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Article
Publication date: 27 September 2011

Mohammad Rezaiee‐Pajand, Cyrus Nasirai and Mehrzad Sharifian

The purpose of this paper is to present a new effective integration method for cyclic plasticity models.

Abstract

Purpose

The purpose of this paper is to present a new effective integration method for cyclic plasticity models.

Design/methodology/approach

By defining an integrating factor and an augmented stress vector, the system of differential equations of the constitutive model is converted into a nonlinear dynamical system, which could be solved by an exponential map algorithm.

Findings

The numerical tests show the robustness and high efficiency of the proposed integration scheme.

Research limitations/implications

The von‐Mises yield criterion in the regime of small deformation is assumed. In addition, the model obeys a general nonlinear kinematic hardening and an exponential isotropic hardening.

Practical implications

Integrating the constitutive equations in order to update the material state is one of the most important steps in a nonlinear finite element analysis. The accuracy of the integration method could directly influence the result of the elastoplastic analyses.

Originality/value

The paper deals with integrating the constitutive equations in a nonlinear finite element analysis. This subject could be interesting for the academy as well as industry. The proposed exponential‐based integration method is more efficient than the classical strategies.

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Article
Publication date: 1 December 2004

Jaroslav Mackerle

Sheet metal forming is a process of shaping thin sheets of metal by applying pressure through male or female dies or both. In most of used sheet‐formating processes the…

Abstract

Sheet metal forming is a process of shaping thin sheets of metal by applying pressure through male or female dies or both. In most of used sheet‐formating processes the metal is subjected to primarily tensile or compressive stresses or both. During the last three decades considerable advances have been made in the applications of numerical techniques, especially the finite element methods, to analyze physical phenomena in the field of structural, solid and fluid mechanics as well as to simulate various processes in engineering. These methods are useful because one can use them to find out facts or study the processes in a way that no other tool can accomplish. Finite element methods applied to sheet metal forming are the subjects of this paper. The reason for writing this bibliography is to save time for readers looking for information dealing with sheet metal forming, not having an access to large databases or willingness to spend own time with uncertain information retrieval. This paper is organized into two parts. In the first one, each topic is handled and current trends in the application of finite element techniques are briefly mentioned. The second part, an Appendix, lists papers published in the open literature. More than 900 references to papers, conference proceedings and theses/dissertations dealing with subjects that were published in 1995‐2003 are listed.

Details

Engineering Computations, vol. 21 no. 8
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 28 August 2007

M. Rezaiee‐Pajand and Cyrus Nasirai

This paper aims to provide a more rapid stress updating algorithm for von‐Mises plasticity with mixed‐hardening and to compare it with the previous works.

Abstract

Purpose

This paper aims to provide a more rapid stress updating algorithm for von‐Mises plasticity with mixed‐hardening and to compare it with the previous works.

Design/methodology/approach

An augmented stress vector is defined. This can convert the original nonlinear differential equation system to a quasi‐linear one. Then the dynamical system can be solved with an exponential map approach in a semi‐implicit manner.

Findings

The presented stress updating algorithm gives very accurate results and it has a quadratic convergence rate.

Research limitations/implications

Von‐Mises plasticity in a small strain regime is considered. Furthermore, the material is supposed to have linear hardening.

Practical implications

Stress updating is the heart of a nonlinear finite element analysis due to the large consumption of computation time. The efficiency and accuracy of the calculations of nonlinear finite element analysis are strongly influenced by the efficiency and accuracy of stress updating schemes.

Originality/value

The paper offers a new stress updating strategy based on exponential maps. This may be used as a routine in a nonlinear finite element analysis software to enhance its performance.

Details

Engineering Computations, vol. 24 no. 6
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 1 March 1994

E.A. De Souza Neto, Djordje Perić and D.R.J. Owen

This work addresses the computational aspects of a model forelastoplastic damage at finite strains. The model is a modification of apreviously established model for large…

Abstract

This work addresses the computational aspects of a model for elastoplastic damage at finite strains. The model is a modification of a previously established model for large strain elastoplasticity described by Perić et al. which is here extended to include isotropic damage and kinematic hardening. Within the computational scheme, the constitutive equations are numerically integrated by an algorithm based on operator split methodology (elastic predictor—plastic corrector). The Newton—Raphson method is used to solve the discretized evolution equations in the plastic corrector stage. A numerical assessment of accuracy and stability of the integration algorithm is carried out based on iso‐error maps. To improve the stability of the local N—R scheme, the standard elastic predictor is replaced by improvedinitial estimates ensuring convergence for large increments. Several possibilities are explored and their effect on the stability of the N—R scheme is investigated. The finite element method is used in the approximation of the incremental equilibrium problem and the resulting equations are solved by the standard Newton—Raphson procedure. Two numerical examples are presented. The results are compared with those obtained by the original elastoplastic model.

Details

Engineering Computations, vol. 11 no. 3
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 August 2000

Pankaj and Khalid Moin

Plane strain constitutive behaviour of von Mises and isotropic Hoffman materials is examined using single element tests. Two kinds of tests are conducted – (a) prescribed…

Abstract

Plane strain constitutive behaviour of von Mises and isotropic Hoffman materials is examined using single element tests. Two kinds of tests are conducted – (a) prescribed displacement tests; and (b) tests with a mixture of displacements and boundary tractions prescribed. While (a) are used to understand the manner of stress traversal on the yield surface in principal stress space, (b) are employed to study the load displacement response and the possibility of ensuing localization. Associated plasticity is assumed throughout. The tests are conducted using perfect and strain softening plasticity. It is found that for the von Mises criterion limited exact solutions can be evolved even under softening (or hardening) conditions. For isotropic Hoffman materials the nature of the stress traversal, load deflection response and the satisfaction of the localization conditions are strongly influenced by the ratio and difference of uniaxial yield strengths, in tension and compression, as well as by the softening parameters.

Details

Engineering Computations, vol. 17 no. 5
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 3 August 2015

Mark Messner, Armand Beaudoin and Robert Dodds

The purpose of this paper is to describe several novel techniques for implementing a crystal plasticity (CP) material model in a large deformation, implicit finite element…

Abstract

Purpose

The purpose of this paper is to describe several novel techniques for implementing a crystal plasticity (CP) material model in a large deformation, implicit finite element framework.

Design/methodology/approach

Starting from the key kinematic assumptions of CP, the presentation develops the necessary CP correction terms to several common objective stress rates and the consistent linearization of the stress update algorithm. Connections to models for slip system hardening are isolated from these processes.

Findings

A kinematically consistent implementation is found to require a correction to the stress update to include plastic vorticity developed by slip deformation in polycrystals. A simpler, more direct form for the algorithmic tangent is described. Several numerical examples demonstrate the capabilities and computational efficiency of the formulation.

Research limitations/implications

The implementation assumes isotropic slip system hardening. With simple modifications, the described approach extends readily to anisotropic coupled or uncoupled hardening functions.

Practical implications

The modular formulation and implementation support streamlined development of new models for slip system hardening without modifications of the stress update and algorithmic tangent computations. This implementation is available in the open-source code WARP3D.

Originality/value

In the process of developing the CP formulation, this work realized the need for corrections to the Green-Naghdi and Jaumann objective stress rates to account properly for non-zero plastic vorticity. The paper describes fully the consistent linearization of the stress update algorithm and details a new scheme to implement the model with improved efficiency.

Details

Engineering Computations, vol. 32 no. 6
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 1 March 1996

Adnan Ibrahimbegović

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…

Abstract

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.

Details

Engineering Computations, vol. 13 no. 2/3/4
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 April 1992

A. CUITIÑO and M. ORTIZ

We provide a method for automatically extending small‐strain state‐update algorithms and their correspondent consistent tangents into the finite deformation range within…

Abstract

We provide a method for automatically extending small‐strain state‐update algorithms and their correspondent consistent tangents into the finite deformation range within the framework of multiplicative plasticity. The procedure, when it applies, operates at the level of kinematics and, hence, can be implemented once and for all independently of the material‐specific details of the constitutive model. The versatility of the method is demonstrated by a numerical example.

Details

Engineering Computations, vol. 9 no. 4
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 27 August 2019

Maliheh Tavoosi, Mehrdad Sharifian and Mehrzad Sharifian

The purpose of this paper is to suggest a robust hybrid method for updating the stress and plastic internal variables in plasticity considering damage mechanics.

Abstract

Purpose

The purpose of this paper is to suggest a robust hybrid method for updating the stress and plastic internal variables in plasticity considering damage mechanics.

Design/methodology/approach

By benefiting the properties of the well-known explicit and implicit integrations, a new mixed method is derived. In fact, the advantages of the mentioned techniques are used to achieve an efficient integration.

Findings

The numerical studies demonstrate the high precision and robustness of the suggested algorithm.

Research limitations

The perfect von-Mises plasticity together with Lemaitre damage model is considered within the realm of small deformations.

Practical implications

Updating stress and plastic internal variables are of utmost importance in elastoplastic analyses of structures. The accuracy and efficiency of stress-updating methods significantly affect the final outcomes of nonlinear analyses.

Originality/value

The idea which is used to derive the hybrid method leads to an efficient integration method for updating the constitutive equations of the damage mechanics.

Details

Engineering Computations, vol. 37 no. 2
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 February 1986

H. Burlet and G. Cailletaud

A formulation of non‐linear kinematic hardening in plasticity is given, with a short description of the model properties under cyclic loading. A resolution algorithm based…

Abstract

A formulation of non‐linear kinematic hardening in plasticity is given, with a short description of the model properties under cyclic loading. A resolution algorithm based on the initial stress method is implemented in a two‐dimensional finite element code (ZEBULON). The procedure is tested on examples including mechanical and thermal loading. Some remarks are made on the maximum increment size, the relative efficiency of ‘radial return’ and ‘secant stiffness method’ is discussed. Finally, the possibilities of the model concerning ratchetting, cyclic hardening and softening are shown.

Details

Engineering Computations, vol. 3 no. 2
Type: Research Article
ISSN: 0264-4401

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