On the Study of Distinct Algorithmic Strategies in the Implementation of Advanced Anisotropic Models with Mixed Hardening

2013 ◽  
Vol 554-557 ◽  
pp. 1174-1183 ◽  
Author(s):  
Tiago Jordão Grilo ◽  
Robertt Angelo Fontes Valente ◽  
R.J. Alves de Sousa
Keyword(s):  
Finite Element ◽  
Kinematic Hardening ◽  
Mapping Procedure ◽  
Anisotropic Models ◽  
Mixed Hardening ◽  
Hardening Law ◽  
Fully Implicit ◽  
Return Mapping ◽  
Multi Stage ◽  
Stress Integration

In this study, suitable distinct stress integration algorithms for advanced anisotropic models with mixed hardening, and their implementation in finite element codes, are discussed. The constitutive model studied in the present work accounts for advanced (non-quadratic) anisotropic yield criteria, namely, the Barlat et al. 2004 model with 18 coefficients (Yld2004-18p), combined with a mixed isotropic-nonlinear kinematic hardening law. This phenomenological model allows for an accurate description of complex plastic yielding anisotropy and Bauschinger effects, which are essential for a reliable prediction of deep drawing and springback results using numerical simulations.In the present work distinct algorithm classes are analysed: (i) a semi-explicit algorithm that accounts for the sub-incrementation technique; (ii) the cutting-plane approach (semi-implicit integration); and (iii) the fully-implicit multi-stage return mapping procedure, based on the control of the potential residual. The numerical performance of the developed algorithms is inferred by benchmarks in sheet metal forming processes. The quality of the solution is assessed and compared to reference results. In the end, an algorithmic and programming framework is provided, suitable for a direct implementation in commercial Finite Element codes, such as Abaqus (Simulia) and Marc (MSC-Software) packages.

Implicit Stress Integration and Consistent Tangent Matrix for Yoshida’s 6th Order Polynomial Yield Function Combined with Yoshida-Uemori Kinematic Hardening Rule

2015 ◽  
Vol 651-653 ◽  
pp. 558-563 ◽  
Author(s):  
Hiroshi Hamasaki ◽  
Fusahito Yoshida ◽  
Takeshi Uemori
Keyword(s):  
Finite Element ◽  
Kinematic Hardening ◽  
Equivalent Plastic Strain ◽  
Yield Function ◽  
Alloy Sheet ◽  
Integration Scheme ◽  
State Variables ◽  
Tangent Matrix ◽  
Fully Implicit ◽  
Stress Integration

This paper describes fully implicit stress integration scheme for Yoshida’s 6thorder yield function combined with Yoshida-Uemori kinematic hardening model and its consistent tangent matrix. Cutting plane method was employed for accurate integrations of stress and state variables appeared in Yoshida-Uemori model. In the present scheme, equivalent plastic strain, stress tensor and all the state variables are treated as independent variables in order to handle the 6th order yield function which is not the J2 yield function, and the equilibriums for each variables are solved for the stress integration. Subsequently, exact consistent tangent matrix which is necessary for implicit static finite element simulation was obtained. The proposed scheme was implemented into finite element code LS-DYNA and deep drawing process for aluminum alloy sheet was calculated. The earing appearance after drawing was compared with the experiment.

3-D Elastic-Plastic Constitutive Relationship of Mixed Hardening

2012 ◽  
Vol 249-250 ◽  
pp. 927-930
Author(s):  
Ze Yu Wu ◽  
Xin Li Bai ◽  
Bing Ma
Keyword(s):  
Finite Element ◽  
Constitutive Relation ◽  
Kinematic Hardening ◽  
Constitutive Relationship ◽  
Isotropic Hardening ◽  
Element Analysis ◽  
Hardening Model ◽  
Elastic Plastic ◽  
Mixed Hardening ◽  
Advantages And Disadvantages

In finite element calculation of plastic mechanics, isotropic hardening model, kinematic hardening model and mixed hardening model have their advantages and disadvantages as well as applicability area. In this paper, by use of the tensor analysis method and mixed hardening theory in plastic mechanics, the constitutive relation of 3-D mixed hardening problem is derived in detail based on the plane mixed hardening. Numerical results show that, the proposed 3-D mixed hardening constitutive relation agrees well with the test results in existing references, and can be used in the 3-D elastic-plastic finite element analysis.

scholarly journals On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems

2021 ◽  
Author(s):  
Cyprian Suchocki
Keyword(s):  
Finite Element ◽  
Kinematic Hardening ◽  
Constitutive Models ◽  
Small Strain ◽  
Cyclic Plasticity ◽  
Isotropic Hardening ◽  
Mapping Algorithm ◽  
Hardening Rule ◽  
Return Mapping ◽  
Cyclic Plasticity Model

AbstractIn this work the finite element (FE) implementation of the small strain cyclic plasticity is discussed. The family of elastoplastic constitutive models is considered which uses the mixed, kinematic-isotropic hardening rule. It is assumed that the kinematic hardening is governed by the Armstrong–Frederick law. The radial return mapping algorithm is utilized to discretize the general form of the constitutive equation. A relation for the consistent elastoplastic tangent operator is derived. To the best of the author’s knowledge, this formula has not been presented in the literature yet. The obtained set of equations can be used to implement the cyclic plasticity models into numerous commercial or non-commercial FE packages. A user subroutine UMAT (User’s MATerial) has been developed in order to implement the cyclic plasticity model by Yoshida into the open-source FE program CalculiX. The coding is included in the Appendix. It can be easily modified to implement any isotropic hardening rule for which the yield stress is a function of the effective plastic strain. The number of the utilized backstress variables can be easily increased as well. Several validation tests which have been performed in order to verify the code’s performance are discussed.

Effective Models for Prediction of Springback in Flanging

2000 ◽  
Author(s):  
Nan Song ◽  
Dong Qian ◽  
Jian Cao ◽  
Wing Kam Liu ◽  
Vikram Viswanathan ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Finite Element Method ◽  
Finite Element ◽  
Kinematic Hardening ◽  
Meshfree Method ◽  
Isotropic Hardening ◽  
Solid Model ◽  
Hardening Law ◽  
Effective Models ◽  
Springback Angle

Abstract A study on the prediction of springback angle is presented, with focus on the straight flanging operation. The objective is to evaluate the reliability of different ways of prediction. An experiment of straight flanging operation is conducted. Major prediction approaches such as analytical model, numerical simulation using Finite Element Method (FEM) and Meshfree Method are discussed. A set of sample problems is computed and comparisons are made with the experiment. The numerical analysis shows that the prediction from the 3D meshfree contact code matches well with the data from FEM 2d solid model. A material property described by the kinematic hardening law gives a better prediction of springback than the isotropic hardening law.

Stress integration procedures for inelastic material models within the Finite Element Method

2002 ◽  
Vol 55 (4) ◽  
pp. 389-414 ◽  
Author(s):  
Milosˇ Kojic´
Keyword(s):  
Finite Element ◽  
Large Strain ◽  
Deformation Gradient ◽  
Design And Technology ◽  
Parameter Method ◽  
Material Models ◽  
Mapping Procedure ◽  
Inelastic Material ◽  
Tangent Moduli ◽  
Stress Integration

A review of numerical procedures for stress calculation in the inelastic finite element analysis is presented. The role of stress integration within a time (load) step in the incremental-iterative scheme for the displacements based FE formulation is first given briefly. Then, the basic relations of the explicit algorithms, as the first ones developed in the 70s, are presented. The shortcomings of these algorithms are pointed out. The implicit procedures are presented in some detail, with the emphasis on a general return mapping procedure and the governing parameter method (GPM). Derivation of the consistent tangent moduli represents an important task in the inelastic FE analysis because the overall equilibrium iteration rate depends on these moduli. The basic concepts of this derivation are presented. An important field, very challenging in today’s stage of design and technology, is the large strain deformation of material. A review of the approaches in the large strain domain that includes the rate and the total formulations is given in some detail. Special attention is devoted to the multiplicative decomposition of deformation gradient concept, since that concept is generally favored today. Some unresolved issues, such as the use of the stress and strain measures, are discussed briefly. A number of selected numerical examples illustrate the main topics in the stress integration task, as well as the applications of the stress integration algorithms to various material models. Some concluding remarks and an outline of further research topics are given at the end of the paper. This review article includes 205 references.

Springback Prediction Using Finite Element Simulation Incorporated With Hardening Data Acquired From Cyclic Loading Tool

2019 ◽  
Vol 6 (1) ◽  
pp. 19-39
Author(s):  
Jasri Mohamad ◽  
Mohd Zaidi Sidek
Keyword(s):  
Finite Element ◽  
Cyclic Loading ◽  
Bauschinger Effect ◽  
Fe Simulation ◽  
Kinematic Hardening ◽  
Isotropic Hardening ◽  
Mixed Hardening ◽  
Element Simulation ◽  
Simulation Results ◽  
Springback Prediction

The aims of this article are to present the accuracy of springback prediction in U-bending sheet metal forming processes using finite element (FE) simulation incorporated with kinematics or mixed hardening parameters that are derived from cyclic data provided by the developed cyclic loading tool. The FE simulation results in the form of springback angles are compared with the experimental results for validation. It was found that the mixed hardening model provides better simulation results in predicting springback. This is due to the capability of the isotropic hardening part of this model to describe cyclic transient and the kinematic hardening part to improve description of the Bauschinger effect. Kinematic hardening however, on its own is capable of providing relatively good springback simulation illustrated by errors of less than 8 percent. Overall, the data provided by cyclic loading from the newly developed bending-unbending tool is considered valuable for simulating springback prediction.

Shakedown Limit Load Determination for a Kinematically Hardening 90-Degree Pipe Bend Subjected to Constant Internal Pressure and Cyclic Bending

2007 ◽  
Author(s):  
Hany F. Abdalla ◽  
Mohammad M. Megahed ◽  
Maher Y. A. Younan
Keyword(s):  
Finite Element ◽  
Internal Pressure ◽  
Plastic Material ◽  
Kinematic Hardening ◽  
Limit Load ◽  
Material Behavior ◽  
Pipe Bend ◽  
Cyclic Bending ◽  
Perfectly Plastic ◽  
Shakedown Limit

A simplified technique for determining the shakedown limit load of a structure employing an elastic-perfectly-plastic material behavior was previously developed and successfully applied to a long radius 90-degree pipe bend. The pipe bend is subjected to constant internal pressure and cyclic bending. The cyclic bending includes three different loading patterns namely; in-plane closing, in-plane opening, and out-of-plane bending moment loadings. The simplified technique utilizes the finite element method and employs small displacement formulation to determine the shakedown limit load without performing lengthy time consuming full cyclic loading finite element simulations or conventional iterative elastic techniques. In the present paper, the simplified technique is further modified to handle structures employing elastic-plastic material behavior following the kinematic hardening rule. The shakedown limit load is determined through the calculation of residual stresses developed within the pipe bend structure accounting for the back stresses, determined from the kinematic hardening shift tensor, responsible for the translation of the yield surface. The outcomes of the simplified technique showed very good correlation with the results of full elastic-plastic cyclic loading finite element simulations. The shakedown limit moments output by the simplified technique are used to generate shakedown diagrams of the pipe bend for a spectrum of constant internal pressure magnitudes. The generated shakedown diagrams are compared with the ones previously generated employing an elastic-perfectly-plastic material behavior. These indicated conservative shakedown limit moments compared to the ones employing the kinematic hardening rule.

An inhomogeneous cell-based smoothed finite element method for the nonlinear transient response of functionally graded magneto-electro-elastic structures with damping factors

2018 ◽  
Vol 30 (3) ◽  
pp. 416-437 ◽  
Author(s):  
Liming Zhou ◽  
Ming Li ◽  
Bingkun Chen ◽  
Feng Li ◽  
Xiaolin Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Element Model ◽  
Micro Electro Mechanical System ◽  
Functionally Graded ◽  
Elastic Structures ◽  
Mapping Procedure ◽  
Gaussian Integration ◽  
Smoothed Finite Element Method ◽  
Element Method

In this article, an inhomogeneous cell-based smoothed finite element method (ICS-FEM) was proposed to overcome the over-stiffness of finite element method in calculating transient responses of functionally graded magneto-electro-elastic structures. The ICS-FEM equations were derived by introducing gradient smoothing technique into the standard finite element model; a close-to-exact system stiffness was also obtained. In addition, ICS-FEM could be carried out with user-defined sub-routines in the business software now available conveniently. In ICS-FEM, the parameters at Gaussian integration point were adopted directly in the creation of shape functions; the computation process is simplified, for the mapping procedure in standard finite element method is not required; this also gives permission to utilize poor quality elements and few mesh distortions during large deformation. Combining with the improved Newmark scheme, several numerical examples were used to prove the accuracy, convergence, and efficiency of ICS-FEM. Results showed that ICS-FEM could provide solutions with higher accuracy and reliability than finite element method in analyzing models with Rayleigh damping. Such method is also applied to complex structures such as typical micro-electro-mechanical system–based functionally graded magneto-electro-elastic energy harvester. Hence, ICS-FEM can be a powerful tool for transient problems of functionally graded magneto-electro-elastic models with damping which is of great value in designing intelligence structures.

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