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On the modelling of complex kinematic hardening and nonquadratic anisotropic yield criteria at finite strains: application to sheet metal forming

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Abstract

In the present paper, a finite strain model for complex combined isotropic-kinematic hardening is presented. It accounts for finite elastic and finite plastic strains and is suitable for any anisotropic yield criterion. In order to model complex cyclic hardening phenomena, the kinematic hardening is described by several back stress components. To that end, a new procedure is proposed in which several multiplicative decompositions of the plastic part of the deformation gradient are considered. The formulation incorporates a completely general format of the yield function, which means that any yield function can by employed by following a procedure that ensures the principle of material frame indifference. The constitutive equations are derived in a thermodynamically consistent way and numerically integrated by means of a backward-Euler algorithm based on the exponential map. The performance of the constitutive model is assessed via numerical simulations of industry-relevant sheet metal forming processes (U-channel forming and draw/re-draw of a panel benchmarks), the results of which are compared to experimental data. The comparison between numerical and experimental results shows that the use of multiple back stress components is very advantageous in the description of springback. This holds in particular if one carries out a comparison with the results of using only one component. Moreover, the numerically obtained results are in excellent agreement with the experimental data.

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Acknowledgments

The authors acknowledge the financial support by the grants SFRH/BD/82286/2011 and PTDC/ EME-TME/115876/2009 from the Fundação para a Ciência e a Tecnologia, Ministerio da Educação e Ciência (Portugal).

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Author notes

  1. Ivaylo N. Vladimirov

    Present address: MTU Aero Engines AG, 80995, Muenchen, Germany

Authors and Affiliations

  1. GRIDS Research Group, Centre for Mechanical Technology & Automation, University of Aveiro, 3810-193, Aveiro, Portugal

    Tiago J. Grilo & Robertt A. F. Valente

  2. Institute of Applied Mechanics, RWTH Aachen University, 52074, Aachen, Germany

    Ivaylo N. Vladimirov & Stefanie Reese

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  1. Tiago J. Grilo
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  2. Ivaylo N. Vladimirov
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  3. Robertt A. F. Valente
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  4. Stefanie Reese
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Correspondence to Tiago J. Grilo.

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Grilo, T.J., Vladimirov, I.N., Valente, R.A.F. et al. On the modelling of complex kinematic hardening and nonquadratic anisotropic yield criteria at finite strains: application to sheet metal forming. Comput Mech 57, 931–946 (2016). https://doi.org/10.1007/s00466-016-1270-6

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  • DOI: https://doi.org/10.1007/s00466-016-1270-6

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