Thermomechanical modeling and simulation of aluminum alloys during extrusion process

The purpose of this work is to simulate the microstructure development of aluminum alloys during hot metal forming processes such as extrusion with the help of the Finite Element Method (FEM). To model the thermomechanical coupled behavior of the material during the extrusion process an appropriate material model is required. In the current work a Johnson–Cook like thermoelastic viscoplastic material model is used. To overcome the numerical difficulties during simulation of extrusion such as contact problem and element distortion an adaptive meshing system is developed and applied. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling and simulation of extrusion of aluminum alloys

The purpose of this work is the modeling and simulation of the material behavior of aluminum alloys during extrusion, cooling and metal forming processes. In particular, the alloys of the 6000 series (Al-Mg-Si) and 7000 series (Al-Zn-Mg) are relevant here. Under the corresponding conditions, their behavior is controlled mainly by dynamic recovery during the extrusion and static recrystallization during cooling. The current material model is based on the role of the energy stored in the material during extrusion as the driving force for microstructural evolution. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling and simulation of extrusion of aluminum alloys

The purpose of this work is the modeling and simulation of the material behavior of aluminum alloys during extrusion, cooling and metal forming processes. In particular, the alloys of the 6000 series (Al-Mg-Si) and 7000 series (Al-Zn-Mg) are relevant here. Under the corresponding conditions, their behavior is controlled mainly by dynamic recovery during the extrusion and static recrystallization during cooling. The current material model is based on the role of the energy stored in the material during extrusion as the driving force for microstructural evolution. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Damage processes coupled with phase separation in elastically stressed alloys

In micro-electronic materials such as solder alloys, phase-separation and coarsening as well as damage phenomena occur at the same time and influences each other. In this note, a unifying model which couples multi-component Cahn-Hilliard systems with elasticity and uni-directional damage processes is presented. We outline the equations and their initial-boundary conditions in a classical setting and cite some existence results for weak solutions recently proved in [8, 9]. The damage is assumed to be incomplete, i.e. the maximal damaged material parts still feature elastic properties. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On an implicit particle method for simulation of forming processes

Task is the simulation of forming processes using particle methods. We implemented some mesh-free methods (the element free Galerkin method [1] and others) and the finite element method in one programme system which permits a direct comparison. For the mesh-free methods a moving least squares approximation is applied. The shape functions are not zero or one at the nodes, thus essential boundary conditions cannot be imposed directly [2]. We use a penalty method to enforce essential boundary conditions and contact conditions. The contact algorithm (normal contact of nodes to C¹-continuous surfaces) is checked by means of the element free Galerkin method and the FEM on the basis of numerical examples which deal with forming processes. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Phase-field-based modeling and simulation of solidification and deformation behavior of technological alloys

The purpose of this work is the formulation and application of a continuum field approach to the phenomenological modeling of the behavior of technological alloys undergoing phase transitions and attendant inelastic deformation. To describe the phase transition, a phase–field approach is utilized. For the fully coupled system, an algorithmic formulation is derived based on efficient finite element techniques. Applications will be discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental and theoretical investigation on the microstructure of aluminum alloys during extrusion

The purpose of this work is the investigation of the material behavior of aluminum alloys during extrusion and cooling. In particular, the alloys of the 6000 series (Al–Mg–Si) and 7000 series (Al–Zn–Mg) are relevant here. Under the corresponding conditions, their behavior is controlled mainly by dynamic recovery during the extrusion and static recrystallization during cooling. For the development of a suitable material model EBSD measurements are done on different parts of an extruded Al6060 specimen. For this sample a microstructure picture is generated and a statistical analysis is performed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

3D dynamic modeling of powder forming processes via a simple and efficient node-to-surface contact algorithm

In this paper, a simple and efficient contact algorithm is presented for the evaluation of density distribution in three-dimensional dynamic modeling of powder compaction processes. The contact node-to-surface algorithm is employed to impose the contact constraints in large deformation frictional contact, and the contact frictional slip is modified by the Coulomb friction law to simulate the frictional behavior between the rigid punch and the work-piece. The 3D nonlinear contact friction algorithm is employed together with a double-surface cap plasticity model within the framework of large finite element deformation in order to predict the non-uniform relative density distribution during the dynamic simulation of powder die-pressing. The accuracy and robustness of contact algorithm is verified by the impact analysis of two elastic rods, which is compared with the analytical solution. Finally, the performance of computational schemes is illustrated in dynamic modeling of a set of powder components.     

Application and evaluation of hyper- and hypoelastic-based plasticity models in the FE simulation of metal forming processes

Metal forming processes are usually accompanied by large plastic strains and rotations of the material elements which emphasizes the need for reliable finite strain elastoplasticity models in corresponding FE simulations. In this work, two specific finite strain hyper- and hypoelastic-based plasticity models with combined nonlinear isotropic and kinematic hardening are presented and compared in numerical FE simulations. Although both models led to remarkably different results in a shear-dominated single element deformation test, the structural simulation of a standard deep drawing process delivered nearly congruent results which suggests that both models are equally well-suited for modeling metals in common forming processes. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical modeling of the processes occurring during high-temperature spray coating

We give a generalization of the mathematical model of the processes occurring in the preparation of gasthermal coatings in order to compute the radiation energy, thermal effects of turbulent flow of the gas jet of a plasmotron, spraying distance and required degree of preliminary heating of the base. The boundary conditions obtained describe the radiational/convective heat exchange of bodies with a medium through thin coatings taking account of the speed of flow of the gas jet.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 33, 1991, pp. 13–18.     

Mathematical modeling of industrial aluminum electrolysis

The problem of aluminum electrolysis is discussed. The mathematical model of an industrial electrolyzer presented in the paper is written under the assumption that the electrolyte and metal media are immiscible. At the basis of the mathematical statement is a three-dimensional, nonstationary, and nonlinear system of magnetic hydrodynamics equations which is written separately in the aluminum medium and in the electrolyte medium with a geometric account for wall accretion, skull, and arrangement of anodes. The proposed system allows one to model various forms of anodes, the number of anodes in a bath, and their sizes. Interfaces of media are connected by a viscous friction. Initial values of speeds and electromagnetic fields in the media and the medium interface are considered as set. On the skull, bottom, and anodes the attachment conditions are set. The speed of change of a magnetic field in the metal and electrolyte on the interface is considered zero. On the basis of a numerical method of solution of the system of equations, there is a well-proved method of division over physical processes. The analysis of results of the numerical experiment has shown that it is actually possible to allocate a ??middle?? layer for modeling of the electrolysis process. The proposed model allows one to investigate media behavior upon the occurrence of a long anode effect due to sharp reduction of the electric conductivity of the electrolyte and subsequent sharp growth of the electric-field strength.     

Mathematical modeling of demographic processes

The article examines a mathematical model that describes the dynamics of the total population and its age structure. Time-dependent birth and death rates are assumed. The mathematical model is a first-order partial differential equation. The analytical solution makes it possible to determine the age distribution at each time instant depending on the birth and death functions and the initial distribution. The model can be used for demographic planning and forecasting. It has been applied to analyze the demographics of Russia. Translated from Prikladnaya Matematika i Informatika, No. 28, pp. 50–65, 2008.     

Mathematical modeling of the dissolving and deposition processes during solution seepage in a porous medium

A mathematical model that describes solution seepage in a porous medium and the processes of mineral dissolving and secondary deposition is proposed. Self-similar solutions describing the motion of the leading and trailing fronts, that is, the boundaries of the complete-dissolving zone, are determined. The main features of the processes under consideration are studied and numerical calculations are performed. It is shown that the model describes well the experimental data on mineral leaching by sulfate solutions. The dynamics of mineral extraction from productive solutions in a medium with a nonuniformacidity distribution are investigated. It is shown that, in the elevated-PH zones, the mineral is dissolved; whereas, in the low-acidity zones, secondary deposition of the mineral occurs. In the latter case, after the work has been completed, the bed may contain more or less considerable mineral resources, depending on the extent of the low-PH zone and its proximity to an extraction well.     

Finite element modeling of welding processes

This work deals with the simulation of fusion welding by the Finite Element Method. The implemented models include a moving heat source, temperature dependence of thermo-physical properties, elasto-plasticity, non-steady state heat transfer, and mechanical analysis. The thermal problem is assumed to be uncoupled from the mechanical one, so the thermal analysis is performed separately and previously to the mechanical analysis at each time step. The mechanical problem is based on the thermal history. A special treatment is performed on mechanical elements during the liquid/solid and solid/liquid phase changes to account for stress states. The three-dimensional stress state of a butt-welded joint is obtained as an example of an application.     

Continuous simulation of storm processes

Extremes - Storm processes constitute prototype models for spatial extremes. They are classically simulated on a finite number of points within a given domain. We propose a new algorithm that...     

Structural-information modeling of administrative control processes

We consider the fundamental principles of structural-information modeling of administrative control processes. We present a formal model for investigation of these processes, and we formulate criteria for efficiency of the facilities used for automated administrative control. Translated fromDinamicheskie Sistemy. Vol. 12. pp. 135–140, 1993.     

Regenerative simulation of TES processes

Regenerative simulation has become a familiar and established tool for simulation-based estimation. However, many applications (e.g., traffic in high-speed communications networks) call for autocorrelated stochastic models to which traditional regenerative theory is not directly applicable. Consequently, extensions of regenerative simulation to dependent time series is increasingly gaining in theoretical and practical interest, with Markov chains constituting an important case. Fortunately, a regenerative structure can be identified in Harris-recurrent Markov chains with minor modification, and this structure can be exploited for standard regenerative estimation. In this paper we focus on a versatile class of Harris-recurrent Markov chains, called TES (Transform-Expand-Sample). TES processes can generate a variety of sample paths with arbitrary marginal distributions, and autocorrelation functions with a variety of functional forms (monotone, oscillating and alternating). A practical advantage of TES processes is that they can simultaneously capture the first and second order statistics of empirical sample paths (raw field measurements). Specifically, the TES modeling methodology can simultaneously match the empirical marginal distribution (histogram), as well as approximate the empirical autocorrelation function. We explicitly identify regenerative structures in TES processes and proceed to address efficiency and accuracy issues of prospective simulations. To show the efficacy of our approach, we report on a TES/M/1 case study. In this study, we used the likelihood ratio method to calculate the mean waiting time performance as a function of the regenerative structure and the intrinsic TES parameter controlling burstiness (degree of autocorrelation) in the arrival process. The score function method was used to estimate the corresponding sensitivity (gradient) with respect to the service rate. Finally, we demonstrated the importance of the particular regenerative structure selected in regard to the estimation efficiency and accuracy induced by the regeneration cycle length.