A canonical form return mapping algorithm for rate independent plasticity

2001 ◽  
Vol 53 (6) ◽  
pp. 1491-1510 ◽  
Author(s):  
M. A. Keavey
Keyword(s):  
Canonical Form ◽  
Mapping Algorithm ◽  
Return Mapping ◽  
Return Mapping Algorithm

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.

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