A return mapping algorithm for elastoplastic and ductile damage constitutive equations using the subloading surface method

2017 ◽  
Vol 113 (11) ◽  
pp. 1729-1754 ◽  
Author(s):  
R. Fincato ◽  
S. Tsutsumi
Keyword(s):  
Constitutive Equations ◽  
Ductile Damage ◽  
Mapping Algorithm ◽  
Return Mapping ◽  
Return Mapping Algorithm ◽  
Surface Method

Application of an efficient anisotropic damage model to the prediction of the failure of metal forming processes

2019 ◽  
Vol 28 (10) ◽  
pp. 1556-1579 ◽  
Author(s):  
Ali Salehi Nasab ◽  
Mohammad Mashayekhi
Keyword(s):  
Constitutive Equations ◽  
Metal Forming ◽  
Kinematic Hardening ◽  
Ductile Damage ◽  
Irreversible Processes ◽  
Anisotropic Damage ◽  
Mapping Algorithm ◽  
Return Mapping ◽  
Integration Schemes ◽  
Return Mapping Algorithm

The main objective of this study is the numerical implementation of an advanced elastic–plastic model fully coupled with anisotropic ductile damage. The implemented formulation has been defined in the framework of thermodynamics of irreversible processes and a symmetric second-order tensor is adopted to describe the anisotropic damage state variable. After a summary of the main constitutive equations is given, the numerical integration of constitutive equations is performed using implicit and asymptotic integration schemes. Finite element simulation is performed using ABAQUS/Explicit software and the developed VUMAT subroutine. Next, the application of the developed model to T-shaped hydroforming of tubes and square-cup deep drawing metal forming processes is thoroughly discussed and failure onset zones due to anisotropic ductile damage growth are predicted and the results were consistent with the literature. Finally, by making an assumption that kinematic hardening can be ignored, an elastic predictor/plastic corrector algorithm requiring the solution of one equation is introduced. The assessment of the developed one-equation return-mapping algorithm is carried out by applying it to the simulation of the tensile test of a pre-notched bar. The Central Prossessing Unit time decreases noticeably using one-equation return mapping algorithm compared to the conventional return mapping algorithm and the numerical results are in good agreement with previous numerical simulations and experiments.

Coupled Damage and Plasticity Modeling in Failure Analysis of Heated Concrete

2013 ◽  
Vol 671-674 ◽  
pp. 1531-1534
Author(s):  
Rong Tao Li
Keyword(s):  
Constitutive Model ◽  
Constitutive Equations ◽  
Iterative Procedure ◽  
Mechanical Analysis ◽  
Mapping Algorithm ◽  
Return Mapping ◽  
Return Mapping Algorithm ◽  
Damage Constitutive Model ◽  
Heated Concrete ◽  
Elastoplastic Damage

A coupled elastoplastic-damage constitutive model with consideration of chemo-induced material elastoplastic-damage effects due to heating concrete is proposed. A consistent return mapping algorithm for the integration of the rate coupled constitutive equations is developed. Consistent tangent modulus matrices for coupled chemo-thermo-hygro-mechanical analysis are derived to preserve the quadratic rate of convergence of the global Newton iterative procedure. Numerical results demonstrate the validity of the presented algorithm and illustrate the performance of the proposed constitutive model in reproducing coupled chemo-thermo-hygro-mechanical behavior in concretes subjected to fire.

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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