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Technical elastomers are usually quasi-incompressible. For simulations they are, therefore, often modeled as ideal incompressible hyperelastic materials, or a linear relation between the hydrostatic pressure and the (volumetric) d...
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Technical elastomers are usually quasi-incompressible. For simulations they are, therefore, often modeled as ideal incompressible hyperelastic materials, or a linear relation between the hydrostatic pressure and the (volumetric) dilation is assumed, i.e., a linear compression model with constant bulk modulus is used. However, for strongly compressed structural components, like sealings or damper elements, a nonlinear compression model might be required as well, in order to achieve accurate results. In general, the numerical ill-posedness of irreducible (purely displacement-based) finite element formulations for quasiincompressible materials demands for a hybrid/mixed finite element implementation. State of the art hybrid/mixed-elements still suffer from numerical stability issues that can be greatly amplified by the usage of nonlinear compression models. In the talk, a robust hybrid-element family is introduced that can readily be used in combination with any isotropic, invariant-based hyperelastic material model. The mesh convergence behavior and the numerical stability of the new element family are assessed by benchmark testing and compared to classical Simo-Taylor-Pister (STP) elements as well as the hybridelement family (C3D8H, C3D20H, C3D10H) implemented in the commercial finite element code Abaqus Standard, Simulia (Dassault Systèmes). The presented finite element family is free of volumetric locking and more robust than STP or Abaqus hybrid-elements, especially in combination with strongly nonlinear compression models.
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With a universally accepted abuse of terminology, materials having much larger stiffness for volumetric than for shear deformations are called incompressible. This work proposes two approaches for the evaluation of the correct for...
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With a universally accepted abuse of terminology, materials having much larger stiffness for volumetric than for shear deformations are called incompressible. This work proposes two approaches for the evaluation of the correct form of the linear elasticity tensor of so-called incompressible materials, both stemming from non-linear theory. In the approach of strict incompressibility, one imposes the kinematical constraint of isochoric deformation. In the approach of quasi-incompressibility, which is often employed to enforce incompressibility in numerical applications such as the Finite Element Method, one instead assumes a decoupled form of the elastic potential (or strain energy), which is written as the sum of a function of the volumetric deformation only and a function of the distortional deformation only, and then imposes that the bulk modulus be much larger than all other moduli. The conditions which the elasticity tensor has to obey for both strict incompressibility and quasi-incompressibility have been derived, regardless of the material symmetry. The representation of the linear elasticity tensor for the quasi-incompressible case differs from that of the strictly incompressible case by one parameter, which can be conveniently chosen to be the bulk modulus. Some important symmetries have been studied in detail, showing that the linear elasticity tensors for the cases of isotropy, transverse isotropy and orthotropy are characterised by one, three and six independent parameters, respectively, for the case of strict incompressibility, and two, four and seven independent parameters, respectively, for the case of quasi-incompressibility, as opposed to the two, five and nine parameters, respectively, of the general compressible case.
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In the present paper, we make an attempt to explain the formation of complicated turbulent spectra on the basis of an asymptotic approach. It is shown that complicated spectra formation is due to two factors. On the one hand, the ...
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In the present paper, we make an attempt to explain the formation of complicated turbulent spectra on the basis of an asymptotic approach. It is shown that complicated spectra formation is due to two factors. On the one hand, the zone of energy generation by external sources, their scales, topological properties and other features affect the behavior of an adjacent region of the inertial interval. On the other hand, the dissipation zone affects the remaining region of the inertial interval. (c) 2006 Elsevier B.V. All rights reserved.
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Accurate prediction of oil dispersion has been challenging due to its highly deformed/dispersed interface as well as small-scale oil-water mixing. In this paper, a refined Incompressible SPH (Smoothed Particle Hydrodynamics)-based...
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Accurate prediction of oil dispersion has been challenging due to its highly deformed/dispersed interface as well as small-scale oil-water mixing. In this paper, a refined Incompressible SPH (Smoothed Particle Hydrodynamics)-based method is proposed for simulations of oil spill problems. In the proposed method, the presence of oil is taken into consideration with concentration function and physical properties of computational points (particles), i.e. density and viscosity, are varied based on the concentration of oil. The proposed method incorporates a LES-based turbulence model, namely SPS (Sub-Particle-Scale) turbulence model, in order to capture small-scale turbulence effects. Diffusion equation is further implemented so as to reproduce the sub-particle-scale oil-water mixing effects. Interfacial surface tension is considered through potential-based modeling with consideration of the highly deformed/dispersed interface. A set of previously proposed refined schemes are also applied for accurate/robust simulations. The stability and accuracy of proposed ISPH-based method are investigated by conducting benchmark tests.
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Models of incompressible and slightly compressible magnetostrictive materials are introduced. They are given by the free energy functionals which depend on magnetization and elastic deformation as well as on their gradients. We de...
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Models of incompressible and slightly compressible magnetostrictive materials are introduced. They are given by the free energy functionals which depend on magnetization and elastic deformation as well as on their gradients. We demonstrate the existence of minimum of an energy functional for a slightly compressible material. We also prove a theorem on convergence of a sequence of minimizers of less and less compressible material energy functionals to a minimizer of energy of incompressible material. Besides the existence of solution of the incompressible magnetostrictive problem is obtained.
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We consider the flows of ideal (Euler equations) and Newtonian viscous (Navier-Stokes equations) incompressible fluids in the gravitational field of mass forces. In this case, the gravitational field created by the liquid itself (...
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We consider the flows of ideal (Euler equations) and Newtonian viscous (Navier-Stokes equations) incompressible fluids in the gravitational field of mass forces. In this case, the gravitational field created by the liquid itself (self-gravity) is also taken into account. It is shown that some well-known principles of maximum pressure, according to which either the pressure is constant in the flow region, or the minimum pressure is reached at the boundary of this region if the forces of self-gravity are taken into account, exclude the case of constant pressure. It is also demonstrated that self-gravity makes it impossible for waves and solitons to pass with pressure minima to the surface of a body flown around by a viscous fluid.
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This work deals with the computation of incompressible thermal flow under the Boussinesq hypothesis, and a characteristic projection method is proposed for this. First, characteristic temporal discretization is used to obtain an u...
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This work deals with the computation of incompressible thermal flow under the Boussinesq hypothesis, and a characteristic projection method is proposed for this. First, characteristic temporal discretization is used to obtain an upwind scheme, then at each time step the energy equation can be decoupled from momentum equations. For the remaining Stokes problem we present an improved projection method, which can overcome the numerical boundary-layer problem of the traditional projection method. In conclusion, only three independent linear elliptic equations need to be calculated at each time step; moreover, the stiffness matrices of finite-element approximation are symmetrical, positive, and time-invariant.
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This paper is dedicated to the global well-posedness issue of the incompressible Oldroyd-B model in the whole space R~d with d ≥ 2. It is shown that this set of equations admits a unique global solution in a certain critical L p-...
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This paper is dedicated to the global well-posedness issue of the incompressible Oldroyd-B model in the whole space R~d with d ≥ 2. It is shown that this set of equations admits a unique global solution in a certain critical L p-type Besov space provided that the initial data, but not necessarily the coupling parameter, is small enough. As a consequence, even through the coupling effect between the equations of velocity u and the symmetric tensor of constrains τ is not small, one may construct the unique global solution to the Oldroyd-Bmodel for a class of large highly oscillating initial velocity. The proof relies on the estimates of the linearized systems of (u, τ) and (u, Pdivτ) which may be of interest for future works. This result extends thework by Chemin and Masmoudi (SIAM J Math Anal 33:84-112, 2001) to the non-small coupling parameter case.
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We study the incompressible limit for the full Navier-Stokes-Fourier system on unbounded domains with boundaries, supplemented with the complete slip boundary condition for the velocity field. Using an abstract result of Tosio Kat...
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We study the incompressible limit for the full Navier-Stokes-Fourier system on unbounded domains with boundaries, supplemented with the complete slip boundary condition for the velocity field. Using an abstract result of Tosio Kato we show that the energy of acoustic waves decays to zero on any compact subset of the physical space. This in turn implies strong convergence of the velocity field to its limit in the incompressible regime.
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We construct a hyperbolic 3-manifold M (with partial derivative M totally geodesic) which contains no essential closed surfaces, but for any even integer g > 0, there are infinitely many separating slopes r on partial derivative M...
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We construct a hyperbolic 3-manifold M (with partial derivative M totally geodesic) which contains no essential closed surfaces, but for any even integer g > 0, there are infinitely many separating slopes r on partial derivative M so that M[r], the 3-manifold obtained by attaching 2-handle to M along r, contains an essential separating closed surface of genus g and is still hyperbolic. The result contrasts sharply with those known finiteness results for the cases g = 0, 1. Our 3-manifold M is the complement of a simple small knot in a handlebody.
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