Authors:C. S. K. Raju; K. R. Sekhar; S. M. Ibrahim; G. Lorenzini; G. Viswanatha Reddy; E. Lorenzini Pages: 699 - 713 Abstract: 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: 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: 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: 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: 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:Sergey G. Fedosin Pages: 361 - 371 Abstract: Abstract The virial theorem is considered for a system of randomly moving particles that are tightly bound to each other by the gravitational and electromagnetic fields, acceleration field and pressure field. The kinetic energy of the particles of this system is estimated by three methods, and the ratio of the kinetic energy to the absolute value of the energy of forces, binding the particles, is determined, which is approximately equal to 0.6. For simple systems in classical mechanics, this ratio equals 0.5. The difference between these ratios arises by the consideration of the pressure field and acceleration field inside the bodies, which make additional contribution to the acceleration of the particles. It is found that the total time derivative of the system’s virial is not equal to zero, as is assumed in classical mechanics for systems with potential fields. This is due to the fact that although the partial time derivative of the virial for stationary systems tends to zero, but in real bodies the virial also depends on the coordinates and the convective derivative of the virial, as part of the total time derivative inside the body, is not equal to zero. It is shown that the convective derivative is also necessary for correct description of the equations of motion of particles. PubDate: 2017-03-01 DOI: 10.1007/s00161-016-0536-8 Issue No:Vol. 29, No. 2 (2017)

Authors:M. Vaz; M. R. Lange Pages: 373 - 383 Abstract: Abstract Modeling strategies aimed at thermo-mechanical coupled problems has been developed for a wide range of engineering applications. Staggered-type coupling procedures have been largely used in materials processing operations, especially in commercial codes, owing to their simplicity and flexibility. The present work shows that, in thermo-plastic problems, the classical implementation of the most common coupling procedure may present accuracy issues and time-stepping dependency. Numerical experiments indicate that an iterative coupling scheme constitutes a viable and simple approach to this class of problems. PubDate: 2017-03-01 DOI: 10.1007/s00161-016-0537-7 Issue No:Vol. 29, No. 2 (2017)

Authors:J. F. Ganghoffer; M. B. Boubaker Pages: 429 - 455 Abstract: Abstract We adopt in this paper the physically and micromechanically motivated point of view that growth (resp. resorption) occurs as the expansion (resp. contraction) of initially small tissue elements distributed within a host surrounding matrix, due to the interfacial motion of their boundary. The interface motion is controlled by the availability of nutrients and mechanical driving forces resulting from the internal stresses that built in during the growth. A general extremum principle of the zero potential for open systems witnessing a change of their mass due to the diffusion of nutrients is constructed, considering the framework of open systems thermodynamics. We postulate that the shape of the tissue element evolves in such a way as to minimize the zero potential among all possible admissible shapes of the growing tissue elements. The resulting driving force for the motion of the interface sets a surface growth models at the scale of the growing tissue elements, and is conjugated to a driving force identified as the interfacial jump of the normal component of an energy momentum tensor, in line with Hadamard’s structure theorem. The balance laws associated with volumetric growth at the mesoscopic level result as the averaging of surface growth mechanisms occurring at the microscopic scale of the growing tissue elements. The average kinematics has been formulated in terms of the effective growth velocity gradient and elastic rate of deformation tensor, both functions of time. This formalism is exemplified by the simulation of the avascular growth of multicell spheroids in the presence of diffusion of nutrients, showing the respective influence of mechanical and chemical driving forces in relation to generation of internal stresses. PubDate: 2017-03-01 DOI: 10.1007/s00161-016-0539-5 Issue No:Vol. 29, No. 2 (2017)

Authors:Evgeniy Yu. Vitokhin; Mikhail B. Babenkov Pages: 457 - 475 Abstract: Abstract We consider a series of problems with a short laser impact on a thin metal layer accounting various boundary conditions of the first and second kind. The behavior of the material is modeled by the hyperbolic thermoelasticity of Lord–Shulman type. We obtain analytical solutions of the problems in the semi-coupled formulation and numerical solutions in the coupled formulation. Numerical solutions are compared with the analytical ones. The analytical solutions of the semi-coupled problems and numerical solutions of the coupled problems show qualitative match. The solutions of hyperbolic thermoelasticity problems are compared with those obtained in the frame of the classical thermoelasticity. It was determined that the most prominent difference between the classical and hyperbolic solutions arises in the problem with fixed boundaries and constant temperature on them. The smallest differences were observed in the problem with unconstrained, thermally insulated edges. It was shown that a cooling zone is observed if the boundary conditions of the first kind are given for the temperature. Analytical expressions for the velocities of the quasiacoustic and quasithermal fronts as well as the critical value for the attenuation coefficient of the excitation impulse are verified numerically. PubDate: 2017-03-01 DOI: 10.1007/s00161-016-0540-z Issue No:Vol. 29, No. 2 (2017)

Authors:Alireza Beheshti Pages: 493 - 507 Abstract: Abstract This paper concerns finite deformation in the strain-gradient continuum. In order to take account of the geometric nonlinearity, the original strain-gradient theory which is based on the infinitesimal strain tensor is rewritten given the Green–Lagrange strain tensor. Following introducing the generalized isotropic Saint Venant–Kirchhoff material model for the strain-gradient elasticity, the boundary value problem is investigated in not only the material configuration but also the spatial configuration building upon the principle of virtual work for a three-dimensional solid. By presenting one example, the convergence of the strain-gradient and classical theories is studied. PubDate: 2017-03-01 DOI: 10.1007/s00161-016-0542-x Issue No:Vol. 29, No. 2 (2017)

Authors:Martina Costa Reis; Yongqi Wang Pages: 509 - 534 Abstract: Abstract Based on the Eulerian spatial averaging theory and the Müller–Liu entropy principle, a two-fluid model for reactive dilute solid–liquid mixtures is presented. Initially, some averaging theorems and properties of average quantities are discussed and, then, averaged balance equations including interfacial source terms are postulated. Moreover, constitutive equations are proposed for a reactive dilute solid–liquid mixture, where the formation of the solid phase is due to a precipitation chemical reaction that involves ions dissolved in the liquid phase. To this end, principles of constitutive theory are used to propose linearized constitutive equations that account for diffusion, heat conduction, viscous and drag effects, and interfacial deformations. A particularity of the model is that the mass interfacial source term is regarded as an independent constitutive variable. The obtained results show that the inclusion of the mass interfacial source term into the set of independent constitutive variables permits to easily describe the phase changes associated with precipitation chemical reactions. PubDate: 2017-03-01 DOI: 10.1007/s00161-016-0546-6 Issue No:Vol. 29, No. 2 (2017)

Authors:U. S. Mahabaleshwar; K. R. Nagaraju; P. N. Vinay Kumar; Dumitru Baleanu; Giulio Lorenzini Pages: 559 - 567 Abstract: Abstract In this paper, we investigate the theoretical analysis for the unsteady magnetohydrodynamic laminar boundary layer flow due to impulsively stretching sheet. The third-order highly nonlinear partial differential equation modeling the unsteady boundary layer flow brought on by an impulsively stretching flat sheet was solved by applying Adomian decomposition method and Pade approximants. The exact analytical solution so obtained is in terms of rapidly converging power series and each of the variants are easily computable. Variations in parameters such as mass transfer (suction/injection) and Chandrasekhar number on the velocity are observed by plotting the graphs. This particular problem is technically sound and has got applications in expulsion process and related process in fluid dynamics problems. PubDate: 2017-03-01 DOI: 10.1007/s00161-016-0543-9 Issue No:Vol. 29, No. 2 (2017)

Authors:Ioannis Tsagrakis; Elias C. Aifantis Abstract: 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: 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: 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: 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: 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

Authors:Leonell Serrano; Yann Marco; Vincent Le Saux; Gilles Robert; Pierre Charrier Abstract: Abstract Short-fiber-reinforced thermoplastics components for structural applications are usually very complex parts as stiffeners, ribs and thickness variations are used to compensate the quite low material intrinsic stiffness. These complex geometries induce complex local mechanical fields but also complex microstructures due to the injection process. Accounting for these two aspects is crucial for the design in regard to fatigue of these parts, especially for automotive industry. The aim of this paper is to challenge an energetic approach, defined to evaluate quickly the fatigue lifetime, on three different heterogeneous cases: a classic dog-bone sample with a skin-core microstructure and two structural samples representative of the thickness variations observed for industrial components. First, a method to evaluate dissipated energy fields from thermal measurements is described and is applied to the three samples in order to relate the cyclic loading amplitude to the fields of cyclic dissipated energy. Then, a local analysis is detailed in order to link the energy dissipated at the failure location to the fatigue lifetime and to predict the fatigue curve from the thermomechanical response of one single sample. The predictions obtained for the three cases are compared successfully to the Wöhler curves obtained with classic fatigue tests. Finally, a discussion is proposed to compare results for the three samples in terms of dissipation fields and fatigue lifetime. This comparison illustrates that, if the approach is leading to a very relevant diagnosis on each case, the dissipated energy field is not giving a straightforward access to the lifetime cartography as the relation between fatigue failure and dissipated energy seems to be dependent on the local mechanical and microstructural state. PubDate: 2017-03-21 DOI: 10.1007/s00161-017-0561-2

Authors:A. Paglietti Abstract: Abstract In laminar flow, viscous fluids must exert appropriate elastic shear stresses normal to the flow direction. This is a direct consequence of the balance of angular momentum. There is a limit, however, to the maximum elastic shear stress that a fluid can exert. This is the ultimate shear stress, \(\tau _\mathrm{y}\) , of the fluid. If this limit is exceeded, laminar flow becomes dynamically incompatible. The ultimate shear stress of a fluid can be determined from experiments on plane Couette flow. For water at \(20\,^{\circ }\hbox {C}\) , the data available in the literature indicate a value of \(\tau _\mathrm{y}\) of about \(14.4\times 10^{-3}\, \hbox {Pa}\) . This study applies this value to determine the Reynolds numbers at which flowing water reaches its ultimate shear stress in the case of Taylor–Couette flow and circular pipe flow. The Reynolds numbers thus obtained turn out to be reasonably close to those corresponding to the onset of turbulence in the considered flows. This suggests a connection between the limit to laminar flow, on the one hand, and the occurrence of turbulence, on the other. PubDate: 2017-01-10 DOI: 10.1007/s00161-016-0549-3

Authors:Teodor M. Atanacković; Marko Janev; Sanja Konjik; Stevan Pilipović Abstract: Abstract We study waves in a viscoelastic rod whose constitutive equation is of generalized Zener type that contains fractional derivatives of complex order. The restrictions following from the Second Law of Thermodynamics are derived. The initial boundary value problem for such materials is formulated and solution is presented in the form of convolution. Two specific examples are analyzed. PubDate: 2017-01-06 DOI: 10.1007/s00161-016-0548-4