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.

scholarly journals About an approximate method to solve the static boundary value problems in the isotropic hardening elastic-plastic solid

2006 ◽  
Vol 28 (2) ◽  
pp. 74-82
Author(s):  
Ngo Thanh Phong ◽  
Nguyen Thoi Trung ◽  
Nguyen Phu Vinh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Approximate Method ◽  
Weak Form ◽  
Theory Model ◽  
Isotropic Hardening ◽  
Mapping Algorithm ◽  
Elastic Plastic ◽  
Return Mapping ◽  
Return Mapping Algorithm

The paper presents the theory, model, weak form, finite element method and return-mapping algorithm for the isotropic hardening elastic-plastic problem. Then applying the algorithm to numerically simulate a variety of plane strain problems.

Finite Element Analysis of V-Bending of Polypropylene Using Hydrostatic-Pressure Dependent Plastic Constitutive Equation

2007 ◽  
Vol 340-341 ◽  
pp. 1103-1108 ◽  
Author(s):  
Kunio Hayakawa ◽  
Yukio Sanomura ◽  
Mamoru Mizuno ◽  
Yukio Kasuga ◽  
Tamotsu Nakamura
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Hydrostatic Pressure ◽  
Constitutive Equations ◽  
Kinematic Hardening ◽  
Uniaxial Stress ◽  
Isotropic Hardening ◽  
Element Analysis ◽  
Hardening Rule ◽  
Stress Strain Relation

Finite element analysis of V-bending process of polypropylene was performed using hydrostatic-dependent elastic-plastic constitutive equations proposed by the present authors. Kinematic and isotropic hardening rule was employed for the plastic constitutive equations. The kinematic hardening rule was more suitable for the expression of the stress reversal in uniaxial stress - strain relation than the isotropic hardening. For the result of the finite element analysis of V-bending, the kinematic hardening rule was able to predict the experimental behavior of springback more properly than the isotropic hardening. Moreover, the effects of hydrostatic pressure-dependence were revealed by examining the calculated distribution of bending plastic strain, bending stress and the width of the bent specimen.

An Evaluation of Recent Developments in Hardening and Flow Rules for Rate-Independent, Nonproportional Cyclic Plasticity

1987 ◽  
Vol 54 (2) ◽  
pp. 323-334 ◽  
Author(s):  
D. L. McDowell
Keyword(s):  
Kinematic Hardening ◽  
Cyclic Plasticity ◽  
Modulus Function ◽  
Isotropic Hardening ◽  
Hardening Rule ◽  
Hardening Modulus ◽  
Recent Developments ◽  
Distance Vector ◽  
Plastic Hardening ◽  
Hardening Rules

The Mroz kinematic hardening rule has previously demonstrated superior capability to correlate cyclically stable nonproportional stress-strain response. In this paper, recently proposed kinematic hardening rules for single and multiple surface cyclic plasticity models are evaluated. Significant improvement over the Mroz rule, without loss of generality, is achieved with a deviatoric stress rate-dominated rule proposed by Tseng and Lee for two surface theory. Recent approaches for correlation of the modulus function and isotropic hardening are discussed. The norm of the Mroz distance vector is found to uniquely correlate the variation of plastic hardening modulus through a cycle; it is necessary to include a measure of instantaneous nonproportionality, however, to properly normalize the modulus function. A new evolution equation is offered to correlate the additional isotropic hardening observed during nonproportional loading, and several contemporary approaches are also considered.

Cyclic Plasticity for Nonproportional Paths: Part 2—Comparison With Predictions of Three Incremental Plasticity Models

1978 ◽  
Vol 100 (1) ◽  
pp. 104-111 ◽  
Author(s):  
H. S. Lamba ◽  
O. M. Sidebottom
Keyword(s):  
Cyclic Loading ◽  
Material Property ◽  
Yield Surface ◽  
Strain Path ◽  
Kinematic Hardening ◽  
Cyclic Plasticity ◽  
Limit Surface ◽  
Hardening Rule ◽  
Hardening Models ◽  
Hardening Rules

Experiments that demonstrate the basic quantitative and qualitative aspects of the cyclic plasticity of metals are presented in Part 1. Three incremental plasticity kinematic hardening models of prominence are based on the Prager, Ziegler, and Mroz hardening rules, of which the former two have been more frequently used than the latter. For a specimen previously fully stabilized by out of phase cyclic loading the results of a subsequent cyclic nonproportional strain path experiment are compared to the predictions of the above models. A formulation employing a Tresca yield surface translating inside a Tresca limit surface according to the Mroz hardening rule gives excellent predictions and also demonstrates the erasure of memory material property.

Measurement of Cyclic Biaxial Elastoplastic Stresses at Notch Roots

1995 ◽  
Vol 62 (3) ◽  
pp. 646-653 ◽  
Author(s):  
C. H. Yang ◽  
W. N. Sharpe
Keyword(s):  
Constitutive Models ◽  
Measuring System ◽  
Cyclic Plasticity ◽  
Elastoplastic Behavior ◽  
Cyclic Stresses ◽  
Fine Grain ◽  
Notch Geometry ◽  
Cyclic Plasticity Model ◽  
Elastoplastic Constitutive Model ◽  
Good Agreement

A straightforward procedure is demonstrated for measuring local cyclic elastoplastic biaxial stresses at notch roots. First, the biaxial cyclic strains are measured over short gage lengths (150 or 200 micrometers) with a laser-based strain measuring system. Then, cyclic stresses are computed from those measured strains by using an elastoplastic constitutive model. The material selected for this study is HY-80 steel which has a fine grain size and is isotropic. Double-notched specimens were prepared with two different notch geometries: a U-shaped notch with a 4.76 mm radius and a V-shaped notch with a 1.0 mm radius. Two thicknesses, 2.54 and 12.7 mm, were tested for each notch geometry to produce four different amounts of notch constraint. The results of cyclic biaxial strain measurements show good reproducibility. Stress computations based on two different constitutive models were used to compute stresses for the first cycle and a stable cycle. One of the constitutive models is the classical J2flow theory and the other is a two-surface cyclic plasticity model. The results computed using these two models show good agreement with each other. The measured stresses show the effect of constraint on the elastoplastic behavior at notch roots under cyclic loading conditions.

Prediction of Fatigue Crack Initiation Life Based on the Extended Cyclic Plasticity Model

2012 ◽  
Author(s):  
Seiichiro Tsutsumi
Keyword(s):  
Cyclic Loading ◽  
Kinematic Hardening ◽  
Fatigue Crack Initiation ◽  
Fatigue Cracking ◽  
Carbon Steels ◽  
Cyclic Plasticity ◽  
Plasticity Model ◽  
Hardening Law ◽  
Crack Initiation Life ◽  
Cyclic Plasticity Model

In order to simulate mechanical fatigue phenomena under macroscopically elastic condition, the plastic stretching within a yield surface has to be described, whilst the plastic strain is induced remarkably as the stress approaches the dominant yielding state. In this study, a phenomenological plasticity model, proposed for the description of the cyclic loading behavior observed for typical carbon steels during the high-cycle fatigue subjected to stresses lower than the yield stress, is applied for the prediction of fatigue initiation life. The model is formulated based on the unconventional plasticity model and is applied for materials obeying isotropic and kinematic hardening law. The mechanical responses under cyclic loading conditions are examined briefly. Finally, the initiation life of fatigue cracking is discussed based on the proposed model with the damage counting parameter.

Cyclic Loading of Beams Based on Kinematics Hardening Behavior Coupled With Isotropic Damage

2006 ◽  
Author(s):  
Ali Nayebi ◽  
Kourosh H. Shirazi
Keyword(s):  
Cyclic Loading ◽  
Strain Hardening ◽  
Kinematic Hardening ◽  
Damage Model ◽  
Mapping Algorithm ◽  
Return Mapping ◽  
Tension And Compression ◽  
Computational Aspects ◽  
Isotropic Damage ◽  
Path Dependent

The kinematic hardening theory of plasticity based on the Prager model and incremental isotropic damage is used to evaluate the cyclic loading behavior of a beam under the axial, bending, and thermal loads. This allows damage to be path-dependent. The damage and inelastic deformation are incorporated and they are used for the analysis of the beam. The beam material is assumed to follow linear strain hardening property coupled with isotropic damage. The material strain hardening curves in tension and compression are assumed to be both identical for the isotropic material. Computational aspects of rate independent model is discussed and the constitutive equation of the rate independent plasticity coupled with the damage model are decomposed into the elastic, plastic and damage parts. Return Mapping Algorithm method is used for the correction of the elastoplastic state and for the damage model the algorithm is used according to the governed damage constitutive relation. The effect of the damage phenomenon coupled with the elastoplastic kinematic hardening is studied for deformation and load control loadings.

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.

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