Authors:Felix A. Reich; Wilhelm Rickert; Wolfgang H. Müller Pages: 233 - 266 Abstract: This study investigates the implications of various electromagnetic force models in macroscopic situations. There is an ongoing academic discussion which model is “correct,” i.e., generally applicable. Often, gedankenexperiments with light waves or photons are used in order to motivate certain models. In this work, three problems with bodies at the macroscopic scale are used for computing theoretical model-dependent predictions. Two aspects are considered, total forces between bodies and local deformations. By comparing with experimental data, insight is gained regarding the applicability of the models. First, the total force between two cylindrical magnets is computed. Then a spherical magnetostriction problem is considered to show different deformation predictions. As a third example focusing on local deformations, a droplet of silicone oil in castor oil is considered, placed in a homogeneous electric field. By using experimental data, some conclusions are drawn and further work is motivated. PubDate: 2018-03-01 DOI: 10.1007/s00161-017-0596-4 Issue No:Vol. 30, No. 2 (2018)

Authors:Marin Marin; Andreas Öchsner Pages: 267 - 278 Abstract: This study deals with the first initial boundary value problem in elasticity of piezoelectric dipolar bodies. We consider the most general case of an anisotropic and inhomogeneous elastic body having a dipolar structure. For two different types of restrictions imposed on the problem data, we prove two results regarding the uniqueness of solution, by using a different but accessible method. Then, the mixed problem is transformed in a temporally evolutionary equation on a Hilbert space, conveniently constructed based on the problem data. With the help of a known result from the theory of semigroups of operators, the existence and uniqueness of the weak solution for this equation are proved. PubDate: 2018-03-01 DOI: 10.1007/s00161-017-0599-1 Issue No:Vol. 30, No. 2 (2018)

Authors:Sarah Welzenbach; Tim Fischer; Felix Meier; Ewald Werner; Sonun Ulan kyzy; Oliver Munz Pages: 279 - 290 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: 2018-03-01 DOI: 10.1007/s00161-017-0600-z Issue No:Vol. 30, No. 2 (2018)

Authors:Tijani A. Apalara Pages: 291 - 300 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: 2018-03-01 DOI: 10.1007/s00161-017-0601-y Issue No:Vol. 30, No. 2 (2018)

Authors:Michal Beneš; Igor Pažanin Pages: 301 - 317 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: 2018-03-01 DOI: 10.1007/s00161-017-0603-9 Issue No:Vol. 30, No. 2 (2018)

Authors:Balázs Tóth Pages: 319 - 345 Abstract: Some new dual and mixed variational formulations based on a priori nonsymmetric stresses will be developed for linearly coupled irreversible thermoelastodynamic problems associated with second sound effect according to the Lord–Shulman theory. Having introduced the entropy flux vector instead of the entropy field and defining the dissipation and the relaxation potential as the function of the entropy flux, a seven-field dual and mixed variational formulation will be derived from the complementary Biot–Hamilton-type variational principle, using the Lagrange multiplier method. The momentum-, the displacement- and the infinitesimal rotation vector, and the a priori nonsymmetric stress tensor, the temperature change, the entropy field and its flux vector are considered as the independent field variables of this formulation. In order to handle appropriately the six different groups of temporal prescriptions in the relaxed- and/or the strong form, two variational integrals will be incorporated into the seven-field functional. Then, eliminating the entropy from this formulation through the strong fulfillment of the constitutive relation for the temperature change with the use of the Legendre transformation between the enthalpy and Gibbs potential, a six-field dual and mixed action functional is obtained. As a further development, the elimination of the momentum- and the velocity vector from the six-field principle through the a priori satisfaction of the kinematic equation and the constitutive relation for the momentum vector leads to a five-field variational formulation. These principles are suitable for the transient analyses of the structures exposed to a thermal shock of short temporal domain or a large heat flux. PubDate: 2018-03-01 DOI: 10.1007/s00161-017-0605-7 Issue No:Vol. 30, No. 2 (2018)

Authors:David Grégoire; Carine Malheiro; Christelle Miqueu Pages: 347 - 363 Abstract: This study aims at characterising the adsorption-induced pore pressure and confinement in nanoscopic pores by molecular non-local density functional theory (DFT). Considering its important potential industrial applications, the adsorption of methane in graphitic slit pores has been selected as the test case. While retaining the accuracy of molecular simulations at pore scale, DFT has a very low computational cost that allows obtaining highly resolved pore pressure maps as a function of both pore width and thermodynamic conditions. The dependency of pore pressure on these parameters (pore width, pressure and temperature) is carefully analysed in order to highlight the effect of each parameter on the confined fluid properties that impact the solid matrix. PubDate: 2018-03-01 DOI: 10.1007/s00161-017-0602-x Issue No:Vol. 30, No. 2 (2018)

Authors:Fumioki Asakura; Andrea Corli Pages: 365 - 380 Abstract: In a previous paper, we studied the thermodynamic and kinetic theory for an ionized gas, in one space dimension; in this paper, we provide an application of those results to the reflection of a shock wave in an electromagnetic shock tube. Under some reasonable limitations, which fully agree with experimental data, we prove that both the incident and the reflected shock waves satisfy the Lax entropy conditions; this result holds even outside genuinely nonlinear regions, which are present in the model. We show that the temperature increases in a significant way behind the incident shock front but the degree of ionization does not undergo a similar growth. On the contrary, the degree of ionization increases substantially behind the reflected shock front. We explain these phenomena by means of the concavity of the Hugoniot loci. Therefore, our results not only fit perfectly but explain what was remarked in experiments. PubDate: 2018-03-01 DOI: 10.1007/s00161-017-0607-5 Issue No:Vol. 30, No. 2 (2018)

Authors:Tim Fischer; Sarah Welzenbach; Felix Meier; Ewald Werner; Sonun Ulan kyzy; Oliver Munz Pages: 381 - 395 Abstract: Metallic honeycomb labyrinth seals are commonly used as sealing systems in gas turbine engines. Because of their capability to withstand high thermo-mechanical loads and oxidation, polycrystalline nickel-based superalloys, such as Hastelloy X and Haynes 214, are used as sealing material. In addition, these materials must exhibit a tolerance against rubbing between the rotating part and the stationary seal component. The tolerance of the sealing material against rubbing preserves the integrity of the rotating part. In this article, the rubbing behavior at the rotor–stator interface is considered numerically. A simulation model is incorporated into the commercial finite element code ABAQUS/explicit and is utilized to simulate a simplified rubbing process. A user-defined interaction routine between the contact surfaces accounts for the thermal and mechanical interfacial behavior. Furthermore, an elasto-plastic constitutive material law captures the extreme temperature conditions and the damage behavior of the alloys. To validate the model, representative quantities of the rubbing process are determined and compared with experimental data from the literature. The simulation results correctly reproduce the observations made on a test rig with a reference stainless steel material (AISI 304). A parametric study using the nickel-based superalloys reveals a clear dependency of the rubbing behavior on the sliding and incursion velocity. Compared to each other, the two superalloys studied exhibit a different rubbing behavior. PubDate: 2018-03-01 DOI: 10.1007/s00161-017-0608-4 Issue No:Vol. 30, No. 2 (2018)

Authors:Shubhankar Roy Chowdhury; Gurudas Kar; Debasish Roy; J. N. Reddy Pages: 397 - 420 Abstract: Posed within the two-temperature theory of non-equilibrium thermodynamics, we propose a model for thermoviscoplastic deformation in metals. We incorporate the dynamics of dislocation densities–mobile and forest—that play the role of internal state variables in the formulation. The description based on two temperatures appears naturally when one recognizes that the thermodynamic system undergoing viscoplastic deformation is composed of two weakly interacting subsystems, viz. a kinetic-vibrational subsystem of the vibrating atomic lattices and a configurational subsystem of the slower degrees of freedom relating to defect motion, each with its own temperature. Starting with a basic model that involves only homogeneous deformation, a three-dimensional model for inhomogeneous viscoplasticity applicable to finite deformation is charted out in an overstress driven viscoplastic deformation framework. The model shows how the coupled evolutions of mobile and forest dislocation densities, which are critically influenced by the dynamics of configurational temperature, govern the strength and ductility of the metal. Unlike most contemporary models, the current proposal also affords a prediction of certain finer details as observed in the experimental data on stress–strain behaviour of metals and this in turn enhances the understanding of the evolving and interacting dislocation densities. Graphical PubDate: 2018-03-01 DOI: 10.1007/s00161-017-0606-6 Issue No:Vol. 30, No. 2 (2018)

Authors:J. D. Clayton; J. Knap Pages: 421 - 455 Abstract: A continuum mechanical theory is used to model physical mechanisms of twinning, solid-solid phase transformations, and failure by cavitation and shear fracture. Such a sequence of mechanisms has been observed in atomic simulations and/or experiments on the ceramic boron carbide. In the present modeling approach, geometric quantities such as the metric tensor and connection coefficients can depend on one or more director vectors, also called internal state vectors. After development of the general nonlinear theory, a first problem class considers simple shear deformation of a single crystal of this material. For homogeneous fields or stress-free states, algebraic systems or ordinary differential equations are obtained that can be solved by numerical iteration. Results are in general agreement with atomic simulation, without introduction of fitted parameters. The second class of problems addresses the more complex mechanics of heterogeneous deformation and stress states involved in deformation and failure of polycrystals. Finite element calculations, in which individual grains in a three-dimensional polycrystal are fully resolved, invoke a partially linearized version of the theory. Results provide new insight into effects of crystal morphology, activity or inactivity of different inelasticity mechanisms, and imposed deformation histories on strength and failure of the aggregate under compression and shear. The importance of incorporation of inelastic shear deformation in realistic models of amorphization of boron carbide is noted, as is a greater reduction in overall strength of polycrystals containing one or a few dominant flaws rather than many diffusely distributed microcracks. PubDate: 2018-03-01 DOI: 10.1007/s00161-017-0604-8 Issue No:Vol. 30, No. 2 (2018)

Authors:Z. Śloderbach; J. Pająk Pages: 457 - 457 Abstract: Unfortunately, the original article was online published with error in equations, and the same is corrected here. PubDate: 2018-03-01 DOI: 10.1007/s00161-017-0614-6 Issue No:Vol. 30, No. 2 (2018)

Authors:J. Nordmann; M. Aßmus; H. Altenbach Abstract: In this article, we present the technical realisation for visualisations of characteristic parameters of the fourth-order elasticity tensor, which is classified by three-dimensional symmetry groups. Hereby, expressions for spatial representations of Young’s modulus and bulk modulus as well as plane representations of shear modulus and Poisson’s ratio are derived and transferred into a comprehensible form to computer algebra systems. Additionally, we present approaches for spatial representations of both latter parameters. These three- and two-dimensional representations are implemented into the software MATrix LABoratory. Exemplary representations of characteristic materials complete the present treatise. PubDate: 2018-02-24 DOI: 10.1007/s00161-018-0635-9

Authors:A. K. Lazopoulos Abstract: Fractional differential equations are solved with L-fractional derivatives, using numerical procedures. Two characteristic fractional differential equations are numerically solved. The first equation describes the motion of a thin rigid plate immersed in a Newtonian fluid connected by a massless spring to a fixed point, and the other one the diffusion of gas in a fluid. PubDate: 2018-02-23 DOI: 10.1007/s00161-018-0632-z

Authors:Orestes Marangos; Anil Misra Abstract: Scanning acoustic microscopy (SAM) has been applied to measure the near-surface elastic properties of materials. For many substrates, the near-surface property is not constant but varies with depth. In this paper, we aim to interpret the SAM data from such substrates by modeling the interaction of the focused ultrasonic field with a substrate having a near-surface graded layer. The focused ultrasonic field solutions were represented as spherical harmonic expansions while the substrate solutions were represented as plane wave expansions. The bridging of the two solutions was achieved through the decomposition of the ultrasonic pressure fields in their angular spectra. Parametric studies were performed, which showed that near-surface graded layers exhibit distinctive frequency dependence of their reflectance functions. This behavior is characteristic to the material property gradation profile as well as the extent of the property gradation. The developed model was used to explain the frequency-dependent reflection coefficients measured from an acid-etched dentin substrate. Based on the model calculations, the elastic property variations of the acid-etched dentin near-surface indicate that the topmost part of the etched layer is very soft (3–6 GPa) and transitions to the native dentin through a depth of 27 and 36 microns. PubDate: 2018-02-22 DOI: 10.1007/s00161-018-0625-y

Authors:Elena Ionela Chereches; K. Viswanatha Sharma; Alina Adriana Minea Abstract: Ionic liquids are a new class of fluids to be considered for heat transfer due to their remarkable thermophysical properties. Experimental researches on ionic liquids have increased over the last few years and, as an extension, a new class of heat transfer fluids, the ionanofluids were considered in some recent experimental studies. Ionanofluids consists in suspending little amounts of high conductive nanoparticles in ionic liquids. In spite of a lot of inconsistent reports—mainly due to the deficient understanding of the involved mechanisms—ionanofluids have been demonstrated as a new favorable heat transfer fluid. The enhanced thermal conductivity of ionanofluids over the basic ionic liquids is considered one of the driving factors for enhancing convection. Nonetheless, the thermal conductivity is the most studied parameter in spite of the important influence of viscosity variation on the convective flow. This numerical study employed Ansys Fluent commercial code and showed that a correct description of thermophysical properties may make ionanofluids a very promising new heat transfer fluid since the preliminary results are encouraging. PubDate: 2018-02-20 DOI: 10.1007/s00161-018-0634-x

Authors:Péter B. Béda Abstract: In mechanics, viscoelasticity was the first field of applications in studying geomaterials. Further possibilities arise in spatial non-locality. Non-local materials were already studied in the 1960s by several authors as a part of continuum mechanics and are still in focus of interest because of the rising importance of materials with internal micro- and nano-structure. When material instability gained more interest, non-local behavior appeared in a different aspect. The problem was concerned to numerical analysis, because then instability zones exhibited singular properties for local constitutive equations. In dynamic stability analysis, mathematical aspects of non-locality were studied by using the theory of dynamic systems. There the basic set of equations describing the behavior of continua was transformed to an abstract dynamic system consisting of differential operators acting on the perturbation field variables. Such functions should satisfy homogeneous boundary conditions and act as indicators of stability of a selected state of the body under consideration. Dynamic systems approach results in conditions for cases, when the differential operators have critical eigenvalues of zero real parts (dynamic stability or instability conditions). When the critical eigenvalues have non-trivial eigenspace, the way of loss of stability is classified as a typical (or generic) bifurcation. Our experiences show that material non-locality and the generic nature of bifurcation at instability are connected, and the basic functions of the non-trivial eigenspace can be used to determine internal length quantities of non-local mechanics. Fractional calculus is already successfully used in thermo-elasticity. In the paper, non-locality is introduced via fractional strain into the constitutive relations of various conventional types. Then, by defining dynamic systems, stability and bifurcation are studied for states of thermo-mechanical solids. Stability conditions and genericity conditions are presented for constitutive relations under consideration. PubDate: 2018-02-17 DOI: 10.1007/s00161-018-0633-y

Authors:Giovanni Romano; Raimondo Luciano; Raffaele Barretta; Marina Diaco Abstract: Nonlocal elasticity is addressed in terms of integral convolutions for structural models of any dimension, that is bars, beams, plates, shells and 3D continua. A characteristic feature of the treatment is the recourse to the theory of generalised functions (distributions) to provide a unified presentation of previous proposals. Local-nonlocal mixtures are also included in the analysis. Boundary effects of convolutions on bounded domains are investigated, and analytical evaluations are provided in the general case. Methods for compensation of boundary effects are compared and discussed with a comprehensive treatment. Estimates of limit behaviours for extreme values of the nonlocal parameter are shown to give helpful information on model properties, allowing for new comments on previous proposals. Strain-driven and stress-driven models are shown to emerge by swapping the mechanical role of input and output fields in the constitutive convolution, with stress-driven elastic model leading to well-posed problems. Computations of stress-driven nonlocal one-dimensional elastic models are performed to exemplify the theoretical results. PubDate: 2018-02-14 DOI: 10.1007/s00161-018-0631-0

Authors:Yahui Zheng; Jiulin Du; Faku Liang Abstract: We have constructed a nonextensive thermodynamic formalism consisting of two sets of parallel Legendre transformation structures in previous papers. One is the physical set and the other is the Lagrange set. In this paper, we study the thermodynamic stability criterion with a dual interpretation of the thermodynamic relations and quantities. By recourse to the assumption that volume in nonextenstive system is nonadditive, we conclude that it is the physical pressure that is responsible for the mechanical balance between any two parts in a given nonextensive system. It is verified that in the physical set of transformation structures, the stability criterion can be expressed in terms of heat capacity and isothermal compressibility. We also discuss the fluctuation theory in nonextensive thermodynamics. PubDate: 2018-02-09 DOI: 10.1007/s00161-018-0628-8

Authors:Xu Wang; Peter Schiavone Abstract: We consider an Eshelby inclusion of arbitrary shape with uniform anti-plane eigenstrains embedded in one of two bonded dissimilar anisotropic half planes containing a semi-infinite interface crack situated along the negative real axis. Using two consecutive conformal mappings, the upper and lower halves of the physical plane are first mapped onto two separate quarters of the image plane. The corresponding boundary value problem is then analyzed in this image plane rather than in the original physical plane. Corresponding analytic functions in all three phases of the composite are derived via the construction of an auxiliary function and repeated application of analytic continuation across the real and imaginary axes in the image plane. As a result, the local stress intensity factor is then obtained explicitly. Perhaps most interestingly, we find that the satisfaction of a particular condition makes the inclusion (stress) invisible to the crack. PubDate: 2018-02-07 DOI: 10.1007/s00161-018-0630-1