Line 1: Line 1:
 +
==Abstract==
 +
In this work we compare two frameworks for thermodynamically consistent
 +
hyperelasto-plasticity with kinematic hardening. The first was formulated by Dettmer and
 +
Reese (2004), inspired by Lion (2000), and has been used to model sheet metal forming.
 +
The second, formulated by Wallin et al. (2003), has been used to model large shear
 +
strains and cyclic ratcheting behavior of pearlitic steel (Johansson et al. 2006). In this
 +
paper we show that these frameworks can result in equivalent models for certain choices
 +
of free energies. Furthermore, it is shown that the choices of free energy found in the
 +
literature only result in minor differences. These differences are discussed theoretically
 +
and investigated numerically.
 +
 +
==Full document==
 
<pdf>Media:Meyer_2017a_7099_complas2017.pdf</pdf>
 
<pdf>Media:Meyer_2017a_7099_complas2017.pdf</pdf>
 +
 +
==References==
 +
{|
 +
|- style="vertical-align:top;"
 +
| style="text-align:right;" |[1]
 +
| style="width:20px;"  |
 +
| F. A. M Alwahdi, A. Kapoor, and F. J. Franklin. "Subsurface microstructural analysis and mechanical properties of pearlitic rail steels in service". Wear 302.1-2 (2013), pp. 1453-1460. doi: 10.1016/j.wear.2012.12.058.
 +
|- style="vertical-align:top;"
 +
| style="text-align:right;" |[2]
 +
| style="width:20px;"  |
 +
| K. Cvetkovski and J. Ahlström. "Characterisation of plastic deformation and thermal softening of the surface layer of railway passenger wheel treads". Wear 300.1-2 (2013), pp. 200-204. doi: 10.1016/j.wear.2013.01.094.
 +
|- style="vertical-align:top;"
 +
| style="text-align:right;" |[3]
 +
| style="width:20px;"  |
 +
| A. Lion. "Constitutive modelling in finite thermoviscoplasticity: a physical approachbased on nonlinear rheological models". International Journal of Plasticity 16.5 (2000), pp. 469-494. doi: 10.1016/S0749-6419(99)00038-8.
 +
|- style="vertical-align:top;"
 +
| style="text-align:right;" |[4]
 +
| style="width:20px;"  |
 +
| W. Dettmer and S. Reese. "On the theoretical and numerical modelling of Armstrong-Frederick kinematic hardening in the finite strain regime". In: Computer Methods in Applied Mechanics and Engineering 193.1 (2004), pp. 87-116. doi: 10.1016/j.cma.2003.09.005.
 +
|- style="vertical-align:top;"
 +
| style="text-align:right;" |[5]
 +
| style="width:20px;"  |
 +
| M. Wallin, M. Ristinmaa, and N. S. Ottosen. "Kinematic hardening in large strain plasticity". In: European Journal of Mechanics - A/Solids 22.3 (2003), pp. 341-356. doi: 10.1016/S0997-7538(03)00026-3.
 +
|- style="vertical-align:top;"
 +
| style="text-align:right;" |[6]
 +
| style="width:20px;"  |
 +
| M. Wallin and M. Ristinmaa. "Deformation gradient based kinematic hardening model". In: International Journal of Plasticity 21.10 (2005), pp. 2025-2050. doi:10.1016/j.ijplas.2005.01.007.
 +
|- style="vertical-align:top;"
 +
| style="text-align:right;" |[7]
 +
| style="width:20px;"  |
 +
|G. Johansson, J. Ahlström, and M. Ekh. "Parameter identification and modeling of large ratcheting strains in carbon steel". In: Computers and Structures 84.15-16 (2006), pp. 1002-1011. doi: 10.1016/j.compstruc.2006.02.016.
 +
|- style="vertical-align:top;"
 +
| style="text-align:right;" |[8]
 +
| style="width:20px;"  |
 +
| N. Larijani, G. Johansson, and M. Ekh. "Hybrid micro-macromechanical modeling of anisotropy evolution in pearlitic steel". In: European Journal of Mechanics - A/Solids 38 (Mar. 2013), pp. 38-47. doi: 10.1016/j.euromechsol.2012.09.011.
 +
|- style="vertical-align:top;"
 +
| style="text-align:right;" |[9]
 +
| style="width:20px;"  |
 +
| J. C. Simo. "A Framework For Finite Strain Based on Maximum plastic dissipation and the multiplicative decomposition: Part I. Continuum formulation". In: Computer Methods in Applied Mechanics and Engineering 66 (1988), pp. 199-219.
 +
|- style="vertical-align:top;"
 +
| style="text-align:right;" |[10]
 +
| style="width:20px;"  |
 +
| A. Lion. I. N. Vladimirov, M. P. Pietryga, and S. Reese. "On the modelling of non-linear kinematic hardening at finite strains with application to springback - Comparison of time integration algorithms". In: International Journal for Numerical Methods in Engineering 75.1 (July 2008), pp. 1-28. doi: 10.1002/nme.2234.
 +
|- style="vertical-align:top;"
 +
| style="text-align:right;" |[11]
 +
| style="width:20px;"  |
 +
| Y. Zhu et al. "An extended cyclic plasticity model at finite deformations describing the Bauschinger effect and ratchetting behavior". In: 13th International Conference on Fracture 2013, ICF 2013 5 (2013), pp. 1-11.
 +
|- style="vertical-align:top;"
 +
| style="text-align:right;" |[12]
 +
| style="width:20px;"  |
 +
| J. Korelc. "Multi-language and Multi-environment Generation of Nonlinear Finite Element Codes". In: Engineering with Computers 18.4 (Nov. 2002), pp. 312-327. doi: 10.1007/s003660200028.
 +
|}

Latest revision as of 11:46, 16 May 2017

Abstract

In this work we compare two frameworks for thermodynamically consistent hyperelasto-plasticity with kinematic hardening. The first was formulated by Dettmer and Reese (2004), inspired by Lion (2000), and has been used to model sheet metal forming. The second, formulated by Wallin et al. (2003), has been used to model large shear strains and cyclic ratcheting behavior of pearlitic steel (Johansson et al. 2006). In this paper we show that these frameworks can result in equivalent models for certain choices of free energies. Furthermore, it is shown that the choices of free energy found in the literature only result in minor differences. These differences are discussed theoretically and investigated numerically.

Full document

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References

[1] F. A. M Alwahdi, A. Kapoor, and F. J. Franklin. "Subsurface microstructural analysis and mechanical properties of pearlitic rail steels in service". Wear 302.1-2 (2013), pp. 1453-1460. doi: 10.1016/j.wear.2012.12.058.
[2] K. Cvetkovski and J. Ahlström. "Characterisation of plastic deformation and thermal softening of the surface layer of railway passenger wheel treads". Wear 300.1-2 (2013), pp. 200-204. doi: 10.1016/j.wear.2013.01.094.
[3] A. Lion. "Constitutive modelling in finite thermoviscoplasticity: a physical approachbased on nonlinear rheological models". International Journal of Plasticity 16.5 (2000), pp. 469-494. doi: 10.1016/S0749-6419(99)00038-8.
[4] W. Dettmer and S. Reese. "On the theoretical and numerical modelling of Armstrong-Frederick kinematic hardening in the finite strain regime". In: Computer Methods in Applied Mechanics and Engineering 193.1 (2004), pp. 87-116. doi: 10.1016/j.cma.2003.09.005.
[5] M. Wallin, M. Ristinmaa, and N. S. Ottosen. "Kinematic hardening in large strain plasticity". In: European Journal of Mechanics - A/Solids 22.3 (2003), pp. 341-356. doi: 10.1016/S0997-7538(03)00026-3.
[6] M. Wallin and M. Ristinmaa. "Deformation gradient based kinematic hardening model". In: International Journal of Plasticity 21.10 (2005), pp. 2025-2050. doi:10.1016/j.ijplas.2005.01.007.
[7] G. Johansson, J. Ahlström, and M. Ekh. "Parameter identification and modeling of large ratcheting strains in carbon steel". In: Computers and Structures 84.15-16 (2006), pp. 1002-1011. doi: 10.1016/j.compstruc.2006.02.016.
[8] N. Larijani, G. Johansson, and M. Ekh. "Hybrid micro-macromechanical modeling of anisotropy evolution in pearlitic steel". In: European Journal of Mechanics - A/Solids 38 (Mar. 2013), pp. 38-47. doi: 10.1016/j.euromechsol.2012.09.011.
[9] J. C. Simo. "A Framework For Finite Strain Based on Maximum plastic dissipation and the multiplicative decomposition: Part I. Continuum formulation". In: Computer Methods in Applied Mechanics and Engineering 66 (1988), pp. 199-219.
[10] A. Lion. I. N. Vladimirov, M. P. Pietryga, and S. Reese. "On the modelling of non-linear kinematic hardening at finite strains with application to springback - Comparison of time integration algorithms". In: International Journal for Numerical Methods in Engineering 75.1 (July 2008), pp. 1-28. doi: 10.1002/nme.2234.
[11] Y. Zhu et al. "An extended cyclic plasticity model at finite deformations describing the Bauschinger effect and ratchetting behavior". In: 13th International Conference on Fracture 2013, ICF 2013 5 (2013), pp. 1-11.
[12] J. Korelc. "Multi-language and Multi-environment Generation of Nonlinear Finite Element Codes". In: Engineering with Computers 18.4 (Nov. 2002), pp. 312-327. doi: 10.1007/s003660200028.
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