Return mapping algorithm for elasto-plastic deformation of thin walled pipes

2020 ◽  
Vol 188 ◽  
pp. 104245
Author(s):  
F.H. de Vries ◽  
H.J.M. Geijselaers ◽  
A.H. van den Boogaard
Keyword(s):  
Plastic Deformation ◽  
Mapping Algorithm ◽  
Return Mapping ◽  
Return Mapping Algorithm ◽  
Thin Walled

Meshless Analyses of Fracture, Plasticity and Impact

2003 ◽  
Author(s):  
A. Eskandarian ◽  
Y. Chen ◽  
M. Oskard ◽  
J. D. Lee
Keyword(s):  
High Speed ◽  
Large Strain ◽  
Plastic Response ◽  
Governing Equations ◽  
Mapping Algorithm ◽  
High Speed Impact ◽  
Return Mapping ◽  
Return Mapping Algorithm ◽  
Large Strain Plasticity ◽  
Computational Plasticity

The governing equations for rate-independent large strain plasticity are formulated in the framework of meshless method. The numerical procedures, including return mapping algorithm, to obtain the solutions of boundary-value problems in computational plasticity are outlined. The crack growth process in elastic-plastic solid under plane strain conditions is analyzed. The large strain plastic response of material under high-speed impact is simulated. Numerical results are presented and discussed.

Two Efficient Algorithms of Plastic Integration for Sheet Forming Modeling

2007 ◽  
Vol 129 (4) ◽  
pp. 698-704 ◽  
Author(s):  
Y. M. Li ◽  
B. Abbès ◽  
Y. Q. Guo
Keyword(s):  
Equivalent Stress ◽  
Sheet Forming ◽  
Efficient Algorithms ◽  
Integration Scheme ◽  
Fast Method ◽  
Numerical Experience ◽  
Mapping Algorithm ◽  
Inverse Approach ◽  
Return Mapping ◽  
Return Mapping Algorithm

A fast method called the “inverse approach” for sheet forming modeling is based on the assumptions of the proportional loading and simplified tool actions. To improve the stress estimation, the pseudo-inverse approach was recently developed: some realistic intermediate configurations are geometrically determined to consider the deformation paths; two new efficient algorithms of plastic integration are proposed to consider the loading history. In the direct scalar algorithm (DSA), an elastic unloading-reloading factor γ is introduced to deal with the bending-unbending effects; the equation in unknown stress vectors is transformed into a scalar equation using the notion of the equivalent stress, thus the plastic multiplier Δλ can be directly obtained without iterative resolution scheme. In the γ-return mapping algorithm, the equivalent plastic strain increment estimated by DSA is taken as the initial solution in Simo’s return mapping algorithm, leading to a stable, efficient, and accurate plastic integration scheme. The numerical experience has shown that these two algorithms give a considerable reduction of CPU time in the plastic integration.

DUCTILE DAMAGE ANALYSIS BASED ON A J3-GTN-LIKE MODEL

2011 ◽  
Vol 03 (04) ◽  
pp. 189-215 ◽  
Author(s):  
LARBI SIAD
Keyword(s):  
Constitutive Model ◽  
Yield Function ◽  
Shear Loading ◽  
Isotropic Hardening ◽  
Single Element ◽  
Mapping Algorithm ◽  
Failure Initiation ◽  
Fully Implicit ◽  
Return Mapping ◽  
Return Mapping Algorithm

A GTN-like model which yield function explicitly depends upon the third stress invariant is first described in this paper. Subsequently, a fully implicit stress integration procedure of this constitutive model based on the return-mapping algorithm is developed. The validity and the performance of the implementation of the considered algorithm within a finite element code are checked through simulations of single element test and three-element test under hydrostatic tensile conditions and simple shear loading as well. Afterwards, as a numerical example, the presented constitutive model and, for the purpose of comparison, the GTN isotropic hardening model, are used to analyze the classical tensile test of axisymmetric notched specimens. The obtained results highlight similarities, good agreement between both models as long as failure initiation of specimen is not reached, and discrepancy as soon as failure of specimen starts.

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