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This paper addresses the loading/unloading conditions of thediscrete initial—value problem of plastic flow at infinitesimal deformations. As in the continuum problem, it is established that the strain—space formulation of the loading conditions is primary. Generalized trapezoidal and mid‐point rules are discussed. The loading conditions established for the general non‐associated flow problem are shown to naturally reduce to well‐known inequalities for flow rules obeying normality.

The purpose of this paper is to present an efficient return mapping algorithm for elastoplastic constitutive problems of ductile metals with an exact closed form solution of the local constitutive problem in the small strain regime. A Newton Raphson iterative method is adopted for the solution of the boundary value problem.

An efficient return mapping algorithm is illustrated which is based on an elastic predictor and a plastic corrector scheme resulting in an implicit and accurate numerical integration method. Nonlinear kinematic hardening rules and linear isotropic hardening rules are used to describe the components of the hardening variables. In the adopted algorithmic approach the solution of the local constitutive equations reduces to only one straightforward nonlinear scalar equation.

The presented algorithmic scheme naturally leads to a particularly simple form of the nonlinear scalar equation which ultimately scales down to an algebraic (polynomial) equation with a single variable. The straightforwardness of the present approach allows to find the analytical solution of the algebraic equation in a closed form. Further, the consistent tangent operator is derived as associated with the proposed algorithmic scheme and it is shown that the proposed computational procedure ensures a quadratic rate of asymptotic convergence when used with a Newton Raphson iterative method for the global solution procedure.

In the present approach the solution of the algebraic nonlinear equation is found in a closed form and accordingly no iterative method is required to solve the problem of the local constitutive equations. The computational procedure ensures a quadratic rate of asymptotic convergence for the global solution procedure typical of computationally efficient solution schemes. In the paper it is shown that the proposed algorithmic scheme provides an efficient and robust computational solution procedure for elastoplasticity boundary value problems. Numerical examples and computational results are reported which illustrate the effectiveness and robustness of the adopted integration algorithm for the finite element analysis of elastoplastic structures also under elaborate loading conditions.

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 aim of the present work is to describe a numerical approach to the analysis of three‐dimensional reinforced concrete structures subject to prestressing. The finite element approach developed is described, with particular regard to the configuration of finite elements in relation to numerical model generation. An elasto‐viscoplastic material law is adopted. The non‐linear formulation is discussed, pointing out theoretical and numerical aspects. The computational examples, carried out using a specially developed code, aim at illustrating the characteristic aspects of the proposed approach.

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.

Implicit solutions in viscoplastic analysis of structures are very often avoided due to the fact that they lead to non‐symmetric systems of equations. On the other hand, structures such as soils have a marked non‐associate behaviour that has to be taken into consideration. Here the implicit solutions are formulated in a way that, even for non‐associate models, the system of equations is kept as symmetric. Apart from an ‘exact’ formulation of the algorithm other possibilities are considered and tested in the numerical examples given.

This paper gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The bibliography at the end of the paper contains more than 1330 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1999–2002.

The purpose of this paper is to introduce a computational time dependent modeling to investigate propagation of elastic-viscoplastic zones in the shock wave loaded circular plates.

Constitutive equations are implemented incrementally by the Von-Kármán finite deflection system which is coupled with a mixed strain hardening rule and physical-base viscoplastic models. Time integrations of the equations are done by the return mapping technique through the cutting-plane algorithm. An integrated solution is established by pseudo-spectral collocation methodology. The Chebyshev basis functions are utilized to evaluate the coefficients of displacement fields. Temporal terms are discretized by the Houbolt marching method. Spatial linearizations are accomplished by the quadratic extrapolation technique.

Results of the center point deflections, effective plastic strain and stress (dynamic flow stress) and temperature rise are compared for three features of the Von-Kármán system. Identifying time history of resultant stresses, propagations of the viscoplastic plastic zones are illustrated for two circumstances; with considering strain rate and hardening effects, and without them. Some of modeling and computation aspects are discussed, carefully. When the results are compared with experimental data of shock wave loadings and finite element simulations, good agreements between them are observed.

This computational approach makes coupling the structural equations with the physical descriptions of the high rate deformation through step-by-step spectral solution of the constitutive equations.

The purpose of this paper is to provide industrial, education and academic users of computer programs a basic overview of finite elements in metal forming that will enable them to recognize the pitfalls of the existing formulations, identify the possible sources of errors and understand the routes for validating their numerical results.

The methodology draws from the fundamentals of the finite elements, plasticity and material science to aspects of computer implementation, modelling, accuracy, reliability and validation. The approach is illustrated and enriched with selected examples obtained from research and industrial metal forming applications.

The presentation is a step towards diminishing the gap being formed between developers of the finite element computer programs and the users having the know‐how on the metal forming technology. It is shown that there are easy and efficient ways of refreshing and upgrading the knowledge and skills of the users without resorting to complicated theoretical and numerical topics that go beyond their knowledge and most often are lectured out of metal forming context.

The overall content of the paper is enhancement of previous work in the field of sheet and bulk metal forming, and from experience in lecturing these topics to students in graduate and post‐graduate courses and to specialists of metal forming from industry.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.