Modeling Simple Shear Deformation in Hyperelastoplasticity: A Numerical Integration Algorithm in the Intermediate Configuration

Document Type : Original Article

Authors

Department of Mechanical Engineering, Sahand University of Technology, Tabriz, Iran

Abstract

TThe proposal and development of time integration algorithms in hyperelastic-based plasticity or hyperelastoplasticity, are consistently required due to complex issues such as objectivity. Through the multiplicative decomposition of the deformation gradient tensor, a local configuration known as the intermediate or plastic configuration is generated alongside the reference and the current configurations. Utilizing the intermediate configuration for time integrations eliminates the need to analyze the impact of rigid rotations in the current configuration. Moreover, as the Cauchy stress is derived from parameters in the intermediate configuration, there is no necessity to assess its objectivity. By employing the multiplicative decomposition of the gradient tensor of plastic deformation, equations for kinematic hardening can be derived, eliminating the need to verify objectivity. Therefore, in this article, the algorithm for the subloading surface model, based on the intermediate configuration, is derived by adapting the von Mises model. The rationale behind employing the von Mises model lies in its simplicity compared to the subloading surface model, along with its widespread usage. Additionally, in numerical implementation, the subloading surface model is more complex than the von Mises model. Building upon this, the problem of simple shear deformation with small and large elastic strains, incorporating isotropic, kinematic, and combined hardening in plasticity, has been investigated. The obtained results have been compared with the experimental data and findings from various references. The comparison between the results presented in this article and the available data indicates agreement, suggesting the viability of employing this model in practical applications.

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References

  1. Idesman, A.V., “Comparison of Different Isotropic Elastoplastic Models at Finite Strains Used in Numerical Analysis”, Computer Methods in Applied Mechanics and Engineering, Vol. 192 (41-42), pp.4659-4674, 2003.
  2. Dettmer, W. and Reese, S., “On the Theoretical and Numerical Modelling of Armstrong–Frederick Kinematic Hardening in The Finite Strain Regime”, Computer Methods in Applied Mechanics and Engineering, Vol. 193 (1-2), pp. 87-116, 2004.
  3. Vladimirov, I. N., Pietryga, M. P., and Reese, S., “On the Modelling of Non‐Linear Kinematic Hardening at Finite Strains with Application to Spring back—Comparison of Time Integration Algorithms”, International Journal for Numerical Methods in Engineering, Vol. 75 (1), pp. 1-28, 2008.
  4. Heidari, M., Vafai, A., and Desai, C., “An Eulerian Multiplicative Constitutive Model of Finite Elasto plasticity”, European Journal of Mechanics-A/Solids, Vol. 28 (6), pp.1088-1097, 2009.
  5. Ishikawa, H., “Constitutive Model of Plasticity in Finite Deformation”, International Journal of Plasticity, Vol. 15(3), pp.299-317, 2009.
  6. Eshraghi, A., Jahed, H. and Lambert, S., “A Lagrangian Model for Hardening Behaviour of Materials at Finite Deformation Based on The Right Plastic Stretch Tensor”, Materials & Design (1980-2015), Vol. 31 (5), pp. 2342-2354, 2010.
  7. Zhu, Y., Kang, G. , Kan, Q. H., Yu, C., and Ding, J., “An Extended Cyclic Plasticity Model at Finite Deformations Describing The Bauschinger Effect and Ratchetting Behavior”, In13th International Conference on Fracture June (pp. 16-21), 2013.
  8. Pascon, J. P. and Coda, H. B., “Large Deformation Analysis of Elastoplastic Homogeneous Materials via High Order Tetrahedral Finite Elements”, Finite Elements in Analysis and Design, Vol. 76, pp. 21-38, 2013.
  9. Eshraghi, A., Jahed, H. and Papoulia, K. D., “Eulerian Framework for Inelasticity Based on the Jaumann Rate and a Hyperelastic Constitutive Relation—Part II: Finite Strain Elastoplasticity”, Journal of Applied Mechanics,80 (2), pp. 021028, 2013.
  10. Eshraghi, A., Jahed, H. and Papoulia, K. D., “Eulerian Framework for Inelasticity Based on the Jaumann Rate and a Hyperelastic Constitutive Relation—Part II: Finite Strain Elasto plasticity”,  Journal of Applied Mechanics,80(2), pp. 021028, 2013.
  11. Brepols, T., Vladimirov, I. N. and Reese, S., “Numerical Comparison of Isotropic Hypo-and Hyper elastic-Based Plasticity Models with Application to Industrial Forming Processes”, International Journal of Plasticity,63, pp.18-48, 2014.
  12. Iguchi, T., Yamakawa, K., Hashiguchi, K. and Ikeda, K., “Extended Subloading Surface Model Based on Multiplicative Finite Strain Elastoplasticity Framework: Constitutive Formulation and Fully Implicit Return-Mapping Scheme”, Trans Jpn Soc Mech Eng. https://doi. org/10.1299/Transjsme, pp.17-00008, 2017.
  13. Jiao, Y., and Fish, J., “On the Equivalence Between the Multiplicative Hyper-Elasto-Plasticity and The Additive Hypo-Elasto-Plasticity Based on The Modified Kinetic Logarithmic Stress Rate”, Computer Methods in Applied Mechanics and Engineering, Vol. 340, pp. 824-863, 2018.
  14. Zhang, M. and Montans, F. J., “A Simple Formulation for Large-Strain Cyclic Hyperelasto-Plasticity Using Elastic Correctors. Theory and Algorithmic Implementation”, International Journal of Plasticity, Vol. 113, pp.185-217, 2019.
  15. Nguyen, K., Sanz, M.A. and Montáns, F.J., “Plane-Stress Constrained Multiplicative Hyper elasto-Plasticity with Nonlinear Kinematic Hardening. Consistent Theory Based on Elastic Corrector Rates and Algorithmic Implementation ”, International Journal of Plasticity, Vol. 128, pp. 102592, 2020.
  16. Simo, J. C., “On the Computational Significance of The Intermediate Configuration and Hyperelastic Stress Relations in Finite Deformation Elastoplasticity ”, Mechanics of Materials, Vol. 4(3-4), pp. 439-451, 1985.
  17. Toluei, R. and Kharazi, M., “Implementation of Subloading Surface Model for Hyper Elasto Plasticity with Nonlinear Kinematic/Isotropic Hardening Based on Reference and Intermediate Configurations”, Applied Mathematical Modelling, Vol. 121, pp. 751-779, 2023.
  18. Asaro, R. J., “Micromechanics of Crystals and Polycrystals”, Advances in Applied Mechanics, Vol. 23, pp. 1-115, 1983.
  19. Peirce, D., Asaro, R. J. and Needleman, A., “An Analysis of Nonuniform and Localized Deformation in Ductile Single Crystals”, Acta Metallurgica, Vol. 30 (6), pp. 1087-1119, 1982.
  20. Lion, A., “Constitutive Modelling in Finite Thermo Viscoplasticity: A Physical Approach Based on Nonlinear Rheological Models”, International Journal of Plasticity, Vol. 16 (5), pp. 469-494, 2000.
  21. Mandel, J., “Plasticit´e Classique et Viscoplasticit´e”, Vienna: Springer-Verlag, 1972.
  22. De Souza Neto, E. A., Peric, D. and Owen, D. R., “Computational Methods for Plasticity: Theory and Applications”, John Wiley & Sons, 2011.

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