Progress in mixed Eulerian-Lagrangian finite element simulation of forming processes

A review is given of a mixed Eulerian-Lagrangian finite element method for simulation of forming processes. This method permits incremental adaptation of nodal point locations independently from the actual material displacements. Hence numerical difficulties due to large element distortions, as may occur when the updated Lagrange method is applied, can be avoided. Movement of (free) surfaces can be taken into account by adapting nodal surface points in a way that they remain on the surface. Hardening and other deformation path dependent properties are determined by incremental treatment of convective terms. A local and a weighed global smoothing procedure is introduced in order to avoid numerical instabilities and numerical diffusion. Prediction of contact phenomena such as gap openning and/or closing and sliding with friction is accomplished by a special contact element. The method is demonstrated by simulations of an upsetting process and a wire drawing process

Steady-State Properties of Single-File Systems with Conversion

We have used Monte-Carlo methods and analytical techniques to investigate the influence of the characteristic parameters, such as pipe length, diffusion, adsorption, desorption and reaction rate constants on the steady-state properties of Single-File Systems with a reaction. We looked at cases when all the sites are reactive and when only some of them are reactive. Comparisons between Mean-Field predictions and Monte-Carlo simulations for the occupancy profiles and reactivity are made. Substantial differences between Mean-Field and the simulations are found when rates of diffusion are high. Mean-Field results only include Single-File behavior by changing the diffusion rate constant, but it effectively allows passing of particles. Reactivity converges to a limit value if more reactive sites are added: sites in the middle of the system have little or no effect on the kinetics. Occupancy profiles show approximately exponential behavior from the ends to the middle of the system.Comment: 15 pages, 20 figure

Transient behavior in Single-File Systems

We have used Monte-Carlo methods and analytical techniques to investigate the influence of the characteristics, such as pipe length, diffusion, adsorption, desorption and reaction rates on the transient properties of Single-File Systems. The transient or the relaxation regime is the period in which the system is evolving to equilibrium. We have studied the system when all the sites are reactive and when only some of them are reactive. Comparisons between Mean-Field predictions, Cluster Approximation predictions, and Monte Carlo simulations for the relaxation time of the system are shown. We outline the cases where Mean-Field analysis gives good results compared to Dynamic Monte-Carlo results. For some specific cases we can analytically derive the relaxation time. Occupancy profiles for different distribution of the sites both for Mean-Field and simulations are compared. Different results for slow and fast reaction systems and different distribution of reactive sites are discussed.Comment: 18 pages, 19 figure