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Numerical simulation of the single point incremental forming (SPIF) processes can be very demanding and time consuming due to the constantly changing contact conditions between the tool and the sheet surface, as well as the nonlinear material behaviour combined with non-monotonic strain paths. The purpose of this paper is to propose an adaptive remeshing technique implemented in the in-house implicit finite element code LAGAMINE, to reduce the simulation time. This remeshing technique automatically refines only a portion of the sheet mesh in vicinity of the tool, therefore following the tool motion. As a result, refined meshes are avoided and consequently the total CPU time can be drastically reduced.

SPIF is a dieless manufacturing process in which a sheet is deformed by using a tool with a spherical tip. This dieless feature makes the process appropriate for rapid-prototyping and allows for an innovative possibility to reduce overall costs for small batches, since the process can be performed in a rapid and economic way without expensive tooling. As a consequence, research interest related to SPIF process has been growing over the last years.

In this work, the proposed automatic refinement technique is applied within a reduced enhanced solid-shell framework to further improve numerical efficiency. In this sense, the use of a hexahedral finite element allows the possibility to use general 3D constitutive laws. Additionally, a direct consideration of thickness variations, double-sided contact conditions and evaluation of all components of the stress field are available with solid-shell and not with shell elements. Additionally, validations by means of benchmarks are carried out, with comparisons against experimental results.

It is worth noting that no previous work has been carried out using remeshing strategies combined with hexahedral elements in order to improve the computational efficiency resorting to an implicit scheme, which makes this work innovative. Finally, it has been shown that it is possible to perform accurate and efficient finite element simulations of SPIF process, resorting to implicit analysis and continuum elements. This is definitively a step-forward on the state-of-art in this field.

Gives a bibliographical review of the finite element meshing and remeshing from the theoretical as well as practical points of view. Topics such as adaptive techniques for meshing and remeshing, parallel processing in the finite element modelling, etc. are also included. The bibliography at the end of this paper contains 1,727 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1990 and 2001.

In recent years, developments in the field of lightweight armour have been of primary importance to the defence industry. This necessity has led to many organisations adopting composite armours comprising both the traditional heavy armours and new lighter weight ceramic armours. The numerical modelling of metal based armour systems has been well documented over the years using purely continuum based methods; and also the modelling of brittle systems using discrete element methods, therefore it is the objective of this paper to demonstrate how a coupled finite and discrete element approach, can be used in the further understanding of the quantitative response of ceramic systems when subjected to dynamic loadings using a combination of adaptive continuum techniques and discrete element methods. For the class of problems encountered within the defence industry, numerical modelling has suffered from one principal weakness; for many applications the associated deformed finite element mesh can no longer provide an accurate description of the deformed material, whether this is due to large ductile deformation, or for the case of brittle materials, degradation into multiple bodies. Subsequently, two very different approaches have been developed to combat such deficiencies, namely the use of adaptive remeshing for the ductile type materials and a discrete fracture insertion scheme for the modelling of material degradation. Therefore, one of the primary objectives of this paper is to present examples demonstrating the potential benefits of explicitly coupling adaptive remeshing methods to the technique of discrete fracture insertion in order to provide an adaptive discontinuous solution strategy, which is computationally robust and efficient.

Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography at the end contains 2,177 references to papers, conference proceedings and theses/dissertations dealing with the subjects that were published in 1990‐2000.

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.

The simulation of fracture processes for discrete crack propagation is well established for linear‐elastic cracking problems. Applying finite element techniques for the numerical formulation, at every incremental macro‐crack step the element mesh has to be adapted such that the crack path remains independent of the initial mesh. The accuracy of the obtained results has to be controlled by suitable error estimators and error indicators. Considering the dependence of the predicted crack path on the precision of the displacement and stress computation, quality measures for the computed results are recommended. In this research the use of the Babuska/Rheinboldt error indicator in combination with linear‐elastic crack propagation problems is demonstrated. Based on this error measure an adaptive mesh refinement technique is developed. In comparison with classical discrete crack propagation simulations the advantages of the new concept can be clearly observed.

The purpose of this paper is to present an adaptive finite element procedure that improves the quality of convection dominated mid‐ocean ridge (MOR) and subduction zone (SZ) simulations in geodynamics.

The method adapts the mesh automatically around regions of high‐solution gradient, yielding enhanced resolution of the associated flow features. The approach utilizes an automatic, unstructured mesh generator and a finite element flow solver. Mesh adaptation is accomplished through mesh regeneration, employing information provided by an interpolation‐based local error indicator, obtained from the computed solution on an existing mesh.

The proposed methodology works remarkably well at improving solution accuracy for both MOR and SZ simulations. Furthermore, the method is computationally highly efficient.

To date, successful goal‐orientated/error‐guided grid adaptation techniques have, to the knowledge, not been utilized within the field of geodynamics. This paper presents the first true geodynamical application of such methods.

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.

An adaptive mesh refinement procedure that uses nodeless variables and quadratic interpolation functions is presented for analysing transient thermal problems. A temperature based finite element scheme with Crank‐Nicolson time marching is used to obtain the thermal solution. The strategies used for mesh adaptation, computing refinement indicators, and time marching are described. Examples in one and two dimensions are presented and comparisons are made with exact solutions. The effectiveness of this procedure for transient thermal analysis is reflected in good solution accuracy, reduction in number of elements used, and computational efficiency.

A hybrid spectral/boundary element approach is proposed to examine the influence of Couette channel flow on transient coating of highly elastic fluids. The viscoelastic instability of one‐dimensional plane Couette flow is first determined for a large class of Oldroyd fluids with added viscosity, which typically represent polymer solutions composed of a Newtonian solvent and a polymeric solute. The Johnson‐Segalman equation is used as the constitutive model. The velocity profile inside the channel is taken as the exit profile for the emerging free‐surface flow. The flow is assumed to be Newtonian as it emerges from the channel. An estimate of the magnitude of the rate‐of‐strain tensor components in the free‐surface region reveals that they are generally smaller than the shear rate inside the channel. The evolution of the flow front is simulated using the boundary element method. For the channel flow, the problem is reduced to a non‐linear dynamical system using the Galerkin projection method. Stability analysis indicates that the channel velocity may be linear or non‐linear depending on the range of the Weissenberg number. The evolution of the coating flow at the exit is examined for steady as well as transient (monotonic and oscillatory) channel flow. It is found that adverse flow can exist as a result of fluid elasticity, which can hinder the process of blade coating.