Authors:Agathe Chouippe; Markus Uhlmann Pages: 387 - 412 Abstract: We investigate the motion of heavy particles with a diameter of several multiples of the Kolmogorov length scale in the presence of forced turbulence and gravity, resorting to interface-resolved direct numerical simulation based on an immersed boundary method. The values of the particles’ relative density (1.5) and of the Galileo number (180) are such that strong wake-induced particle clustering would occur in the absence of turbulence (Uhlmann and Doychev in J Fluid Mech 752:310–348, 2014. https://doi.org/10.1017/jfm.2014.330). The forced turbulence in the two present cases (with Taylor-scale Reynolds number 95 and 140) would lead to mild levels of clustering in the absence of gravity (Uhlmann and Chouippe in J Fluid Mech 812:991–1023, 2017. https://doi.org/10.1017/jfm.2016.826). Here we detect a tendency to cluster with an intensity (quantified via the standard deviation of the distribution of Voronoï cell volumes) which is intermediate between these two limiting cases, meaning that forced background turbulence decreases the level of clustering otherwise observed under ambient settling. However, the clustering strength does not monotonically decay with the relative turbulence intensity. Various mechanisms by which coherent structures can affect particle motion are discussed. It is argued that the reduced interaction time due to particle settling through the surrounding eddy (crossing trajectories) has the effect of shifting upward the range of eddies with a time-scale matching the characteristic time-scale of the particle. In the present cases this shift might bring the particles into resonance with the energetic eddies of the turbulent spectrum. Concerning the average particle settling velocity, we find very small deviations (of the order of one percent) from the value obtained for an isolated particle in ambient fluid when defining the relative velocity as an apparent slip velocity (i.e., as the difference between the averages computed separately for the velocities of each phase). This is consistent with simple estimates of the nonlinear drag effect. However, the relative velocity based upon the fluid velocity seen by each particle (computed via local averaging over a particle-attached sphere) has on average a smaller magnitude (by 5–7%) than the ambient single-particle value. PubDate: 2019-02-01 DOI: 10.1007/s00707-018-2271-7 Issue No:Vol. 230, No. 2 (2019)

Authors:Walter Fornari; Sagar Zade; Luca Brandt; Francesco Picano Pages: 413 - 430 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: 2019-02-01 DOI: 10.1007/s00707-018-2269-1 Issue No:Vol. 230, No. 2 (2019)

Authors:M. Liu; D. Bothe Pages: 623 - 644 Abstract: Multi-scale simulations have been conducted in order to predict the collision outcome bouncing versus coalescence in numerical simulations. The flow on the macroscopic scale is solved by the Volume of Fluid code FS3D. On the microscopic scale, the flow in the gas film between the colliding droplets before possible coalescence is solved by a Sub-grid-scale (SGS) model, which is derived based on the classical lubrication theory and accounts for rarefaction effects. The SGS model has been implemented in FS3D and validated by means of comparing the obtained pressure field to that computed analytically and by means of direct numerical simulations. For the coupling of the SGS model with FS3D, the pressure field obtained from the SGS model applies as a pressure boundary condition on the collision plane. Employing the intersection of the PLIC surfaces with the collision plane as a coalescence criterion, the simulation has been able to yield both coalescence and bouncing. The predicted critical Weber number so far depends on the grid resolution; hence, further developments of the multi-scale approach are still required. PubDate: 2019-02-01 DOI: 10.1007/s00707-018-2290-4 Issue No:Vol. 230, No. 2 (2019)

Authors:J. J. Derksen; A. E. Komrakova Pages: 657 - 666 Abstract: We study—through numerical simulations—a droplet sliding over a solid substrate as a result of a simple shear flow. We use a free-energy lattice Boltzmann (LB) scheme and compare its results with those of molecular dynamics (MD) simulations. According to the MD, at sufficiently low Reynolds and capillary numbers, the dimensionless sliding speed is a unique function of the equilibrium contact angle. Reproducing the MD results with LB simulations requires the use of a non-equilibrium boundary condition at the substrate and tuning a free parameter in the boundary condition. PubDate: 2019-02-01 DOI: 10.1007/s00707-018-2264-6 Issue No:Vol. 230, No. 2 (2019)

Authors:Ivan I. Argatov; Young S. Chai Abstract: A two-dimensional wear contact problem for an elastic layer and a wear-resisting punch is considered. The contact area and the contact load are assumed to be fixed, whereas the punch’s shape changes according to Archard’s law of wear with variable wear coefficient. By neglecting the effect of tangential tractions, the problem of determining the normal contact pressure is reduced to a two-dimensional integral equation containing a Fredholm coordinate operator and a Volterra time operator. By the method of separation of variables, the transient contact pressure distribution has been constructed in terms of the solutions of some eigenvalue problem. A special attention is paid to quantities of practical interest, such as the wearing-in period and the transient effective wear coefficient. PubDate: 2019-02-19 DOI: 10.1007/s00707-019-2366-9

Authors:Yunze Yang; Jihai Yuan; Mu Fan Abstract: Light-activated shape memory polymer (LaSMP) is a novel smart material, whose stiffness can be tuned by irradiating with UV light. By changing the Young’s modulus of LaSMP patches, the natural frequency of a simply supported beam laminated with LaSMP patches can be actively affected and the dynamic response of the beam can be influenced. Based on the stepped beam theory, dynamic equations were established for a simply supported beam laminated with LaSMP patches. The effect of LaSMP patch properties on the frequency variation of the first three modes was analyzed. It was found that the frequency variation range increases with increasing length. The strategy of locating the LaSMP patch pair on a single location was discussed first, and it was observed that when the LaSMP patch pair was located at antinodes of each mode, the widest frequency control range can be obtained. When multiple LaSMP patch pairs were considered, analytical results showed that the natural frequency ranges were 24.97% and 52.47% higher than by concentrating the patches on a single location for the second and third mode, respectively. When the controllable natural frequency range increases, the control capability of the LaSMP patch on the dynamic response of the beam structure increases as well. As a result, multiple LaSMP patches would have better potential for vibration control than single patches. PubDate: 2019-02-19 DOI: 10.1007/s00707-019-2370-0

Authors:Wen Wang; Jinxing Liu; Ai Kah Soh Abstract: This paper develops a single-crystal plasticity model with Johnson–Cook-type hardening laws to examine the strain rate and temperature sensitivities of magnesium (Mg). Slip, twinning and their interactions are deemed the dominant plastic mechanisms. The twinning-induced lattice reorientation is implemented by taking the initial grain after reorientation as a “new” grain with an updated orientation. Distinct strain rate and temperature dependences are considered for different slip and twinning modes. Non-basal slip is believed strain rate and temperature dependent, while compression twinning (CT) is assumed to exhibit temperature sensitivity in a certain temperature range. To validate the proposed model, plane-strain compression tests of Mg crystals under different strain rates and temperatures are simulated. The experimental data available in the literature are compared with the predicted results, and the tendencies of stress–strain curves are analyzed based on the corresponding evolution of slip and twinning. It is found that twinning-induced lattice reorientation significantly influences the mechanical behavior of Mg, especially when tension twinning (TT) dominates the plastic deformation. High temperatures and low strain rates enhance the activity of non-basal slip, and CT becomes easily activated as the temperature is increased beyond \(150\,^{\circ }\hbox {C}\) , which coincides well with experimental observations. The strain rate sensitivity rising with temperature is also predicted by the model. PubDate: 2019-02-19 DOI: 10.1007/s00707-019-2374-9

Authors:Vasily E. Tarasov; Elias C. Aifantis Abstract: In this paper, we consider extensions of the gradient elasticity models proposed earlier by the second author to describe materials with fractional non-locality and fractality using the techniques developed recently by the first author. We derive a generalization of three-dimensional continuum gradient elasticity theory, starting from integral relations and assuming a weak non-locality of power-law type that gives constitutive relations with fractional Laplacian terms, by utilizing the fractional Taylor series in wave-vector space. In the sequel, we consider more general field equations with fractional derivatives of non-integer order to describe nonlinear elastic effects for gradient materials with power-law long-range interactions in the framework of weak non-locality approximation. The special constitutive relation that we elaborate upon can form the basis for developing a fractional extension of deformation theory of gradient plasticity. Using the perturbation method, we obtain corrections to the constitutive relations of linear fractional gradient elasticity, when the perturbations are caused by weak deviations from linear elasticity or by fractional gradient non-locality. Finally, we discuss fractal materials described by continuum models in non-integer dimensional spaces. Using a recently suggested vector calculus for non-integer dimensional spaces, we consider problems of fractal gradient elasticity. PubDate: 2019-02-19 DOI: 10.1007/s00707-019-2373-x

Authors:Lewin Stein; Jörn Sesterhenn Abstract: Acoustic models of resonant duct systems with turbulent flow depend on fitted constants based on expensive experimental test series. We introduce a new model of a resonant cavity, flush mounted in a duct or flat plate, under grazing turbulent flow. Based on previous work by Goody, Howe and Golliard, we present a more universal model where the constants are replaced by physically significant parameters. This enables the user to understand and to trace back how a modification of design parameters (geometry, fluid condition) will affect acoustic properties. The derivation of the model is supported by a detailed three-dimensional direct numerical simulation as well as an experimental test series. We show that the model is valid for low Mach number flows ( \(M=0.01{-}0.14\) ) and for low frequencies (below higher transverse cavity modes). Hence, within this range, no expensive simulation or experiment is needed any longer to predict the sound spectrum. In principle, the model is applicable to arbitrary geometries: Just the provided definitions need to be applied to update the significant parameters. Utilizing the lumped-element method, the model consists of exchangeable elements and guarantees a flexible use. Even though the model is linear, resonance conditions between acoustic cavity modes and fluid dynamic unstable modes are correctly predicted. PubDate: 2019-02-19 DOI: 10.1007/s00707-018-2354-5

Authors:Robert Winkler Abstract: A hierarchic approach for the derivation of an infinite series of nonlinear \(\ell \) th-order shell theories from three-dimensional continuum mechanics based on a polynomial series expansion of the displacement field is recapitulated. Imposing the static constraints that second- and higher-order moments vanish, a ‘first-order’ shell theory is obtained without employing any kinematic constraints or geometric approximations. In particular, it is shown in full generality that, within the same theoretical framework, this static assumption, on the one hand, and a common Reissner–Mindlin-type kinematic assumption, on the other hand, lead to the same theory, for which the attribute geometrically exact is adopted from the literature. This coincidence can be interpreted as a theoretical justification for the heuristic Reissner–Mindlin assumption. Further, the unexpected but unavoidable appearance of transverse moment components (residual drill moments) is addressed and analysed. Feasible assumptions are formulated which allow to separate these drill components from the remaining balance equations without affecting the equilibrium of the standard static variables. This leads to a favourable structure of the component representation of balance equations in the sense that they formally coincide with the ones of linear shear-deformable shell theory. Finally, it is shown that this result affects the interpretation of applied boundary moments. PubDate: 2019-02-19 DOI: 10.1007/s00707-019-2367-8

Authors:V. Govorukha; A. Sheveleva; M. Kamlah Abstract: An electrically conducting crack along a part of an electrode in the interface of a piezoelectric bimaterial under the action of anti-plane mechanical and in-plane electric loadings is analyzed. The electrode is assumed to be much thinner than the piezoelectric material, and therefore, its mechanical properties are neglected. Using special representations of field variables via sectionally analytic functions, a combined Dirichlet–Riemann boundary value problem is formulated and solved analytically. Explicit expressions for the shear stress, the electric field and the crack faces’ sliding displacement are derived. These quantities are also presented graphically along the corresponding parts of the material interface. The intensity factors for stress and electric field are determined as well. The dependencies of the mentioned values on the magnitude of the external electric loading and different ratios of the crack and electrode lengths are presented. PubDate: 2019-02-16 DOI: 10.1007/s00707-019-2364-y

Authors:Ali Nili; Saeed Adibnazari; Ardavan Karimzadeh Abstract: The two-dimensional thermoelastic tractive rolling contact problem for a half-plane which is coated with a functionally graded material (FGM), under the plane strain deformation, is studied in this paper. A rigid cylinder rolls over the surface of an FGM coating with constant translational velocity, generating frictional heating in the slip zones of the contact area. Thermomechanical properties of the FGM vary exponentially along the thickness direction. It is assumed that the contact area consists of a central stick zone and two slip zones of the same sign. The transfer matrix method and Fourier integral transform technique are used to achieve a system of two Cauchy singular integral equations. The coupling effect of tangential traction is eliminated by adapting the conventional Goodman approximation. The associated governing equations are discretized by applying the Gauss–Chebyshev integration method gaining a system of linear algebraic equations. The effects of Peclet number, material properties’ grading ratios and friction coefficient on surface and in-plane stresses, stick zone boundaries and surface temperature distribution are studied. PubDate: 2019-02-16 DOI: 10.1007/s00707-019-2362-0

Authors:Adam Janečka; Josef Málek; Vít Průša; Giordano Tierra Abstract: We propose a numerical scheme for simulation of transient flows of incompressible non-Newtonian fluids characterised by a non-monotone relation between the symmetric part of the velocity gradient (shear rate) and the Cauchy stress tensor (shear stress). The main difficulty in dealing with the governing equations for flows of such fluids is that the non-monotone constitutive relation allows several values of the stress to be associated with the same value of the symmetric part of the velocity gradient. This issue is handled via a reformulation of the governing equations. The equations are reformulated as a system for the triple pressure–velocity–apparent viscosity, where the apparent viscosity is given by a scalar implicit equation. We prove that the proposed numerical scheme has—on the discrete level—a solution, and using the proposed scheme, we numerically solve several flow problems. PubDate: 2019-02-16 DOI: 10.1007/s00707-019-2372-y

Authors:Dalia Čalnerytė; Vidmantas Rimavičius; Rimantas Barauskas Abstract: This paper presents a 3D nanostructure modal vibration analysis by using finite element models. The modal frequencies and corresponding modal shapes of silicon nanowires of various thickness against length ratios are determined by solving a linear structural eigenvalue problem for the 3D solid finite element model, where surface stress effects are taken into account by using the stress stiffness matrix. The cases of fixed/fixed and fixed/free boundary conditions at the nanowire ends are investigated. The results obtained by 3D solid models and models based on the beam bending theory have been compared with each other, as well as with the results obtained elsewhere in the literature computationally and experimentally. It has been shown that the effects caused by surface stresses are insignificant for wires with length-to-width ratio less than 10. PubDate: 2019-02-14 DOI: 10.1007/s00707-019-2375-8

Authors:Tiantian Fu; Zhiwu Zhu; Chenxu Cao Abstract: To reveal the dynamic mechanical behavior of frozen soil under impact loading, nine groups of frozen-soil samples (the initial moisture content was 20%) under different experimental conditions are tested using the split Hopkinson pressure bar. In this study, a constitutive model for predicting the dynamic strength and compression deformation of frozen soil subjected to impact loading is developed. The model is derived from continuous fracture mechanics, and we assume that frozen soil is a continuous medium with preexisting microcracks. According to the modified Drucker–Prager criterion, a dynamic constitutive model coupled with the plastic and damage phase is established to describe the dynamic mechanical behavior of frozen soil before the peak stress. Considering the post-peak curve, the statistical significance of the uniform stress–strain relationship is not established; therefore, a cohesive crack model is used to model the frozen-soil softening process. Using a comparison, we find that the results of the experiment agree well with the calculated results; thus, the feasibility of the model is proven. PubDate: 2019-02-13 DOI: 10.1007/s00707-019-2369-6

Authors:Petr Beneš; Michael Valášek; Zbyněk Šika; Jan Zavřel; Jan Pelikán Abstract: The fast and precise positioning of flexible mechanical structures is often corrupted by the unwanted dynamics in the form of a residual vibration. Therefore, we would like to find an appropriate control strategy that is capable to suppress this effect. The control strategies can be basically divided into two main groups: feedback control and feedforward control. The feedback control with the information from integrated sensors is capable to ensure the stability and robustness, but it may require large actuator effort, and it may be difficult to design satisfactory controllers for rapid movements. The feedforward methods including command/input shaping are based on the model of the system and usually require no additional sensors. They can significantly eliminate residual vibration, but feedforward methods cannot deal with disturbances, and the quality of their performance is strongly determined by the precision of the used model on which they are based. This paper proposes the novel solution to these problems, the so-called SHAVO (SHAper \(+\) serVO control) strategy that combines advantages of both approaches. Compared to other methods combining command shaping and feedback controller, the SHAVO approach differs in two key features. Firstly, it uses a different structure, the model of the system is used not only for shaper synthesis but also for predicting system outputs and states. Secondly, the shaper itself is highly optimized with arbitrary adjustable time length, not an impulse series, not limited by the system’s natural frequency. PubDate: 2019-02-13 DOI: 10.1007/s00707-019-2363-z

Authors:Nikolay Dimitrov; Yucheng Liu; M. F. Horstemeyer Abstract: In this study, thermodynamic incompatibility issues of the thermo-mechanical coupling of the Bammann-temperature-dependent plasticity-damage internal state variable (ISV) model are investigated. The exclusion of the thermal expansion phenomena from the Helmholtz free energy, as assumed in the model, is proven to contradict the First and Second Law of Thermodynamics, as well as the omnipresence principle. Four different approaches are discussed to address those issues, and the inclusion of the thermal expansion as a dependent variable in the Helmholtz free energy is considered the most appropriate and efficient. Based on these findings, a multiphysics ISV theory that couples the elasto-visco-plasticity-damage model of Bammann with thermal expansion is presented in which the kinematics, thermodynamics, and kinetics are internally consistent. Other material models may benefit from the findings of this study and apply similar modifications with their thermo-mechanical couplings. PubDate: 2019-02-05 DOI: 10.1007/s00707-019-2365-x

Authors:Pengyu Pei; Yan Shi; Luqiao Qi; Cun-Fa Gao Abstract: This paper studies the effects of thermal stress on failure modes of soft matter with a sharp–hard inclusion. Two failure modes, i.e., interface failure and penetration failure, are found, and the influences of mechanical loading on each mode are discussed, respectively. Based on theoretical analysis, we get significant insight into the failure behavior of this soft–hard system. Finite element analysis is employed with consideration of the large deformation of the soft matter, and the results demonstrate the effectiveness of theoretical predictions within a large range of loads. The penetration of the soft matter is determined by the thermal expansion coefficient and the change in temperature. In addition, their effects on the categories of the failure mode are shown in a phase diagram. Suitable remote uniform stress fields can counteract the effects of thermal stresses at the tips of the inclusion and, therefore, counteract penetration or interface separation as well. This paper provides a convenient approach to evaluating failure modes and avoiding failure. PubDate: 2019-02-04 DOI: 10.1007/s00707-019-2360-2

Authors:MingKai Guo; Yuan Li; GuoShuai Qin; MingHao Zhao Abstract: A PN junction between two types of piezoelectric semiconductors (PSCs) is analyzed based on the fully coupled nonlinear equations of PSCs without any assumptions. A perturbation theory is employed to obtain the analytical solution of the considered nonlinear problem. A general solution to one-dimensional problems for PSCs is represented by a sum of a series of perturbation solutions. Typical properties including the electromechanical fields, built-in potential and the current–voltage characteristics of the piezoelectric PN junction are investigated for conditions of mechanical loading combined with a bias. The results reveal that the simplified linear (i.e., first-order perturbation) solution reported in the literature fails to describe the nonlinear characteristics, such as current–voltage characteristics of the piezoelectric PN junction, although it can give the electromechanical fields as well as concentrations of the electrons and holes near the interface of the PN junction for small carrier concentration perturbations. The presented nonlinear solution is valid and corresponds closely with the numerical solutions based on the commercial software COMSOL. PubDate: 2019-02-02 DOI: 10.1007/s00707-019-2361-1