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A synopsis is presented of the numerical finite element methodology currently in use at the Institute for Computer Applications (ICA) for the simulation of industrial forming processes. The development of the method is based on the inelastic properties of the material with an extension towards the inclusion of elastic effects and accounts for the thermal phenomena occurring in the course of the deformation. An essential constituent of the computational procedure is the treatment of the unsteady contact developing between the workpiece material and the tool during forming, and of the associated friction phenomena. Automatic mesh generation and variable discretization adaptable to the development of the numerical solution are of importance for industrial applications. These aspects are presented and discussed. Furthermore, solution techniques for thermomechanically coupled problems are considered and investigated with respect to their numerical properties. Application to industrial forming processes is demonstrated by means of three‐dimensional hot rolling and of superplastic sheet forming.

The paper describes developments in the numerical analysis of metal forming processes mainly motivated by industrial applications. It deals with a complete consideration of the unsteady contact developing between the material and the die, the regeneration of the finite element mesh during the course of the calculation, and with the simulation of superplastic forming processes. In particular, an approach relating both the contact pressure and the friction force to the motion of the material relative to the die surface leads to a convenient computational procedure and to a smooth numerical behaviour under friction. The topological part of the contact algorithm appears well‐suited also for the redefinition of the discretization mesh. As a selected application, superplastic forming is considered in conclusion. Industrial practice requires the adjustment of the forming pressure to a prescribed value of the maximum rate of deformation in the material.

Under restriction of an isotropic elastic response of deformed lattice, develops a covariant theory of finite elastoplasticity in principal axes of a pair of deformation tensors. In material description, the tensor pair consists of the plastic deformation tensor and the total deformation Cauchy‐Green tensor. Applies the proposed theory to elastoplastic membrane shells, whose references and current configurations can be arbitrary space‐curved surfaces. Pressure‐insensitive von Mises yield criterion with isotropic hardening and a quadratic form of the strain energy function given in terms of elastic principal stretches are considered as a model problem. Through an explicit enforcement of the plane stress condition we arrive at a reduced two‐dimensional problem representation, which is set in the membrane tangent plane. Numerical implementation of the presented theory relies crucially on the operator split methodology to simplify the state update computation. Presents a set of numerical examples in order to illustrate the performance of the presented methodology and indicate possible applications in the area of sheet metal forming.

Numerical solutions in computational plasticity are severely challenged when concrete and geomaterials are considered with non‐regular yield surfaces, strain‐softening and non‐associated flow. There are two aspects that are of immediate concern within load steps which are truly finite: first, the iterative corrector must assure that the equilibrium stress state and the plastic process variables do satisfy multiple yield conditions with corners, Fi(σ, q) = 0, at discrete stages of the solution process. To this end, a reliable return mapping algorithm is required which minimizes the error of the plastic return step. Second, the solution of non‐linear equations of motion on the global structural level must account for limit points and premature bifurcation of the equilibrium path. The current paper is mainly concerned with the implicit integration of elasto‐plastic hardening/softening relations considering non‐associated flow and the presence of composite yield conditions with corners.

Application of the finite element method to the simulation of glass forming processes is described. The forming process results in a coupled thermal/mechanical problem with interaction between the heat transfer analysis of the temperature distribution in the glass and the viscous flow formulation describing the deformation of molten glass being a dominant factor. Particular attention must be given to derivation of the appropriate non‐linear thermal boundary conditions and also to monitoring of the mechanical contact between the glass and mould. The technique described provides both the glass and temperature distribution at each instant of the forming process and thus can provide invaluable information for mould and plunger design, optimum operation times, etc. Numerical examples are provided for both wide neck and narrow neck press and blow forming processes and the results obtained compare well with commercial observations.

A numerical model for solving either elastic‐plastic, elastic‐viscoplastic or purely viscoplastic deformation of thin sheets is presented, using a membrane mechanical approach. The finite element method is used associated with an incremental procedure. The mechanical equations are the principle of virtual work written in terms of plane stress, which is solved at the end of each increment, and an incremental semi‐implicit flow rule obtained by the time integration of the constitutive equations over the increment. These equations are written using curvilinear coordinates, and membrane elements are used to discretize them. The resolution method is the Newton‐Raphson algorithm. The contact algorithm is presented and allows for applications to cold stretching and deep‐drawing problems and to the superplastic forming of thin sheets.

Addresses problems in mechanics and physics involving two or more coupled variables of different nature, or a number of distinct domains which interact. For these kinds of problems, considers numerical solution by the coupling of operators appertaining to the individual participating phenomena, or defined in the domains. Reviews the co‐operation of distinct discretized operators in connection with the integration of temporal evolution processes, and the iterative treatment of stationary equations of state. The specification of subtasks complies with the demand for an independent treatment on different processing units arising in parallel computation. Physical subtasks refer to problems of different field variables interacting on the continuum level; their number is usually small. Fine granularity may be achieved by separating the problem region into subdomains which communicate via the boundaries. In multiphysics simulations operators are preferably combined such that subdomains are processed in parallel on different units, while physical phenomena are processed sequentially in the subdomain.

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.

The purpose of the present study is to explore the incomplete substitution of the simplex triangular finite element by either of two models: one evolving out as part of the element flexibility, and the other as part of the element stiffness.

The elastic energy stored in each of the units under stress or strain decides on stiffer and weaker responses. The pertaining Rayleigh quotient in terms of the flexibility matrices allows bounding the distance of the spring cell models to the finite element in dependence of the triangle configuration.

Despite a superiority of the flexibility cell concept observed in computations, the study reveals constellations of shape and stressing of the triangle that favour the stiffness concept. The latter is seen to behave stiffer than its flexibility counterpart and produces results more distant to the finite element in most cases.

The difference between the stiffness and the flexibility approach to spring cells is investigated for triangular elements in dependence of the geometrical configuration under specific conditions of stressing. This suffices to refute an exclusive superiority of the flexibility concept although largely true.

The results of the investigation appear useful in deciding between the spring cell models depending on the case of a spring lattice application.

The flexibility approach to the spring cell is not widely known yet. This cell model deserves a study on performance and comparison to the different, more common stiffness cell model.

The purpose of this paper is to propose a computational model for thin layers, for problems of linear time-dependent heat conduction. The thin layer is replaced by a zero-thickness interface. The advantage of the new model is that it saves the need to construct and use a fine mesh inside the layer and in regions adjacent to it, and thus leads to a reduction in the computational effort associated with implicit or explicit finite element schemes.

Special asymptotic models have been proposed for linear heat transfer and linear elasticity, to handle thin layers. In these models the thin layer is replaced by an interface with zero thickness, and specific jump conditions are imposed on this interface in order to represent the special effect of the layer. One such asymptotic interface model is the first-order Bövik-Benveniste model. In a paper by Sussmann et al., this model was incorporated in a FE formulation for linear steady-state heat conduction problems, and was shown to yield an accurate and efficient computational scheme. Here, this work is extended to the time-dependent case.

As shown here, and demonstrated by numerical examples, the new model offers a cost-effective way of handling thin layers in linear time-dependent heat conduction problems. The hybrid asymptotic-FE scheme can be used with either implicit or explicit time stepping. Since the formulation can easily be symmetrized by one of several techniques, the lack of self-adjointness of the original formulation does not hinder an accurate and efficient solution.

Most of the literature on asymptotic models for thin layers, replacing the layer by an interface, is analytic in nature. The proposed model is presented in a computational context, fitting naturally into a finite element framework, with both implicit and explicit time stepping, while saving the need for expensive mesh construction inside the layer and in its vicinity.