Incompressible Medium Research Articles

Erratum to: “Plane stress state problems for notched bodies whose plastic properties depend on the form of the stress state”

We consider one possible approach to the problem of describing the dependence of material plastic strain characteristics on the stress hydrostatic component arising in many porous, fractured, and other inhomogeneous materials. The plastic strain of the media under study is investigated under the plasticity assumption in the corresponding generalized form with the use of the form parameter of the stress state. The plasticity constitutive relations are stated on the basis of the plastic flow law associated with the accepted plasticity condition. For the conditions of plane stress state in the framework of the material rigid-plastic model, a system of partial differential equations is obtained and conditions for its hyperbolicity are determined. The relations for determining the stress fields and velocity fields in plastic domains are obtained, and their properties are investigated. The problem of tension of a strip with symmetric angular notches is solved, where the stress fields are determined and the continuous displacement rate field is constructed. The problem of uniform symmetric tension of a plane with a circular hole is considered. The stress fields in a strip with symmetric circular notches are examined. A comparison with solutions for plastically incompressible media whose properties are invariant with respect to the form of the stress state is performed.

The Method of Discrete-Continuous Research for Hydraulic Calculations of Circular Distribution Network Lines with Uniform Gridiron Selection

Taking into account the main power factors and laminar flow of compressible and incompressible media have developed a method of hydraulic calculation of the exact circular pipe with one node approach and the limited number of the travel selection.

Growth of confined cancer spheroids: a combined experimental and mathematical modelling approach

A critical step in the dissemination of ovarian cancer is the formation of multicellular spheroids from cells shed from the primary tumour. The objectives of this study were to apply bioengineered three-dimensional (3D) microenvironments for culturing ovarian cancer spheroids in vitro and simultaneously to build on a mathematical model describing the growth of multicellular spheroids in these biomimetic matrices. Cancer cells derived from human epithelial ovarian carcinoma were embedded within biomimetic hydrogels of varying stiffness and grown for up to 4 weeks. Immunohistochemistry, imaging and growth analyses were used to quantify the dependence of cell proliferation and apoptosis on matrix stiffness, long-term culture and treatment with the anti-cancer drug paclitaxel. The mathematical model was formulated as a free boundary problem in which each spheroid was treated as an incompressible porous medium. The functional forms used to describe the rates of cell proliferation and apoptosis were motivated by the experimental work and predictions of the mathematical model compared with the experimental output. This work aimed to establish whether it is possible to simulate solid tumour growth on the basis of data on spheroid size, cell proliferation and cell death within these spheroids. The mathematical model predictions were in agreement with the experimental data set and simulated how the growth of cancer spheroids was influenced by mechanical and biochemical stimuli including matrix stiffness, culture duration and administration of a chemotherapeutic drug. Our computational model provides new perspectives on experimental results and has informed the design of new 3D studies of chemoresistance of multicellular cancer spheroids.

An inhomogeneous boundary value problem for the stationary motion equations of Jeffreys viscoelastic medium

We consider the inhomogeneous Dirichlet problem for the stationary motion equations of an incompressible viscoelastic medium of Jeffreys type. We prove the existence of weak solutions of this problem. Moreover, we show that the weak solution set is sequentially weakly closed.

The development and deceleration of the flow of an elastoplastic medium in a cylindrical tube*

An exact solution of the quasistatic problem of elastoplastic theory of the development of the flow of an incompressible medium in a cylindrical tube of circular cross section due to an increase in the pressure drop with time, and on the subsequent flow when there is a constant pressure and a deceleration due to its slow reduction. The conditions for the occurrence and regularity of the advancement of the elastoplastic boundaries for different types of loading are indicated.

A Hybrid Approach for the Simulation of the Thermal Motion of a Nearly Neutrally Buoyant Nanoparticle in an Incompressible Newtonian Fluid Medium

A hybrid scheme based on Markovian fluctuating hydrodynamics of the fluid and a non-Markovian Langevin dynamics with the Ornstein-Uhlenbeck noise perturbing the translational and rotational equations of motion of a nanoparticle is employed to study the thermal motion of a nearly neutrally buoyant nanoparticle in an incompressible Newtonian fluid medium. A direct numerical simulation adopting an arbitrary Lagrangian-Eulerian based finite element method is employed in simulating the thermal motion of the particle suspended in the fluid contained in a cylindrical vessel. The instantaneous flow around the particle and the particle motion are fully resolved. The numerical results show that (a) the calculated temperature of the nearly neutrally buoyant Brownian particle in a quiescent fluid satisfies the equipartition theorem; (b) the translational and rotational decay of the velocity autocorrelation functions result in algebraic tails, over long time; (c) the translational and rotational mean square displacements of the particle obeys Stokes-Einstein and Stokes-Einstein-Debye relations, respectively; and (d) the parallel and perpendicular diffusivities of the particle closer to the wall are consistent with the analytical results, where available. The study has important implications for designing nanocarriers for targeted drug delivery.

Establishing experiments to find material functions in tensor nonlinear constitutive relations

The basic scheme of an establishing experiment to find two material functions of two invariants in the constitutive relations of a nonlinear incompressible tensor medium, is described. A combination of radial spreading and two one-dimensional shears in mutually perpendicular directions observed in a cylindrical layer is taken as the base flow of such a medium. Percolation is possible at the boundaries of cylinders, but the so-called tangential component of the medium coincides with the velocity of cylinder motion. The fundamental question of a viscous potential existing for each medium is posed.

Stress field and spin axis relaxation for inelastic triaxial ellipsoids

A compact formula for the stress tensor inside a self-gravitating, triaxial ellipsoid in an arbitrary rotation state is given. It contains no singularity in the incompressible medium limit. The stress tensor and the quality factor model are used to derive a solution for the energy dissipation resulting in the damping (short-axis mode) or excitation (long axis) of wobbling. In the limit of an ellipsoid of revolution, we compare our solution with earlier ones and show that, with appropriate corrections, the differences in damping times estimates are much smaller than it has been claimed.

Collapse of a single bubble in a Shvedov-Bingham fluid under pulsating external pressure

The behavior of a spherical bubble in an ideal fluid, a viscous medium, and an incompressible viscoplastic medium with a yield stress is studied numerically and analytically when a time-varying periodic pressure is exerted at a sufficient distance from the surface of the bubble. Various modes of collapse are examined and classified. The critical values of the key parameters that characterize the behavior of this system are found; one of these parameters is the dimensionless frequency of external pressure fluctuations.

Nanocarrier–Cell Surface Adhesive and Hydrodynamic Interactions: Ligand–Receptor Bond Sensitivity Study

A hybrid approach combining fluctuating hydrodynamics with generalized Langevin dynamics is employed to study the motion of a neutrally buoyant nanocarrier in an incompressible Newtonian stationary fluid medium. Both hydrodynamic interactions and adhesive interactions are included, as are different receptor-ligand bond constants relevant to medical applications. A direct numerical simulation adopting an arbitrary Lagrangian-Eulerian based finite element method is employed for the simulation. The flow around the particle and its motion are fully resolved. The temperatures of the particle associated with the various degrees of freedom satisfy the equipartition theorem. The potential of mean force (or free energy density) along a specified reaction coordinate for the harmonic (spring) interactions between the antibody and antigen is evaluated for two different bond constants. The numerical evaluations show excellent comparison with analytical results. This temporal multiscale modeling of hydrodynamic and microscopic interactions mediating nanocarrier motion and adhesion has important implications for designing nanocarriers for vascular targeted drug delivery.

Nonlinear analysis of a wave motion on the surface of a jet moving in a dielectric medium placed in a longitudinal electric field

The possibility of degenerate internal nonlinear resonance interaction between capillary waves with arbitrary symmetry (arbitrary azimuthal numbers) on the surface of a charged cylindrical jet of an ideal incompressible conducting liquid is demonstrated. The jet moves in an ideal incompressible dielectric medium collinearly with an external uniform electrostatic field. It is shown, in particular, that six different resonance situations take place for axisymmetric waves in which primary waves and waves due to the nonlinearity of the equations of hydrodynamics exchange energy.

The motion of charged insulating fine particles in the apparatus of the electron-ion technology

The problems of numerical simulation of the motion of small charged particles in an incompressible viscous medium under the influence of gravitational and electrostatic fields.

Flows of a Bingham-Il’Yushin viscoplastic medium in a symmetric channel of variable width

Flows of a viscoplastic incompressible medium in a channel of periodically varying width are numerically simulated. The effect of the yield stress and the boundary perturbation amplitude on the distribution of rigid zones is studied.

A hybrid formalism combining fluctuating hydrodynamics and generalized Langevin dynamics for the simulation of nanoparticle thermal motion in an incompressible fluid medium

A novel hybrid scheme based on Markovian fluctuating hydrodynamics of the fluid and a non-Markovian Langevin dynamics with the Ornstein–Uhlenbeck noise perturbing the translational and rotational equations of motion of the nanoparticle is employed to study the thermal motion of a nanoparticle in an incompressible Newtonian fluid medium. A direct numerical simulation adopting an arbitrary Lagrangian–Eulerian (ALE) based finite element method (FEM) is employed in simulating the thermal motion of a particle suspended in the fluid confined in a cylindrical vessel. The results for thermal equilibrium between the particle and the fluid are validated by comparing the numerically predicted temperature of the nanoparticle with that obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation function (VACF) and mean squared displacement (MSD) with well-known analytical results. For nanoparticle motion in an incompressible fluid, the fluctuating hydrodynamics approach resolves the hydrodynamics correctly but does not impose the correct equipartition of energy based on the nanoparticle mass because of the added mass of the displaced fluid. In contrast, the Langevin approach with an appropriate memory is able to show the correct equipartition of energy, but not the correct short- and long-time hydrodynamic correlations. Using our hybrid approach presented here, we show for the first time, that we can simultaneously satisfy the equipartition theorem and the (short- and long-time) hydrodynamic correlations. In effect, this results in a thermostat that also simultaneously preserves the true hydrodynamic correlations. The significance of this result is that our new algorithm provides a robust computational approach to explore nanoparticle motion in arbitrary geometries and flow fields, while simultaneously enabling us to study carrier adhesion mediated by biological reactions (receptor–ligand interactions) at the vessel wall at a specified finite temperature.

Hydroforging of Thick-Walled Hollow Aluminum Profiles

Lightweight design of cars is one way to reduce fuel consumption and increase the range of cars. This is an important factor to attain the EU limit values for CO2 emissions for vehicles and so to escape penalties for exceeding these limits as of the year 2012. The increasing uses of high-strength steels or of lightweight structures are adequate means to reducing weight. At IPH – Institut für Integrierte Produktion Hannover gGmbH a method to produce hollow profiles made of aluminum was developed. The method combines flashless forging and tube hydroforming. This is called hydroforging. With this method it is possible to produce thick-walled hollow aluminum profiles with undercuts without complex tool kinematics. The forging is supported by an active medium. A tool concept has been developed that uses the drives of a hydraulic press with die cushion. With this tool various component geometries were produced and analysed. To produce the tools interior pressure and the forming pressure liquid tin as incompressible active medium was used. The forming is initiated by an upsetting of the aluminum profiles and supported by the active medium, so that the profile is pushed against the engraving of the dies. The process was designed based on simulations and verified by practical experiments. This paper describes the development of the forging process with active medium and the discussion of the forging experiment results.

Antiplane Wave Scattering from a Cylindrical Void in a Pre-Stressed Incompressible Neo-Hookean Material

AbstractAn isolated cylindrical void is located inside an incompressible nonlinear-elastic medium whose constitutive behaviour is governed by a neo-Hookean strain energy function. In-plane hydrostatic pressure is applied in the far-field so that the void changes its radius and an inhomogeneous region of deformation arises in the vicinity of the void. We consider scattering from the void in the deformed configuration due to an incident field (of small amplitude) generated by a horizontally polarized shear (SH) line source, a distance r0 (R0) away from the centre of the void in the deformed (undeformed) configuration. We show that the scattering coefficients of this scattered field are unaffected by the pre-stress (initial deformation). In particular, they depend not on the deformed void radius a or distance r0, but instead on the original void size A and original distance R0.

On the basically single-type excitation source of resonance in the wind tunnel and in the hydroturbine channel of a hydraulic power plant

We have investigated the spectra of pressure pulsations in the near field of the open working section of the wind tunnel with a vortex flow behind the tunnel blower formed like the flow behind the hydroturbine of a hydraulic power plant. We have made a comparison between the measurement data for pressure pulsations and the air stream velocity in tunnels of the above type and in tunnels in which a large-scale vortex structure behind the blower is not formed. It has been established that the large-scale vortex formation in the incompressible medium behind the blade system in the wind tunnel is a source of narrow-band acoustic radiation capable of exciting resonance self-oscillations in the tunnel channel.

Effect of Non-Uniform Temperature Gradients on the Onset of Convection in a Couple-Stress Fluid-Saturated Porous Medium

The effect of different forms of basic temperature gradients on the criterion for the onset of convection in a layer of an incompressible couple-stress fluid-saturated porous medium is investigated. It is shown that the principle of exchange of stability is valid, and the eigenvalue problem is solved numerically using the Galerkin technique. The parabolic and inverted parabolic basic temperature profiles have the same effect on the onset of convection and similar is the case between piecewise linear temperature profiles heating from below and above. Amongst the various basic temperature profiles, the linear temperature profile is found to be more stabilizing on the onset of instability. In addition, the influence of thermal depth on the criterion for the onset of convection is assessed in the case of piecewise linear temperature profiles. Moreover, an increase in the value of couple-stress parameter is found to delay the onset of convection and to increase the width of convection cells. It is also noted that the critical wave numbers are slightly affected by the nature of basic temperature profiles.

CFD 기반 유체충격 해석에서 공기 압축성 효과

This paper describes the air compressibility effect in the CFD simulation of water impact load prediction. In order to consider the air compressibility effect, two sets of governing equations are employed, namely the incompressible Navier-stokes equations and compressible Navier-Stokes equations that describe general compressible gas flow. In order to describe violent motion of free surface, volume-of-fluid method is utilized. The role of air compressibility is presented by the comparative study of water impact load obtained from two different air models, i.e. the compressible and incompressible air. For both cases, water is considered as incompressible media. Compressible air model shows oscillatory behavior of pressure on the solid surface that may attribute to the air-cushion effect. Incompressible air model showed no such oscillatory behavior in the pressure history. This study also showed that the CFD simulation can capture the formation of air pockets enclosed by water and solid surface, which may be the location where the air compressibility effect is dominant.

On the stability of a cylindrical jet moving in a material medium along an external electrostatic field

A dispersion relation is derived for capillary waves with arbitrary symmetry (with arbitrary azimuthal numbers) on the surface of a jet of an ideal incompressible dielectric liquid moving in an ideal incompressible dielectric medium along an external uniform electrostatic field. A tangential discontinuity in the velocity field on the jet surface is shown to cause Kelvin-Helmholtz periodical instability at the interface and destabilize axisymmetric, flexural, and flexural-deformational waves. Both the flexural and flexural-deformational instabilities have a threshold and are observed not at an arbitrarily small velocity of the jet but starting from a certain finite value. It is shown that the instability of waves generated by the tangential discontinuity of the velocity field is periodic only formally (from the pure mathematical point of view). Actually, the jet disintegrates within the time of instability development, which is shorter than the half-cycle of the wave.