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In this paper we consider several aspects related to the application of the pseudo‐concentration techniques to the simulation of mould filling processes. We discuss, in particular, the smoothing of the front when finite elements with interior nodes are employed and the evacuation of air through the introduction of temporary free wall nodes. The basic numerical techniques to solve the incompressible Navier—Stokes equations are also briefly described. The main features of the numerical model are the use of div‐stable velocity—pressure interpolations with discontinuous pressures, the elimination of the pressure via an iterative penalty formulation, the use of the SUPG approach to deal with convection‐dominated problems and the temporal integration using the generalized trapezoidal rule. At the end of the paper we present some numerical results obtained for a two‐dimensional test problem showing the ability of the method to capture complicated flow patterns.

The pseudo‐concentration method is applied to the analysis of transient processes. A simple, easy‐to‐handle model is obtained by keeping an Eulerian description: it does not require remeshing after a certain amount of plastic deformation. The range of applicability of the method is extended to non‐confined (even with several free surfaces) processes. It is shown the need of distinct handling of free surfaces according to their orientation to the direction of the flow. A seamless tube rolling process, a cylinder upsetting and a backward extrusion are modelled. Experimental data and results obtained by other methods are used to compare and discuss the performance of the model.

In order to develop an engineering tool for modelling 2D metal forming processes we implemented in the flow formulation the pseudo‐concentrations technique and a quadrilateral element based on mixed interpolation of tensorial components (QMITC). By doing this we obtained a reliable and efficient Eulerian formulation for modelling steady and transient metal forming problems. Some cases were analysed in order to test the performance of the formulation.

To present a numerical model of squeeze casting process.

The modelling consists of two parts, namely, the mould filling and the subsequent thermal stress analysis during and after solidification. Mould filling is described by the Navier‐Stokes equations discretized using the Galerkin finite element method. The free surface is followed using a front tracking procedure. A thermal stress analysis is carried out, assuming that a coupling exists between the thermal problem and the mechanical one. The mechanical problem is described as an elasto‐visco‐plastic formulation in an updated Lagrangian frame. A microstructural solidification model is also incorporated for the mould filling and thermal stress analysis. The thermal problem is solved using enthalpy method.

During the mould‐filling process a quasi‐static arbitrary Lagrangian‐Eulerian (ALE) approach and a microstructural solidification model were found to be applicable. For the case of the thermal stress analysis the influence of gap closure, effect of initial stresses (geometric nonlinearity), large voids and good performance of a microstructural model have been demonstrated.

The model can also be applied to the simulation of indirect castings. The final goal of the model is the ability to simulate the forming of the material after mould filling and during the solidification of the material. This is possible to achieve by applying arbitrary contact surfaces due to the sliding movement of the cast versus the punch and die.

The presented model can be used in engineering practice, as it incorporates selected second‐order effects which may influence the performance of the cast.

During the mould‐filling procedure a quasi‐static ALE approach has been applied to SQC processes and found to be generally applicable. A microstructural solidification model was applied which has been used for the thermal stress analysis only. During the thermal stress analysis the influence of gap closure and initial stresses (geometric nonlinearity) has been demonstrated.

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.

This paper sets out to present developments of a numerical model of squeeze casting process.

The entire process is modelled using the finite element method. The mould filling, associated thermal and thermomechanical equations are discretized using the Galerkin method. The front in the filling analysis is followed using volume of fluid method and the advection equation is discretized using the Taylor Galerkin method. The coupling between mould filling and the thermal problem is achieved by solving the thermal equation explicitly at the end of each time step of the Navier Stokes and advection equations, which allows one to consider the actual position of the front of the filling material. The thermomechanical problem is defined as elasto‐visco‐plastic described in a Lagrangian frame and is solved in the staggered mode. A parallel version of the thermomechanical program is presented. A microstructural solidification model is applied.

During mould filling a quasi‐static Arbitrary Lagrangian Eulerian (ALE) is applied and the resulting temperatures distribution is used as the initial condition for the cooling phase. During mould filling the applied pressure can be used as a control for steering the distribution of the solidified fractions.

The presented model can be used in engineering practice. The industrial examples are shown.

The quasi‐static ALE approach was found to be applicable to model the industrial SQC processes. It was found that the staggered scheme of the solution of the thermomechanical problem could parallelize using a multifrontal parallel solver.

The numerical simulation of dispersed-phase evolution in injection molding process of polymer blends is of great significance in both adjusting material microstructure and improving performances of the final products. This paper aims to present a numerical strategy for the simulation of dispersed-phase evolution for immiscible polymer blends in injection molding.

First, the dispersed-phase modeling is discussed in detail. Then the Maffettone–Minale model, affine deformation model, breakup model and coalescence statistical model are chosen for the dispersed-phase evolution. A general coupled model of microscopic morphological evolution and macroscopic flow field is constructed. Besides, a stable finite element simulation strategy based on pressure-stabilizing/Petrov–Galerkin/streamline-upwind/Petrov–Galerkin method is adopted for both scales.

Finally, the simulation results are compared and evaluated with the experimental data, suggesting the reliability of the presented numerical strategy.

The coupled modeling of dispersed-phase and complex flow field during injection molding and the tracing and simulation of droplet evolution during the whole process can be achieved.

The present work is an experimental and numerical study of a sloshing problem including baffle effects. The purpose of this paper is to assess the numerical behavior of a Lagrangian technique to track free surface flows by comparison with experiments, to report experimental data for sloshing at different conditions and to evaluate the effectiveness of baffles in limiting the wave height and the wave propagation.

Finite element simulations performed with a fixed mesh technique able to describe the free surface evolution are contrasted with experimental data. The experiments consist of an acrylic tank of rectangular section designed to attach baffles of different sizes at different distance from the bottom. The tank is filled with water and mounted on a shake table able to move under controlled horizontal motion. The free surface evolution is measured with ultrasonic sensors. The numerical results computed for different sloshing conditions are compared with the experimental data.

The reported numerical results are in general in good agreement with the experiments. In particular, wave heights and frequencies response satisfactorily compared with the experimental data for the several cases analyzed during steady state forced sloshing and free sloshing. The effectiveness of the baffles increases near resonance conditions. From the set of experiments studied, the major reduction of the wave height was obtained when larger baffles were positioned closer to the water level at rest.

Model validation: evaluation of the effectiveness of non-massive immersed baffles during sloshing.

The value of the present work encompass the numerical and experimental study of the effect of immersed baffles during sloshing under different imposed conditions and the comparison of numerical results with the experimental data. Also, the results shown in the present work are a contribution to the understanding of the role in the analysis of the proposed problem of some specific aspects of the geometry and the imposed motion.

The purpose of this paper is to develop a finite volume approach for the simulation of three-dimensional two-phase (polymer melt and air) flow in plastic injection molding which is capable of robustly handling the mesh non-orthogonality and the discontinuities in fluid properties.

The presented numerical method is based on a cell-centered unstructured finite volume discretization with a volume-of-fluid technique for interface capturing. The over-relaxed approach is adopted to handle the non-orthogonality involved in the discretization of the face normal derivatives to enhance the robustness of the solutions on non-orthogonal meshes. A novel interpolation method for the face pressure is derived to address the numerical stability issues resulting from the density and viscosity discontinuities at the melt–air interface. Various test cases are conducted to evaluate the proposed method.

The presented method was shown to be satisfactorily accurate by comparing simulations with analytical and experimental results. Besides, the effectiveness of the proposed face pressure interpolation method was verified by numerical examples of a two-phase flow problem with various density and viscosity ratios. The proposed method was also successfully applied to the simulation of a practical filling case.

The proposed finite volume approach is more tolerant of non-orthogonal meshes and the discontinuities in fluid properties for two-phase flow simulation; therefore, it is valuable for engineers in engineering computations.

Presents a quasi three‐dimensional formulation for filling a thin section cavity which is derived under the assumption that no transverse flow occurs in the gap. A no‐slip condition was applied on all surfaces occupied by the fluid and a slip condition on all air‐filled (empty) surfaces. The formulation was developed to analyse the sections which lie in the xy‐plane or may be oriented arbitrarily in three‐dimensional space. Solves the discretized thickness‐integrated finite element flow equations by using the implicit mixed velocity‐pressure formulation, and uses the volume of fluid (VOF) method to track the free surfaces. Presents numerical examples which confirm the accuracy of the formulation and demonstrate how it can be used to model the filling of planar and three‐dimensional thin section cavities of irregular shape.