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This paper gives a review of the finite element techniques (FE) applied in the area of material processing. The latest trends in metal forming, non‐metal forming and powder metallurgy are briefly discussed. The range of applications of finite elements on the subjects is extremely wide and cannot be presented in a single paper; therefore the aim of the paper is to give FE users only an encyclopaedic view of the different possibilities that exist today in the various fields mentioned above. An appendix included at the end of the paper presents a bibliography on finite element applications in material processing for the last five years, and more than 1100 references are listed.

To develop a numerical methodology to simulate the lost foam casting (LFC), including the gas back‐pressure effects.

Back‐pressure effects are due to the interactions of many physical processes. The strategy proposed herein tries to model all these processes within a simple formula. The main characteristic of the model consists of assuming that the back‐pressure is a known function of the external parameters (coating, temperature, gravity, etc.) that affects directly the heat transfer coefficient from the metal to the foam. The general framework of the simulation is a finite element model based on an arbitrary Lagrangian Eulerian (ALE) approach and the use of level set function to capture the metal front advance.

After experimental tunings, the model provides a way to include the back‐pressure effects in a simple way.

The method is not completely predictive in the sense that a priori tuning is necessary to calibrate the model.

Provides more realistic results than classical models.

The paper proposes a theoretical framework of a finite element method for the simulation of LFC process. The method uses an ALE method on a fixed mesh and a level‐set function to capture metal front advance. It proposes an original formula for the heat transfer coefficient that enables one to include back‐pressure effects.

Because of the unrealistic demand of computer resources in terms of memory and CPU times for the direct numerical simulation of practical peen forming processes, a two‐stage combined finite/discrete element and explicit/implicit solution strategy is proposed in this paper. The procedure involves, at the first stage, the identification of the residual stress/strain profile under particular peening conditions by employing the combined finite/discrete approach on a small scale sample problem, and then at the second stage, the application of this profile to the entire workpiece to obtain the final deformation and stress distribution using an implicit static analysis. The motivation behind the simulation strategy and the relevant computational and implementation issues are discussed. The numerical example demonstrates the ability of the proposed scheme to simulate a peen forming process.

Natural gas leak from underground pipelines could lead to serious damage and global warming, whose spreading in soil should be systematically investigated. This paper aims to propose a three-dimensional numerical model to analyze the methane–air transportation in soil. The results could help understand the diffusion process of natural gas in soil, which is essential for locating leak source and reducing damage after leak accident.

A numerical model using finite element method is proposed to simulate the methane spreading process in porous media after leaking from an underground pipe. Physical models, including fluids transportation in porous media, water evaporation and heat transfer, are taken into account. The numerical results are compared with experimental data to validate the reliability of the simulation model. The effects of methane leaking direction, non-uniform soil porosity, leaking pressure and convective mass transfer coefficient on ground surface are analyzed.

The methane mole fraction distribution in soil is significantly affected by the leaking direction. Horizontally and vertically non-uniform soil porosity has a stronger effect. Increasing leaking pressure causes increasing methane mole flux and flow rate on the ground surface.

Most existing gas diffusion models in porous media are for one- or two-dimensional simulation, which is not enough for predicting three-dimensional diffusion process after natural gas leak in soil. The heat transfer between gas and soil was also neglected by most researchers, which is very important for predicting the gas-spreading process affected by the soil moisture variation because of water evaporation. In this paper, a three-dimensional numerical model is proposed to further analyze the methane–air transportation in soil using finite element method, with the presence of water evaporation and heat transfer in soil.

Presents a new method for the numerical simulation of diffusion with phase‐change. The method is able to handle hysteresis and finite‐rate kinetics in the phase‐change reaction. Such phenomena are frequent in solid‐solid phase transitions. The model problem discussed concerns hydrogen migration and hydride precipitation in zirconium and its alloys, a problem of interest to the nuclear industry. With respect to previous ones, our method is the first to incorporate an implicit treatment of diffusion, thus avoiding mesh‐dependent stability limits in the time step. The CPU time can in this way be reduced by a factor of 10–20 in applications. Addresses, through numerical studies, convergence with respect to mesh refinement and reduction of the time step. Also reports on an application of the method to the simulation of laboratory experiments. Shows that the method is a powerful tool to deal with general phase‐change problems, extendable to other physical systems.

In the first part of this series of papers on the combined finite/discrete element simulation of shot peening processes, different contact interaction laws for 2D cases are extensively studied with special attention given to the proper selection of the parameter values involved, which is one of the key issues for successful direct simulation. In addition, computational issues including contact forces, partial contact, energy dissipation, and rheological representation are addressed. Numerical examples for a single shot impact system simulated by the coupled finite/discrete element method using different interaction laws are provided to verify the proposed approaches. The results are also compared with those obtained by using only finite element methods. Findings obtained by performing 2D simulations will, in the subsequent article, be used in realistic computational simulations of 3D shot peening processes.

Following earlier work on the combined finite/discrete element simulation of shot peening process in 2D case, 3D representation of the problem is established with respect to DE modelling and contact interaction laws. An important relevant computational issue regarding the critical time step is carefully studied, and a new time stepping scheme that can ensure both short and long term stability of the contact models is developed. Numerical tests are performed to evaluate the proposed normal and frictional contact interaction laws with various model parameters. The influences of single and multiple shot impact, as well as element sizes are also numerically investigated. The established contact interaction laws can also be applied to other multi‐body dynamic simulations.

To reduce the computational costs for electromagnetic simulations of permanent magnet synchronous machines maintaining a high accuracy.

An analytical model is introduced regarding multiple designs of permanent magnet synchronous machines. This electromagnetic model is coupled to a numerical simulation. Thereby, the advantages of both computational methods are combined by parameterizing the analytical model to the numerical solution. This results in a high‐efficient analytical model with the accuracy of the numerical simulation. The results of the analytical model are compared to measurements of a permanent magnet synchronous machine. Various machine modifications are simulated to evaluate possible limitations of the analytical model.

It can be stated, that a once parameterized analytical model achieves a high accuracy. Furthermore, geometric variations can be applied without the need of a new parameterization through a numerical simulation. Only changing the permanent magnet height or the air gap height results in a significant deviation and a new numerical simulation is recommended.

Only measurements for machines up to 5 kW were available. In consequence, the model is only validatet in this range.

With the presented analytical model, an electromagnetic design of a permanent magnet synchronous machine can be performed very time efficient achieving accurate results. Furthermore, optimization studies can be performed with low‐computational costs.

The introduced analytical model can be parameterized by a numerical simulation. The numeric simulation process and the parameterization are performed automatically according to the data calculated by the analytical model. Measurements demonstrate the effectiveness and the limitations of the model.

This article presents a locally conservative projection method which aims to preserve the integral of a function and one operator among grad, div, or curl.

After a theoretical description of the projection methods, the locally conservative projection is analytically tested and compared with the orthogonal method. In the second part, the implementation of the methods is described, and improvements are proposed. An industrial application of the present work, consisting in a magneto-thermal coupled problem, is then presented.

The implementation of the conservative method is simpler than the implementation of the orthogonal method while presenting similar behaviour in terms of accuracy and conservation.

The locally conservative method is extended to curl-conform and div-conform elements. Furthermore, three-dimensional studies are proposed.

In this paper, we present the results of submicron pseudomorphic AlGaAs/InGaAs/ GaAs HEMT simulations. Our main interest is the study of electronic temperature behavior in the device and improvement of the current‐voltage characteristic curves. Three types of models are being used. The first is the well known drift‐diffusion model. The second is of the hydrodynamic type and the third is a combination of the two preceding models. The numerical treatment is based on the discretization by the Galerkin finite element method for both Poisson and continuity equations with the streamline‐diffusion method being used for the energy equation. A comparison of the different approaches have been realized and a synthesis on the validity of each of these models is being drawn.