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# A.S. Nasab, M. Mashayekhi, "Application of an efficient anisotropic damage model to the prediction of the failure of metal forming processes", International Journal of Damage Mechanics 28 (10), PP. 1556-1579, 2019

**Abstract:**

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.