Two-point constitutive equations and integration algorithms for isotropic-hardening rate-independent elastoplastic materials in large deformation

2008 ◽  
Vol 75 (12) ◽  
pp. 1435-1456 ◽  
Author(s):  
Zhi-Qiao Wang ◽  
Guan-Suo Dui
Keyword(s):  
Large Deformation ◽  
Constitutive Equations ◽  
Isotropic Hardening ◽  
Elastoplastic Materials ◽  
Integration Algorithms

Deriving Plastic Constitutive Equations of the Material in Complex Stress State by Means of Simple Test Results

2011 ◽  
Vol 109 ◽  
pp. 100-104 ◽  
Author(s):  
Xiao Jiu Feng ◽  
Li Fu Liang
Keyword(s):  
Stress State ◽  
Constitutive Equations ◽  
Complex Stress ◽  
Complex Stress State ◽  
One Dimension ◽  
Isotropic Hardening ◽  
Flow Rule ◽  
Test Results ◽  
Loading Function ◽  
Simple Tension

By conducting simple tension and torsion tests to material, constitutive equations of one dimension are obtained. Plastic theories of continuum mechanics are used for analyzing deformation behavior of the material after yielding. Here, material is presumed to have isotropic hardening characteristic. By using Mises loading function and the associative flow rule, the derivations are made to extend the constitutive equations of one dimension in the simple tension and torsion tests to that of multi-dimension and obtain the plastic constitutive equations of the material in complex stress state , respectively.

scholarly journals Inelastic Material Models of Type 316H for Elevated Temperature Design of Advanced High Temperature Reactors

Energies ◽  
2020 ◽  
Vol 13 (17) ◽  
pp. 4548
Author(s):  
Gyeong-Hoi Koo ◽  
Ji-Hyun Yoon
Keyword(s):  
High Temperature ◽  
Elevated Temperature ◽  
Constitutive Equations ◽  
Isotropic Hardening ◽  
Material Models ◽  
Material Parameters ◽  
Hardening Behavior ◽  
Inelastic Material ◽  
High Temperature Reactors ◽  
Elevated Temperature Design

In this paper, the inelastic material models for Type 316H stainless steel, which is one of the principal candidate materials for elevated temperature design of the advanced high temperature reactors (HTRs) pressure retained components, are investigated and the required material parameters are identified to be used for both elasto-plastic models and unified viscoplastic models. In the constitutive equations of the inelastic material models, the kinematic hardening behavior is expressed with the Chaboche model with three backstresses, and the isotropic hardening behavior is expressed by the Voce model. The required number of material parameters is minimized to be ten in total. For the unified viscoplastic model, which can express both the time-independent plastic behavior and the time-dependent viscous behavior, the constitutive equations have the same kinematic and isotropic hardening parameters of the elasto-plastic material model with two additional viscous parameters. To identify the material parameters required for these constitutive equations, various uniaxial tests were carried out at isothermal conditions at room temperature and an elevated temperature range of 425–650 °C. The identified inelastic material parameters were validated through the comparison between tests and calculations.

Parameter Evaluation for a Unified Constitutive Model

1993 ◽  
Vol 115 (2) ◽  
pp. 157-162 ◽  
Author(s):  
P. E. Senseny ◽  
N. S. Brodsky ◽  
K. L. DeVries
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Least Squares ◽  
Constitutive Equations ◽  
Laboratory Data ◽  
Constant Strain Rate ◽  
Nonlinear Least Squares ◽  
Evolutionary Equation ◽  
Internal Variables ◽  
Isotropic Hardening

Parameters for the unified constitutive model MATMOD [1] were evaluated for rock salt (NaCl) by using nonlinear least squares to fit the model to isothermal laboratory data. MATMOD incorporates two internal variables that represent the effects of both kinematic and isotropic hardening. The constitutive equations contain nine parameters that must be evaluated to model isothermal deformation. Laboratory data from stress relaxation, constant strain rate, and long-term creep tests were used. The latter two test types included staged tests in which the strain rate or stress was changed step-wise during the test. The test conditions were precisely controlled by a computer and the constitutive equations were integrated to simulate the laboratory conditions closely. The MATMOD parameters were then evaluated by fitting the integrated equations to the laboratory data using nonlinear least squares. The model fits the data well, but the fit may be improved by changing the evolutionary equation for the internal variable that accounts for isotropic hardening.

Cyclic Viscoplastic Constitutive Equations, Part I: A Thermodynamically Consistent Formulation

1993 ◽  
Vol 60 (4) ◽  
pp. 813-821 ◽  
Author(s):  
J.-L. Chaboche
Keyword(s):  
Constitutive Equations ◽  
Evolution Equations ◽  
Internal Variables ◽  
Isotropic Hardening ◽  
State Variables ◽  
Inelastic Analysis ◽  
Hardening Process ◽  
Classical Models ◽  
Energy Dissipated ◽  
Consistent Formulation

Cyclic viscoplastic constitutive equations are increasingly used for the inelastic analysis of structures under severe thermomechanical conditions. The purpose of the paper is to show how the classical models can be modified in order to follow the general principles of thermodynamics with internal variables. Using the restrictive framework of standard generalized materials, the state variables associated to various kinds of kinematic and isotropic hardening are selected. The evolution equations for these internal variables are then formulated in a slightly less restrictive form. For each hardening process, the separation of the total plastic work into energy dissipated as heat and energy stored in the material is discussed in detail.

scholarly journals Accurate Numerical Solutions for Elastic-Plastic Models

1979 ◽  
Vol 101 (3) ◽  
pp. 226-234 ◽  
Author(s):  
H. L. Schreyer ◽  
R. F. Kulak ◽  
J. M. Kramer
Keyword(s):  
Numerical Solutions ◽  
Constant Strain Rate ◽  
Single Step ◽  
Isotropic Hardening ◽  
Contour Plots ◽  
Integration Algorithms ◽  
The Common ◽  
The Difference ◽  
Von Mises ◽  
Two Parameters

The accuracy of two integration algorithms is studied for the common engineering condition of a von Mises, isotropic hardening model under plane stress. Errors in stress predictions for given total strain increments are expressed with contour plots of two parameters; an angle in the pi-plane and the difference between the exact and computed yield surface radii. The two methods are the tangent predictor-radial return approach and the elastic predictor-radial corrector algorithm originally developed by Mendelson. The accuracy of a combined tangent predictor-radial corrector algorithm is also investigated. For single-step constant-strain-rate increments the elastic predictor-radial corrector method is generally the most accurate, although errors in angle can be significant. The use of a simple subincrementation formula with any one of the three approaches yields results that would be acceptable for most engineering problems.

Micromorphic constitutive equations with damage applied to metal forming

2017 ◽  
Vol 26 (2) ◽  
pp. 314-339 ◽  
Author(s):  
Evangelia Diamantopoulou ◽  
Weijie Liu ◽  
Carl Labergere ◽  
Houssem Badreddine ◽  
Khemais Saanouni ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Constitutive Equations ◽  
Metal Forming ◽  
Degrees Of Freedom ◽  
Dual Phase Steel ◽  
Isotropic Hardening ◽  
Dual Phase ◽  
Bending Tests ◽  
Assumed Strain ◽  
Explicit Solver

The micromorphic constitutive model developed in previous works and accounting for isotropic plasticity, mixed kinematic and isotropic hardening and micromorphic damage is revised in order to enhance some coupling aspects. The associated numerical aspects are investigated and implemented into ABAQUS®/Explicit solver by developing two subroutines VUMAT to implement the micromorphic model and VUEL to implement an assumed strain-based element with additional micromorphic degrees of freedom. The tensional and bending tests of DP1000 dual phase steel are simulated and used to validate the model by comparing with experimental results.

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