Comparison of two integration algorithms for finite plasticity combined with nonlinear kinematic and isotropic hardening at the example of springback

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 4060033-4060034
Author(s):  
Michael P. Pietryga ◽  
Ivaylo N. Vladimirov ◽  
Stefanie Reese
Keyword(s):  
Isotropic Hardening ◽  
Finite Plasticity ◽  
Integration Algorithms

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.

Finite Element Implementation of a Thermoviscoplastic Model for Ratcheting

2004 ◽  
Author(s):  
Rashid K. Abu Al-Rub ◽  
George Z. Voyiadjis
Keyword(s):  
Finite Element ◽  
Strain Rate ◽  
Yield Criterion ◽  
Isotropic Hardening ◽  
Strain Rate Effects ◽  
Finite Element Implementation ◽  
Rate Dependent ◽  
Proposed Model ◽  
Integration Algorithms ◽  
Von Mises

A thermoviscoplastic constitutive model is proposed to simulate the uniaxial/multiaxial ratcheting of cyclically stable materials and its finite element implementation is also achieved. The kinematic and isotropic hardening rules used in the proposed model are similar to that developed by Voyiadjis and Abu Al-Rub [1], except for the coupling with temperature and strain-rate effects. The proposed constitutive equations include thermo-elasto-viscoplasticity, a dynamic yield criterion of a von Mises type, the associated flow rules, non-linear strain hardening, strain-rate hardening, and temperature softening. In the finite element implementation of the proposed model new implicit stress integration algorithms are proposed. The proposed unified integration algorithms are extensions of the classical rate-independent radial return scheme to the rate-dependent problems. A new expression of consistent tangent modulus is also derived for rate- and temperature-dependent inelasticity. The proposed model is verified by simulating the uniaxial ratcheting of a metallic material.

Explicit and Implicit Integration Algorithms for an Elastoplastic Pipe-Soil Interaction Macroelement Model

2008 ◽  
Author(s):  
Yinghui Tian ◽  
Mark J. Cassidy
Keyword(s):  
Yield Surface ◽  
Nodal Point ◽  
Elastic Behaviour ◽  
Integration Scheme ◽  
Isotropic Hardening ◽  
Flow Rule ◽  
Implicit Integration ◽  
Soil System ◽  
Total Displacement ◽  
Integration Algorithms

This paper presents the numerical formulation of an elastoplastic force-resultant model to numerically simulate the interaction of a pipe with the soil. This approach, which accounts for the load-displacement behaviour of the pipe-soil system on a macroelement level, is becoming increasingly popular in offshore engineering. The model consists of a yield surface, a non-associated flow rule, an isotropic hardening law and a description of purely elastic behaviour. It can be used to predict the behavior of one segment of pipe or numerous models can be attached to structural finite elements as nodal point elements. The latter allows the practical analysis of long pipelines. Further, by removing a number of macroelements from the pipeline, the effect of free span can be studied. To numerically incorporate large numbers of macroelements into a structural analysis, efficient and robust integration algorithms are essential. The use of both explicit and implicit integration algorithms are explored in this paper. In the explicit algorithm, the Euler forward integration scheme is adopted to achieve the real force state incrementally for each substep. On the other hand, the Euler backward integration scheme is adopted in the implicit algorithm. In this case the load state is iteratively “returned” back to the yield surface according to the end of the total displacement increment. Illustrative calculation examples are provided in this paper to demonstrate and compare the performance of the suggested algorithms.

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.

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