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The analysis of error estimation is addressed in the framework of viscoplasticity problems, this is to say, of incompressible and non‐linear materials. Firstly, Zienkiewicz—Zhu (Z²) type error estimators are studied. They are based on the comparison between the finite element solution and a continuous solution which is computed by smoothing technique. From numerical examples, it is shown that the choice of a finite difference smoothing method (Orkisz’ method) improves the precision and the efficiency of this type of estimator. Then a Δ estimator is introduced. It makes it possible to take into account the fact that the smoothed solution does not verify the balance equations. On the other hand, it leads us to introduce estimators for the velocity error according to the L² and L^∞norms, since in metal forming this error is as important as the energy error. These estimators are applied to an industrial problem of extrusion, demonstrating all the potential of the adaptive remeshing method for forming processes.

A finite‐element model for calculating the die temperature profile for a hot‐forging operation is presented. The workpiece is modelled as a thermo‐viscoplastic material, while the dies are considered undeformable. Heat transfer between the dies and the workpiece is modelled using an iteratively coupled, fixed‐point calculation of the temperature in each domain. Transfer of temperature boundary conditions across contact interfaces is performed for non‐coincident meshes, using a boundary integration point contact analysis. Two industrial‐type examples are presented. In the first example, the effectiveness of the transfer of the temperature boundary conditions for a non steady‐state forging process is evaluated and determined to be satisfactory. Then weakly‐ and strongly‐coupled temperature resolutions are compared. It was found that the strongly‐coupled resolution may be necessary in order to obtain reasonably accurate results. In the second example, the weakly‐coupled resolution is compared to a constant‐temperature die approach for a relatively slow forging process, which shows the influence of the die temperature on the flow of the material.

Focuses on the inverse problems arising from the simulation of forming processes. Considers two sets of problems: parameter identification and shape optimization. Both are solved using an optimization method for the minimization of a suitable objective function. The convergence and convergence rate of the method depend on the accuracy of the derivatives of this function. The sensitivity analysis is based on a discrete approach, e.g. the differentiation of the discrete problem equations. Describes the method for non‐linear, non‐steady‐state‐forming problems involving contact evolution. First, it is applied to the parameter identification and to the torsion test. It shows good convergence properties and proves to be very efficient for the identification of the material behaviour. Then, it is applied to the tool shape optimization in forging for a two‐step process. A few iterations of the inverse method make it possible to suggest a suitable shape for the preforming tools.

Numerical modelling and simulation of metal forming is rapidly gaining prominence in many industries all over the world due to its effective saving of production time, effort and economy. In order to meet this need a special finite element code FORGE2 has been developed at CEMEF. In this work the theoretical basis of the FORGE2 along with its features such as thermo‐viscoplastic coupling, material compressibility and automatic mesh regeneration is reviewed and an attempt is made to simulate a few industrial forming processes taking into account the complex friction phenomena and thermal environment.

The finite element analysis of deformation of viscoplastic material involves contact between the tool and the workpiece. Here unilateral contact condition with the possibility of nodes originally in contact, losing contact subsequently, is analysed in non‐steady state forming processes. Friction has been taken into consideration through a potential function. Node to node contact is analysed and contact forces at the node are used to decide if the node is to be released. Two different algorithms are presented for treating the nodal contact condition. The one step explicit method with projections on the surface of contact was already implemented in the FORGE2^® software. An implicit scheme is proposed and compared with the existing scheme. The advantages of this scheme are numerically shown by solving some examples. It is observed that the volume losses are reduced. This makes it possible to use larger time steps or increase the computational accuracy.

To provide a selective bibliography for researchers working with bulk material forming (specifically the forging, rolling, extrusion and drawing processes) with sources which can help them to be up‐to‐date.

A range of published (1996‐2005) works, which aims to provide theoretical as well as practical information on the material processing namely bulk material forming. Bulk deformation processes used in practice change the shape of the workpiece by plastic deformations under forces applied by tools and dies.

Provides information about each source, indicating what can be found there. Listed references contain journal papers, conference proceedings and theses/dissertations on the subject.

It is an exhaustive list of papers (1,693 references are listed) but some papers may be omitted. The emphasis is to present papers written in English language. Sheet material forming processes are not included.

A very useful source of information for theoretical and practical researchers in computational material forming as well as in academia or for those who have recently obtained a position in this field.

There are not many bibliographies published in this field of engineering. This paper offers help to experts and individuals interested in computational analyses and simulations of material forming processes.

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, powder metallurgy and composite material processing are briefly discussed. The range of applications of finite elements on these subjects is extremely wide and cannot be presented in a single paper; therefore the aim of the paper is to give FE researchers/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 1994‐1996, where 1,370 references are listed. This bibliography is an updating of the paper written by Brannberg and Mackerle which has been published in Engineering Computations, Vol. 11 No. 5, 1994, pp. 413‐55.

This paper presents the results of the simulation of the forging of a connecting rod. The calculation has been carried out by the code FORGE3 developed at the CEMEF laboratory. FORGE3 is a three‐dimensional finite element computer program that can simulate hot forging of industrial parts. The flow problem is solved using a thermomechanical analysis. The mechanical resolution and the thermal one are coupled by the way of the consistency K which is thermodependent, the plastic deformation in the volume of the material and the friction heat flux on the surface. The material behaviour is assumed to be incompressible and viscoplastic (Norton—Hoff law) with the associated friction law. The thermal resolution includes the case of non‐linear physical properties and boundary conditions. An explicit Euler scheme is used for the mechanical resolution and two‐step schemes for the thermal one. For the computation of other parameters, it is necessary to have a good approximation for the strain rate tensor. The Orkisz method has been used to determine the deviatoric stress tensor and p is calculated by an original smoothing method. The results show that it is possible to get good information on the flow and on the physical properties during forging of automotive parts. Comparisons have been made with experimental measurements with a reasonably good agreement.

A numerical method for shape optimisation in forging is presented. The goal of the optimisation is to eliminate work‐piece defects that may arise during the forging process. A two‐dimensional finite element code has been developed for the simulation of the mechanical process. The material is incompressible and it follows the Norton‐Hoff law. To deal with contact constraint the velocity projection algorithm is used. The optimisation process is conducted using a genetic algorithm supported by an elitist strategy. A new genetic operator called adaptive mutation has been developed to increase the efficiency of the search. The developed scheme is used to design optimal preform shapes for several axisymmetric examples. Continuous and discrete design variables are considered. The objective function of the optimisation problem is associated with the quality of the final product. Comparing the obtained optimal results with the literature validates the proposed optimisation method.

An optimisation method for design of intermediate die shapes needed in some forging operations is presented. The basic problem consists of finding an optimal two‐step forging sequence by automatically designing the shape of the preforming tools. The optimisation problem is defined based on an inverse formulation. The objective function of the optimisation problem is a function describing the quality of the obtained part by measuring the die underfill. The finite element method is used to simulate the forging problem. The optimisation method is based on a modified sequential unconstrained minimisation technique and a gradient method. The sensitivity‐dependent algorithm requires computing the derivatives of the objective function with respect to the design variables defining the preform shapes. A direct differentiation method has been developed for this purpose. The optimisation scheme is demonstrated with two axisymmetric forging examples in which optimal preform dies are obtained.