A sufficient condition for a positive definite configuration tensor in differential models

Analogous to the Giesekus theory it is possible to identify a positive definite (configuration) tensor in other theories for dfferential models. For a rather general class of differential models a simple condition is given that is sufficient to prove that such tensors are positive definite

The deformation fields method revisited:Stable simulation of instationary viscoelastic fluid flow using integral models

\u3cp\u3eThe implementation of the deformation fields method for integral models within a finite element context [1,2] has been updated with various techniques to have a numerical stability that is comparable to state-of-the-art implementations of differential models. In particular, the time-dependent stability in shear flow, decoupled schemes for zero or small solvent viscosities and the log-conformation representation now have counterparts in the numerical implementation of integral models leading to similar numerical stability. The new techniques have been tested in transient shear flow and the flow around a cylinder confined between two plates for the integral version of upper-convected Maxwell model and for integral models having a non-constant damping function.\u3c/p\u3

Flow of viscoelastic fluids past a cylinder at high Weissenberg number : stabilized simulations using matrix logarithms

The log conformation representation proposed in Fattal et al. has been implemented in a FEM context using the DEVSS/DG formulation for viscoelastic fluid flow. We present a stability analysis in 1D and identify the failure of the numerical scheme to balance exponential growth as a possible source for numerical instabilities at high Weissenberg numbers. A different derivation of the log based evolution equation than in Fattal at al. is also presented. We show numerical results for the flow around a cylinder for an Oldroyd-B and a Giesekus model. We provide evidence that the numerical instability identified in the 1D problem is also the actual reason for the failure of the standard FEM implementation of the problem. With the log conformation representation we are able to obtain solutions beyond the limiting Weissenberg numbers in the standard scheme. In particular, for the Giesekus model the improvement is rather dramatic: there does not seem to be a limit for the chosen model parameter(alpha=0.01). However, it turns out that although in large parts of the flow the solution converges, we have not been able to obtain convergence in localized regions of the flow. Possible reasons include artefacts of the model and unresolved small scales. However, more work is necessary, including the use of more refined meshes and/or higher-order schemes, before any conclusion can be made on the local convergence problems

Problems, Analysis and solutionsof the equations for viscoelastic flow

After summarizing the basic equations, the type of the equations for theupper-convected Maxwell model and for the Jeffreys-type models is derived.It is shown that the corotational Maxwell model changes type which isunacceptable from a physical point of view. The Jeffreys-type models(including the Leonov model) have a drastic different type compared to theMaxwell models and are physically more appealing. Correct boundaryconditions are briefly discussed for a linearized upper-convected Maxwellmodel. The boundary conditions for the Jeffreys models are shown to be equalto the boundary conditions for the Navier-Stokes equations, supplemented byboundary conditions for all the extra stresses at the inflow boundary. Jumpconditions are derived for Jeffreys-type models. It is shown that in complexflows with sharp co! rners discontinuities may arise. Numerical methods arediscussed that take into account the special type of the equations

Transient 3D finite element method for predicting extrudate swell of domains containing sharp edges

\u3cp\u3eA new transient 3D finite element method for predicting extrudate swell of domains containing sharp edges is proposed. Here, the sharp edge is maintained over a large distance in the extrudate by describing the corner lines as material lines. The positions of these lines can be used to describe the transverse swelling of the 2D free surfaces and expand the domain over which a 2D height function on the free surfaces is applied. Solving the 2D height functions gives the positions of the free surfaces. First a 2D axisymmetric case was tested for comparison, using three different constitutive models. The Giesekus, linear Phan-Thien Tanner (PTT) and exponential PTT constitutive models all showed convergence upon mesh- and time-step refinement. It was found that convergence remains challenging due to the singularity at the die exit. The new method is validated by comparing the final volume change of the extrudate of a 3D cylinder to the final volume change of a reference mesh of the 2D axisymmetric case. Finally, simulations were performed for different, complex, die shapes for a viscous fluid and for viscoelastic fluids. The results compared favorably with literature. Viscoelastic results, using the Giesekus model and the exponential PTT model, were compared for different Weissenberg numbers and different values for the non-linear parameters of the constitutive models. It was found that the swell is highly dependent on the rheological parameters and the constitutive model used.\u3c/p\u3

Multi-Material 3D Food Printing Towards Simulation Driven Powder Depositor Design

3D food printing is a new and rapidly developing technology capable of creating entirely new food structures. One of the challenges in 3D food printing is the creation of a multi-material object from a powder bed. A key challenge is the deposition of a variety of powders in order to create a multi-material powder bed. Simulating powder flow of the deposition process is done with a 2D Discrete Element Method (DEM) model capable of simulating arbitrarily shaped powder particles. \u3cbr/\u3