Three-dimensional plasticity with kinematic and isotropic hardening

2020 ◽  
pp. 421-428
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Plastic Strain ◽  
Kinematic Hardening ◽  
Three Dimensional ◽  
Small Strain ◽  
Back Stress ◽  
Isotropic Hardening ◽  
Evolution Law ◽  
Hardening Model ◽  
Rate Dependent ◽  
Viscoplastic Models

This chapter provides an introduction to combined isotropic-kinematic hardening plasticity models in the three-dimensional small strain setting. The additive decomposition of the strain is introduced along with the concepts of plastic strain, equivalent tensile plastic strain, and back stress for three-dimensional problems. Plastic flow is discussed and defined, and a complete model of plasticity is formulated with Kuhn-Tucker loading/unloading conditions. The kinematic hardening model is based upon the Armstrong-Fredrick evolution law. Both rate-independent and rate-dependent (viscoplastic) models are discussed.

Three-dimensional plasticity with isotropic hardening

2020 ◽  
pp. 406-420
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Plastic Strain ◽  
Plastic Flow ◽  
Three Dimensional ◽  
Small Strain ◽  
Isotropic Hardening ◽  
Flow Rule ◽  
Additive Decomposition ◽  
Flow Models ◽  
Rate Dependent ◽  
Viscoplastic Models

This chapter provides an introduction to isotropic hardening plasticity models in the three-dimensional small strain setting. The additive decomposition of the strain is introduced along with the concepts of plastic strain and equivalent tensile plastic strain for three-dimensional problems. Plastic flow is discussed and defined, and a complete model of plasticity is formulated with Kuhn-Tucker loading/unloading conditions. Both rate independent and rate dependent (viscoplastic) models are discussed with an emphasis on Mises-Hill type theories which utilizes a Prandtl-Reuss flow rule. A variety of important flow models are presented.

One-dimensional plasticity

2020 ◽  
pp. 369-405
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Numerical Methods ◽  
Plastic Strain ◽  
Plastic Flow ◽  
Kinematic Hardening ◽  
Equivalent Plastic Strain ◽  
Additive Decomposition ◽  
One Dimensional ◽  
Rate Dependent ◽  
Viscoplastic Models ◽  
The One

This chapter provides an introduction to plasticity models in the one-dimensional setting. The phenomenology of plasticity is discussed together with concepts of isotropic and kinematic hardening. The additive decomposition of the strain is introduced along with the concepts of plastic strain and equivalent plastic strain. Plastic flow is discussed and defined, and complete models of plasticity are formulated with loading/unloading conditions. Both rate independent and rate dependent (viscoplastic) models are discussed. In addition, basic numerical methods for evaluating plasticity models are presented.

Constitutive Modeling for Simulating a Broad Set of Uniaxial and Multiaxial Cyclic and Ratcheting Responses

2009 ◽  
Author(s):  
Shree Krishna ◽  
Tasnim Hassan
Keyword(s):  
Constitutive Modeling ◽  
Kinematic Hardening ◽  
Cyclic Hardening ◽  
Back Stress ◽  
Multiaxial Loading ◽  
Nonproportional Loading ◽  
Hardening Model ◽  
Rate Dependent ◽  
Chaboche Model ◽  
Cyclic Relaxation

A set of cyclic and ratcheting experimental responses obtained under proportional to various degrees of nonproportional loading cycles are simulated using the modified Chaboche model in its rate-independent and rate-dependent forms. Features of the modified Chaboche nonlinear-kinematic hardening model needed for simulating cyclic hardening-softening, cyclic relaxation and ratcheting responses under uniaxial and multiaxial loading are elaborated. Significance of “rate-dependent” and novel “back stress shift” modeling features in improving the hysteresis loop and ratcheting rate simulations are demonstrated. Influence of the isotropic and kinematic hardening parameters in improving the multiaxial ratcheting response simulation by the modified Chaboche model are illustrated.

Surface plastic strain in contact problems: Prediction by a simplified non-linear kinematic hardening model

2009 ◽  
Vol 44 (3) ◽  
pp. 187-199 ◽  
Author(s):  
A Mazzù
Keyword(s):  
Plastic Strain ◽  
Contact Surface ◽  
Kinematic Hardening ◽  
Contact Problems ◽  
Rolling Contact ◽  
Isotropic Hardening ◽  
Surface Plastic ◽  
Direction Parallel ◽  
Hardening Model ◽  
Non Linear

A previously published model for plasticity assessment in rolling contact, based on a simplification of the non- linear kinematic and isotropic hardening model of Chaboche and Lemaitre, is discussed, and an update is introduced in order to improve its accuracy in the plastic strain prediction within the region just underneath the contact surface. The update is based on a correction of the yield limit and of the strain rate as a function of the load ratio of the tensile stress in the direction parallel to the contact surface. The effectiveness and the accuracy of the updated model in not too severe conditions are demonstrated through comparisons with results obtained by finite element model (FEM) analyses. An application of the model to some experimental results obtained on rail and railway wheel steels is also carried out, and quite good agreement is found in plastic strain prediction, although some discrepancies are found. The method appears to be a valid tool for practical application, especially for its ability of combining the effects of different phenomena and of simulating a number of cycles of the order of millions in a reasonable time.

Analytical Solutions for Circular Bars Subjected to Large Strain Plastic Torsion

1990 ◽  
Vol 57 (2) ◽  
pp. 298-306 ◽  
Author(s):  
K. W. Neale ◽  
S. C. Shrivastava
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Large Strain ◽  
Kinematic Hardening ◽  
Flow Theory ◽  
Constitutive Laws ◽  
Isotropic Hardening ◽  
Large Strains ◽  
Inelastic Behavior ◽  
Rate Dependent

The inelastic behavior of solid circular bars twisted to arbitrarily large strains is considered. Various phenomenological constitutive laws currently employed to model finite strain inelastic behavior are shown to lead to closed-form analytical solutions for torsion. These include rate-independent elastic-plastic isotropic hardening J2 flow theory of plasticity, various kinematic hardening models of flow theory, and both hypoelastic and hyperelastic formulations of J2 deformation theory. Certain rate-dependent inelastic laws, including creep and strain-rate sensitivity models, also permit the development of closed-form solutions. The derivation of these solutions is presented as well as numerous applications to a wide variety of time-independent and rate-dependent plastic constitutive laws.

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.

Influence of the Hardening Model on the Predicted Welding Distortion of DP600 Lap Joints

2010 ◽  
Vol 638-642 ◽  
pp. 3710-3715
Author(s):  
T. Schenk ◽  
I.M. Richardson ◽  
G. Eßer ◽  
M. Kraska
Keyword(s):  
Kinematic Hardening ◽  
Tensile Tests ◽  
Lap Joints ◽  
Welding Distortion ◽  
Isotropic Hardening ◽  
Hardening Model ◽  
Mixed Hardening ◽  
Overlap Joint ◽  
Definition Of ◽  
Robust Process

The accurate prediction of welding distortion is an important requirement for the industry in order to allow the definition of robust process parameters without the need to perform expensive experiments. Many models have been developed in the past decades in order to improve prediction. Assumptions are made to make the models tractable; however, the consequences are rarely discussed. One example for such an assumption is the strain hardening model, which is often a choice between either kinematic or isotropic hardening. This paper presents the results of tensile tests for DP600 performed from room temperature up to one thousand degrees and for different strain-rates. In order to employ a mixed isotropic-kinematic hardening model, the fractions of each hardening contribution have been determined by means of bend testing. The welding distortion of a DP600 overlap joint has been simulated and it is shown that such a mixed-hardening model results in more accurate and reliable results.

Revisiting the Deshpande-Fleck Foam Model

2019 ◽  
Vol 803 ◽  
pp. 134-139
Author(s):  
Chang Feng Zhu ◽  
Zhi Jun Zheng ◽  
Shi Long Wang ◽  
Kai Zhao ◽  
Ji Lin Yu
Keyword(s):  
Finite Element ◽  
Plastic Strain ◽  
Equivalent Plastic Strain ◽  
Element Model ◽  
The Self ◽  
Isotropic Hardening ◽  
Hardening Model ◽  
Foam Model ◽  
A Cell ◽  
Self Similar

The self-similar isotropic hardening model developed by Deshpande and Fleck has been widely used. An important issue in this model is to determine the value of ellipticity. The ellipticity was treated as a constant in the subsequent yield, but different values were suggested in the literature. In this paper a cell-based finite element model based on the 3D Voronoi technique is used to verify the Deshpande-Fleck foam model. It is found that the ellipticity determined from uniaxial and hydrostatic compressions varies with the equivalent plastic strain.

Sign in / Sign up

Export Citation Format

Share Document