings. It is shown that the definition of the equivalent geometry is dependent on the thermal boundary conditions, which are usually unknowns of the thermal problem. The proposed approach is finally applied to the identification of cyclic dissipation from infrared thermography measurements. PubDate: 2017-05-16 DOI: 10.1007/s00161-017-0572-z

Authors:Leif Kari Abstract: The constitutive equations of chemically and physically ageing rubber in the audible frequency range are modelled as a function of ageing temperature, ageing time, actual temperature, time and frequency. The constitutive equations are derived by assuming nearly incompressible material with elastic spherical response and viscoelastic deviatoric response, using Mittag-Leffler relaxation function of fractional derivative type, the main advantage being the minimum material parameters needed to successfully fit experimental data over a broad frequency range. The material is furthermore assumed essentially entropic and thermo-mechanically simple while using a modified William–Landel–Ferry shift function to take into account temperature dependence and physical ageing, with fractional free volume evolution modelled by a nonlinear, fractional differential equation with relaxation time identical to that of the stress response and related to the fractional free volume by Doolittle equation. Physical ageing is a reversible ageing process, including trapping and freeing of polymer chain ends, polymer chain reorganizations and free volume changes. In contrast, chemical ageing is an irreversible process, mainly attributed to oxygen reaction with polymer network either damaging the network by scission or reformation of new polymer links. The chemical ageing is modelled by inner variables that are determined by inner fractional evolution equations. Finally, the model parameters are fitted to measurements results of natural rubber over a broad audible frequency range, and various parameter studies are performed including comparison with results obtained by ordinary, non-fractional ageing evolution differential equations. PubDate: 2017-05-09 DOI: 10.1007/s00161-017-0569-7

Authors:Artur V. Dmitrenko 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: 2017-05-06 DOI: 10.1007/s00161-017-0566-x

Authors:Fadi Aldakheel 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: 2017-05-06 DOI: 10.1007/s00161-017-0571-0

Authors:A. Herzig; L. Sekerakova; M. Johlitz; A. Lion Abstract: The influence of oxygen on elastomers, known as oxidation, is one of the most important ageing processes and becomes more and more important for nowadays applications. The interaction with thermal effects as well as antioxidants makes oxidation of polymers a complex process. Based on the polymer chosen and environmental conditions, the ageing processes may behave completely different. In a lot of cases the influence of oxygen is limited to the surface layer of the samples, commonly referred to as diffusion-limited oxidation. For the lifetime prediction of elastomer components, it is essential to have detailed knowledge about the absorption and diffusion behaviour of oxygen molecules during thermo-oxidative ageing and how they react with the elastomer. Experimental investigations on industrially used elastomeric materials are executed in order to develop and fit models, which shall be capable of predicting the permeation and consumption of oxygen as well as changes in the mechanical properties. The latter are of prime importance for technical applications of rubber components. Oxidation does not occur homogeneously over the entire elastomeric component. Hence, material models which include ageing effects have to be amplified in order to consider heterogeneous ageing, which highly depends on the ageing temperature. The influence of elevated temperatures upon accelerated ageing has to be critically analysed, and influences on the permeation and diffusion coefficient have to be taken into account. This work presents phenomenological models which describe the oxygen uptake and the diffusion into elastomers based on an improved understanding of ongoing chemical processes and diffusion limiting modifications. On the one side, oxygen uptake is modelled by means of Henry’s law in which solubility is a function of the temperature as well as the ageing progress. The latter is an irreversible process and described by an inner differential evolution equation. On the other side, further diffusion of oxygen into the material is described by a model based on Fick’s law, which is modified by a reaction term. The evolved diffusion-reaction equation depends on the ageing temperature as well as on the progress of ageing and is able to describe diffusion-limited oxidation. PubDate: 2017-04-27 DOI: 10.1007/s00161-017-0568-8

Authors:Ioannis Tsagrakis; Elias C. Aifantis 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: 2017-04-08 DOI: 10.1007/s00161-017-0565-y

Authors:Martin Heida Abstract: We study the stochastic and periodic homogenization 1-homogeneous convex functionals. We prove some convergence results with respect to stochastic two-scale convergence, which are related to classical \(\Gamma \) -convergence results. The main result is a general \(\liminf \) -estimate for a sequence of 1-homogeneous functionals and a two-scale stability result for sequences of convex sets. We apply our results to the homogenization of rate-independent systems with 1-homogeneous dissipation potentials and quadratic energies. In these applications, both the energy and the dissipation potential have an underlying stochastic microscopic structure. We study the particular homogenization problems of Prandtl–Reuss plasticity, Tresca friction on a macroscopic surface and Tresca friction on microscopic fissures. PubDate: 2017-04-03 DOI: 10.1007/s00161-017-0564-z

Authors:Matthias Wunde; Manfred Klüppel Abstract: Based on a viscoelastic model, the filler distribution and the amount of interphase of carbon black-filled blends of natural rubber (NR) with styrene-butadiene rubber (SBR) are evaluated. Hereby, the total dissipated energy \(G''\) during dynamical straining is decomposed into the contributions of the different polymer phases and the interphase. For the NR/SBR blends, we find a higher filling of the SBR phase and the interphase and a lower filling of the NR phase. The filler distribution itself depends not only on the affinity of the polymer to the filler but also on the mixing procedure. This is investigated by studying NR/SBR blends prepared by two different mixing procedures. In the standard mixing procedure, the polymers are mixed first, and then, the filler is added. In the batch mixing procedure, the filler is previously mixed in the NR only and then blended with SBR. Batch mixing is resulting in an increase in the filling of the interphase due to filler transfer from NR to SBR. The results for the filler distribution are compared to fatigue crack propagation rates under pulsed excitation. The crack propagation is accelerated when substituting NR with SBR. The batched samples show higher crack propagation rates at higher tearing energies due to a worse dispersion of the carbon black and/or higher filler loading of the interphase. PubDate: 2017-03-30 DOI: 10.1007/s00161-017-0562-1

Authors:R. V. M. S. S. Kiran Kumar; S. Vijaya Kumar Varma; C. S. K. Raju; S. M. Ibrahim; G. Lorenzini; E. Lorenzini Abstract: Carbon nanotubes are allotropes of carbon with a cylindrical nanostructure. These cylindrical carbon molecules have unusual properties, which are valuable for nanotechnology, electronics, optics and other fields of materials science and technology. With this intention, we investigate the three-dimensional magnetohydrodynamic convective heat and mass transfer of nanofluid over a slendering stretching sheet filled with porous medium and heat source/sink. For balancing the flow, temperature and concentration slip mechanisms are also taken into account. In this investigation simulation performed by mixing the two types of carbon nanotubes, namely single- and multi-walled carbon nanotubes, into water as base fluid. The governing system of partial differential equations is transformed into nonlinear ordinary differential equations which answered by using R–K–Fehlberg-integration scheme. The impact of various pertinent parameters on velocity, temperature and concentration as well as the friction factor coefficient, local Nusselt and local Sherwood number is derived and discussed through graphs and tables for both single- and multi-walled carbon nanotubes cases. It is found that the momentum boundary layer thickness of SWCNTs is thicker than MWCNTs. These results can help us to conclude that SWCNTs are helpful for minimizing the friction between the particles, whereas MWCNTs are helpful for boosting the heat and mass transfer rate. PubDate: 2017-03-27 DOI: 10.1007/s00161-017-0563-0

Authors:D. Soldatos; S. P. Triantafyllou; V. P. Panoskaltsis Abstract: In this work, we address several theoretical and computational issues which are related to the thermomechanical modeling of shape memory alloy materials. More specifically, in this paper we revisit a non-isothermal version of the theory of large deformation generalized plasticity which is suitable for describing the multiple and complex mechanisms occurring in these materials during phase transformations. We also discuss the computational implementation of a generalized plasticity-based constitutive model, and we demonstrate the ability of the theory in simulating the basic patterns of the experimentally observed behavior by a set of representative numerical examples. PubDate: 2017-03-24 DOI: 10.1007/s00161-017-0559-9