Authors:Z.-H. Jin Pages: 3993 - 4004 Abstract: This work describes a thermo-poroelasticity theory to investigate the effects of temperature gradients on infiltration kinetics, pore pressure distribution of the liquid phase, and liquid content variation due to preform deformation for infiltration processing of interpenetrating phase composites. Governing equations for three-dimensional infiltration processing are presented. A similarity solution is derived for one-dimensional infiltration assuming no solidification of the liquid phase. The solution indicates that besides the liquid viscosity, the infiltration front also depends on the poroelastic properties of the preform. A numerical example for a polymer–ceramic IPC shows that the temperature gradients may produce significant liquid content increment beyond the amount that can be accommodated by the initial pore volume of the preform. This liquid content increment may compensate some solidification shrinkage of the liquid phase, thereby suppressing occurrence of microdefects in the composite. PubDate: 2018-10-01 DOI: 10.1007/s00707-018-2202-7 Issue No:Vol. 229, No. 10 (2018)

Authors:B. Herrmann-Priesnitz; W. R. Calderón-Muñoz; R. Soto Pages: 4005 - 4015 Abstract: The analysis of the disturbances on a spiraling base flow is relevant for the design, operation, and control of technological devices such as parallel-disk turbines and swirl flow channel heat sinks. Spiraling inflow inside an annular cavity closed at the top and bottom is analyzed in the framework of modal and nonmodal stability theories. Local and parallel flow approximations are applied, and the inhomogeneous direction is discretized using the Chebyshev collocation method. The optimal growth of initial disturbances and the optimal response to external harmonic forcing are characterized by the exponential and the resolvent of the dynamics matrix. As opposed to plane Poiseuille flow, transient growth is small, and consequently, it does not play a role in the transition mechanism. The transition is attributed to a crossflow instability that occurs because of the change in the shape of the velocity profile due to rotational effects. Agreement is found between the critical Reynolds number predicted in this work and the deviation of laminar behavior observed in the experiments conducted by Ruiz and Carey (J Heat Transfer 137(7):071702, 2015). For the harmonically driven problem, an energy amplification of \(\textit{O}(100)\) is observed for spiral crossflow waves. Transition to turbulence should be avoided to ensure the safe operation of a parallel-disk turbine, whereas large forcing amplification may be sought to promote mixing in a swirl flow channel heat sink. The analysis presented predicts and provides insight into the transition mechanisms. Due to its easy implementation and low computational cost, it is particularly useful for the early stages of engineering design. PubDate: 2018-10-01 DOI: 10.1007/s00707-018-2214-3 Issue No:Vol. 229, No. 10 (2018)

Authors:Yu. A. Chirkunov Pages: 4045 - 4056 Abstract: A generalization of Leith’s model of the phenomenological theory of the wave turbulence is investigated. With the methods of group analysis, the basic models possessing non-trivial symmetries are obtained. For each model, all the invariant submodels are found. For nonlinear differential equations describing these models, formulas for the production of new solutions containing arbitrary constants are obtained. By virtue of these formulas, each solution generates a family of the new solutions. In an explicit form, some invariant solutions (not connected by point transformations) describing invariant submodels are found. The physical meaning of these solutions is obtained. In particular, with the help of these solutions the turbulent processes for which there are “destructive waves” both with fixed wave numbers and with varying wave numbers are described. On the example of an invariant solution of rank 1, it was shown that the search of the invariant solutions of rank 1, which cannot be found explicitly, can be reduced to solve the integral equations. For this solution, turbulent processes are investigated for which at the initial instant of a time and for a fixed value of the wave number either the turbulence energy and rate of its change or the turbulence energy and its gradient are given. Under certain conditions, the existence and uniqueness of the solutions of the boundary value problems describing these processes are established. PubDate: 2018-10-01 DOI: 10.1007/s00707-018-2217-0 Issue No:Vol. 229, No. 10 (2018)

Authors:S. Srividhya; K. Basant; R. K. Gupta; A. Rajagopal; J. N. Reddy Pages: 4071 - 4089 Abstract: Functionally graded materials (FGM) are an advanced class of engineering composites constituting of two or more distinct phase materials described by continuous and smooth varying composition of material properties in the required direction. In this work, the effect of the material homogenization scheme on the flexural response of a thin to moderately thick FGM plate is studied. The plate is subjected to different loading and boundary conditions. The formulation is developed based on the first-order shear deformation theory. The mechanical properties are assumed to vary continuously through the thickness of the plate and obey a power-law distribution of the volume fraction of the constituents. The variation of volume fraction through the thickness is computed using two different homogenization techniques, namely rule of mixtures and Mori–Tanaka scheme. Comparative studies have been carried out to demonstrate the efficiency of the present formulation. The results obtained from the two techniques have been compared with the analytical solutions available in the literature. In addition to the above a parametric study bringing out the effect of boundary conditions, loads, and power-law index has also been presented. PubDate: 2018-10-01 DOI: 10.1007/s00707-018-2223-2 Issue No:Vol. 229, No. 10 (2018)

Authors:Guo Yao; Fengming Li Pages: 4091 - 4100 Abstract: In this paper, the nonlinear forced vibration properties of the lattice sandwich beam with pyramidal truss core and viscoelastic surfaces subjected to harmonic external excitation are investigated. The nonlinear dynamic model of the lattice sandwich beam is formulated based on the Kelvin–Voigt viscoelastic model and discretized into nonlinear ordinary equations with multiple degrees of freedom by using the assumed mode method. The nonlinear amplitude–frequency curves of the steady-state responses of the beam are obtained by an iterative algorithm. The effects of the external excitation amplitude, the inclination angle of the truss core, and the viscoelastic coefficient of the surface material on the nonlinear forced vibration behaviors of the beam are analyzed. From the research results, it can be seen that the lattice sandwich beam shows very rich and novel nonlinear dynamic behavior. The viscoelastic damping of the surfaces can decrease the resonance amplitudes of most modes of the beam. An acceptable optimal inclination angle considering the equivalent mass density of the pyramidal truss core and the resonance amplitude of the beam is obtained. The evolution rules of the lattice sandwich beam with the material and structural parameters obtained from the preset study are helpful for the engineering applications of this kind of lightweight sandwich structures. PubDate: 2018-10-01 DOI: 10.1007/s00707-018-2229-9 Issue No:Vol. 229, No. 10 (2018)

Authors:Davood Ghorbannia; Afshin Eghbalzadeh Pages: 4101 - 4111 Abstract: Side weirs are among hydraulic structures which are utilized in flood control, urban sewage disposal networks, irrigation, and drainage channels. Today, thanks to computer science advancement, the use of numerical models has been increased owing to lesser time and lower costs compared with experimental models. The present study deals with investigating the flow pattern on a side weir in a converging rectangular channel using a commercial software employing RNG turbulence model and VOF method to simulate turbulence and free surface, respectively. One of the advantages of using side weirs is that after drainage it is unnecessary to continue the downstream channel with the previous width, and consequently it will be cost-effective. Comparing longitudinal velocities, water surface profiles, and flow discharge over a side weir with experimental results indicated the capability of the numerical model to simulate the flow pattern over a side weir. The effects of length changes of the side weir on the flow characteristics also were studied. Comparing parameters in different sections at the middle of the side weir showed that decreasing the length of the side weir increases the longitudinal velocity. Also, by decreasing the side weir length the passing discharge declined, and the free surface profile formed in higher height as well. The discrepancy between the specific energy at the upstream and that of the downstream of the weir for different side weir lengths was negligible. PubDate: 2018-10-01 DOI: 10.1007/s00707-018-2215-2 Issue No:Vol. 229, No. 10 (2018)

Authors:Sergey V. Kuznetsov Pages: 4131 - 4139 Abstract: Propagation of harmonic Lamb waves in plates made of functionally graded materials with transverse inhomogeneity is studied by the modified Cauchy six-dimensional formalism. For arbitrary transverse inhomogeneity, a closed-form dispersion equation is derived. Dispersion relations for materials with different kinds of inhomogeneity are obtained and compared. PubDate: 2018-10-01 DOI: 10.1007/s00707-018-2226-z Issue No:Vol. 229, No. 10 (2018)

Authors:G. Y. Zhang; X.-L. Gao; S. R. Ding Pages: 4199 - 4214 Abstract: A new model for determining band gaps for wave propagation in two-dimensional (2-D) periodic composite structures is developed using a modified couple stress theory. The general equation of motion and boundary conditions in the elasto-dynamics of the modified couple stress theory are first derived by a variational formulation based on Hamilton’s principle. The in-plane and anti-plane wave equations incorporating microstructure effects are then obtained explicitly from the general equation of motion. The plane wave expansion method and the Bloch theorem for periodic media are used to solve the in-plane and anti-plane wave equations, which are reduced to an eigenvalue problem in each case. The band gaps are determined from solving the characteristic equation and plotting the resulting eigen-frequencies. The new model recovers the classical elasticity-based model when microstructure effects are not considered. To quantitatively illustrate the newly developed model, a parametric study is conducted for 2-D periodic composite structures containing circular and square inclusions. The numerical results reveal that the microstructure effects on the band gaps are significant only when the unit cell size is small for both the composite structures. In addition, it is found that the volume fraction has a significant effect on the band gap size, and the inclusion shape has a large influence on the band gaps. PubDate: 2018-10-01 DOI: 10.1007/s00707-018-2207-2 Issue No:Vol. 229, No. 10 (2018)

Authors:Diletta Burini; Silvana De Lillo; Gioia Fioriti Pages: 4215 - 4228 Abstract: A free boundary problem on a finite interval is formulated and solved for a nonlinear diffusion–convection equation. The model is suitable to describe drug diffusion in arterial tissues after the drug is released by an arterial stent. The problem is reduced to a system of nonlinear integral equations, admitting a unique solution for small time. The existence of an exact solution corresponding to a moving front is also shown, which is in agreement with numerical results existing in the literature. PubDate: 2018-10-01 DOI: 10.1007/s00707-018-2220-5 Issue No:Vol. 229, No. 10 (2018)

Authors:Amares Chattopadhyay; Akanksha Srivastava; Pulkit Kumar; Abhishek Kumar Singh Pages: 4229 - 4238 Abstract: The present article aims to unravel the propagation characteristics of a shear wave in the context of reinforcement and frictional bonding in a composite structure. The geometrical configuration of the composite structure is comprised with a fibre-reinforced layer and an isotropic homogeneous semi-infinite medium which are frictionally bonded to each other. An analytical technique is employed to find the complex form of the frequency equation which is separated into real and imaginary parts representing the dispersion and damping relation, respectively. As a particular case of the problem, the deduced results are matched with the classical Love equation. The numerical simulation is performed to graphically portray the analytical findings and to trace out the effect of reinforcement by a comparative study which is a major highlight of the study. The significant influence of reinforcement, frictional bonding, and spectral decay parameter on the phase, group, and damped velocities are revealed. The outcome of the present study may be helpful to gain deeper insight into the propagation characteristics of a shear wave in a frictionally bonded composite structure which may provide useful information in engineering applications. PubDate: 2018-10-01 DOI: 10.1007/s00707-018-2219-y Issue No:Vol. 229, No. 10 (2018)

Authors:Marin Marin; Andreas Öchsner; Dumitru Baleanu Pages: 4267 - 4277 Abstract: Our study is concerned with the initial boundary value problem in the context of the thermoelastostatics of dipolar bodies. We will derive a result which describes the exponential spatial decay of solutions of this problem. We will also find a superior limit for the amplitude, which is dependent on the initial and boundary conditions. PubDate: 2018-10-01 DOI: 10.1007/s00707-018-2237-9 Issue No:Vol. 229, No. 10 (2018)

Authors:J. H. Merkin Pages: 4279 - 4294 Abstract: The similarity equations that arise when there is a power-law outer flow, characterized by the parameter \(\beta \) , over a surface moving with the same power-law speed, described by the dimensionless parameter \(\lambda \) , are considered. The critical values \(\lambda _c\) of \(\lambda \) are calculated in terms of \(\beta \) , except in a range \(0.139 \lesssim \beta \lesssim 0.5\) where there are no critical points. The behaviour of the solution with \(\lambda \) for representative values of \(\beta \) is examined, including cases where there are no critical points and one or two critical points leading to two and three solution branches. The asymptotic behaviour for large \(\lambda \) is derived. For \(-2<\beta <-1\) , the solution proceeds to large negative values of \(\lambda \) with this asymptotic limit derived. Aiding flow, \(\lambda >0\) , shows the existence of additional critical points, with a range \(-2.6583<\beta <-2\) over which \(\lambda _c\) takes all values both positive and negative. Relatively weak, \(\lambda =-0.5\) , and stronger, \(\lambda =-5.0\) , cases of opposing are treated. The weak case shows two disjoint sections of the solution. For the larger value of \( \lambda \) , one section of the solution in which \(f''(0)\) decreases monotonically as \(\beta \) is increased and another section where there is a critical point with two solution branches is seen. In all the cases considered, the solution became singular as \(\beta \rightarrow -2\) , this limit being discussed. PubDate: 2018-10-01 DOI: 10.1007/s00707-018-2221-4 Issue No:Vol. 229, No. 10 (2018)

Authors:K. Y. Volokh Pages: 4295 - 4301 Abstract: The remarkable phenomenon of the drag reduction via addition of small amounts of polymer molecules to a Newtonian solvent was observed experimentally long ago. However, the theoretical explanations of this observation are not overwhelming yet. In this note, we present a possible theoretical account of the phenomenon. It is based on the use of the Navier–Stokes model with viscous strength for the solvent and the upper-convected Maxwell model for the polymer solute. Simple analytical calculation shows that the laminar flow of the solvent is stabilized by an addition of the polymer solute and, thus, the transition to the chaotic and slower on average turbulent motion is suppressed. PubDate: 2018-10-01 DOI: 10.1007/s00707-018-2206-3 Issue No:Vol. 229, No. 10 (2018)

Authors:Kazumi Watanabe Pages: 4303 - 4311 Abstract: A simple and exact closed form solution for a rotating cylinder is presented. The cylinder is inserted in a bored dissimilar elastic solid. The exact form of the absolute acceleration and the Coulomb’s rule for the friction on the circular interface are employed. After discussing the resonant frequency/velocity, numerical computations are carried out for all stress components in the cylinder. It is found that the hoop stress on the cylinder edge changes its nature from extensive to compressive as the rigidity of the surrounding solid increases. The torque and power to keep the cylinder rotation are also discussed, briefly. PubDate: 2018-10-01 DOI: 10.1007/s00707-018-2228-x Issue No:Vol. 229, No. 10 (2018)

Authors:Walter Fornari; Sagar Zade; Luca Brandt; Francesco Picano Abstract: We study the settling of finite-size rigid spheres in quiescent fluid and in sustained homogeneous isotropic turbulence (HIT) by direct numerical simulations using an immersed boundary method to account for the dispersed solid phase. We consider semi-dilute and dense suspensions of rigid spheres with solid volume fractions \(\phi =0.5{-}10\%\) , solid-to-fluid density ratio \(R=1.02\) , and Galileo number (i.e., the ratio between buoyancy and viscous forces) \(Ga=145\) . In HIT, the nominal Reynolds number based on the Taylor microscale is \(Re_{\lambda } \simeq 90\) , and the ratio between the particle diameter and the nominal Kolmogorov scale is \((2a)/\eta \simeq 12\) (being a the particle radius). We find that in HIT the mean settling speed is less than that in quiescent fluid for all \(\phi \) . For \(\phi =0.5\%\) , the mean settling speed in HIT is \(8\%\) less than in quiescent fluid. However, by increasing the volume fraction the difference in the mean settling speed between quiescent fluid and HIT cases reduces, being only \(1.7\%\) for \(\phi =10\%\) . Indeed, while at low \(\phi \) the settling speed is strongly altered by the interaction with turbulence, at large \(\phi \) this is mainly determined by the (strong) hindering effect. This is similar in quiescent fluid and in HIT, leading to similar mean settling speeds. On the contrary, particle angular velocities are always found to increase with \(\phi \) . These are enhanced by the interaction with turbulence, especially at low \(\phi \) . In HIT, the correlations of particle lateral velocity fluctuations oscillate around zero before decorrelating completely. The time period of the oscillation seems proportional to the ratio between the integral lengthscale of turbulence and the particle characteristic terminal velocity. Regarding the mean square particle displacement, we find that it is strongly enhanced by turbulence in the direction perpendicular to gravity, even at the largest \(\phi \) . Finally, we investigate the collision statistics for all cases and find the interesting result that the collision frequency is larger in quiescent fluid than in HIT for \(\phi =0.5{-}1\%\) . This is due to frequent drafting–kissing–tumbling events in quiescent fluid. The collision frequency becomes instead larger in HIT than in still fluid for \(\phi =5{-}10\%\) , due to the larger relative approaching velocities in HIT, and to the less intense drafting–kissing–tumbling events in quiescent fluid. The collision frequency also appears to be almost proportional to the estimate for small inertial particles uniformly distributed in space, though much smaller. Concerning the turbulence modulation, we find that the mean energy dissipation increases almost linearly with \(\phi \) , leading to a large reduction of \(Re_{\lambda }\) . PubDate: 2018-10-19 DOI: 10.1007/s00707-018-2269-1

Authors:Marco E. Rosti; Francesco De Vita; Luca Brandt Abstract: We present a modification of a recently developed volume of fluid method for multiphase problems (Ii et al. in J Comput Phys 231(5):2328–2358, 2012), so that it can be used in conjunction with a fractional-step method and fast Poisson solver, and validate it with standard benchmark problems. We then consider emulsions of two-fluid systems and study their rheology in a plane Couette flow in the limit of vanishing inertia. We examine the dependency of the effective viscosity \(\mu \) on the volume fraction \(\varPhi \) (from 10 to \(30\%\) ) and the Capillary number Ca (from 0.1 to 0.4) for the case of density and viscosity ratio 1. We show that the effective viscosity decreases with the deformation and the applied shear (shear-thinning) while exhibiting a non-monotonic behavior with respect to the volume fraction. We report the appearance of a maximum in the effective viscosity curve and compare the results with those of suspensions of rigid and deformable particles and capsules. We show that the flow in the solvent is mostly a shear flow, while it is mostly rotational in the suspended phase; moreover, this behavior tends to reverse as the volume fraction increases. Finally, we evaluate the contributions to the total shear stress of the viscous stresses in the two fluids and of the interfacial force between them. PubDate: 2018-10-13 DOI: 10.1007/s00707-018-2265-5

Authors:Xue-Yang Zhang; Zeng-Tao Chen; Xian-Fang Li Abstract: This paper analyzes a thermal shock problem of an elastic half-space with a penny-shaped crack near the surface based on a fractional thermoelasticity theory. The embedded crack is assumed to be insulated. The Hankel transform and Laplace transform are employed to solve an initial-boundary value problem associated with a fractional partial differential equation. Explicit expressions of temperature and thermal stresses induced by the penny-shaped crack are obtained by solving a system of singular integral equations. Numerical results of the thermoelastic fields in the time domain are given by applying the numerical inverse Laplace transform. The temperature jump between the upper and lower crack surfaces and the thermal stress intensity factors at the crack front are illustrated graphically for various relaxation times and fractional orders, as well as the distance between the crack plane and the half-space surface. A comparison of the temperature, thermal stresses, and their intensity factors is made when adopting the fractional heat conduction model and the classical Fourier heat conduction model. Numerical results show that the temperature overshooting phenomenon may occur for the fractional heat conduction model, whereas it does not occur for the classical Fourier heat conduction model. PubDate: 2018-10-03 DOI: 10.1007/s00707-018-2252-x

Authors:Chun-Ron Chiang Abstract: Explicit expressions for Eshelby’s tensor of an elliptic inclusion in orthotropic materials are derived in this paper. The main approach is based on the general solution for elliptic-hole problems in orthotropic materials. The derivation based on a direct integration of elastic Green’s function along the elliptic contour is also used to illustrate a certain useful connection between these two approaches; this connection has not been fully recognized and published before. The theoretical results are checked with those obtained via the Fourier transform method and those found by direct numerical integration. PubDate: 2018-10-01 DOI: 10.1007/s00707-018-2254-8

Authors:Anatoly M. Polyanskiy; Vladimir A. Polyanskiy; Alexander K. Belyaev; Yury A. Yakovlev Abstract: The paper is concerned with the main factors that determine the mechanical characteristics of materials. The values of these factors are shown to be related to the size of structural elements. These elements are the lattice atoms in the case of calculation of Young’s modulus and the crystallites of various sizes in the case of determining the yield stress and ultimate strength. The models are constructed which allow obtaining fundamental relationships that adequately determine the mechanical characteristics of solid metals. Verification of the dependences is carried out on the basis of experimental data, and the adequacy of the proposed models is proved. PubDate: 2018-10-01 DOI: 10.1007/s00707-018-2262-8