An Eulerian rate formulation of finite strain elastoplasticity is developed based on a fully integrable rate form of hyperelasticity proposed in Part I of this work. A flow rule is proposed in the Eulerian framework, based on the principle of maximum plastic dissipation in six-dimensional stress space for the case of J2 isotropic plasticity. The proposed flow rule bypasses the need for additional evolution laws and/or simplifying assumptions for the skew-symmetric part of the plastic velocity gradient, known as the material plastic spin. Kinematic hardening is modeled with an evolution equation for the backstress tensor considering Prager’s yielding-stationarity criterion. Nonlinear evolution equations for the backstress and flow stress are proposed for an extension of the model to mixed nonlinear hardening. Furthermore, exact deviatoric/volumetric decoupled forms for kinematic and kinetic variables are obtained. The proposed model is implemented with the Zaremba–Jaumann rate and is used to solve the problem of rectilinear shear for a perfectly plastic and for a linear kinematic hardening material. Neither solution produces oscillatory stress or backstress components. The model is then used to predict the nonlinear hardening behavior of SUS 304 stainless steel under fixed-end finite torsion. Results obtained are in good agreement with reported experimental data. The Swift effect under finite torsion is well predicted by the proposed model.
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March 2013
Research-Article
Eulerian Framework for Inelasticity Based on the Jaumann Rate and a Hyperelastic Constitutive Relation—Part II: Finite Strain Elastoplasticity
Amin Eshraghi,
Amin Eshraghi
1
Research Associate
e-mail: maeshrag@uwaterloo.ca
e-mail: maeshrag@uwaterloo.ca
1Corresponding author.
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Hamid Jahed,
Hamid Jahed
Professor
e-mail: hjahedmo@uwaterloo.ca
e-mail: hjahedmo@uwaterloo.ca
Department of Mechanical
and Mechatronics Engineering
,University of Waterloo
,Waterloo, ON, N2L 3G1
, Canada
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Katerina D. Papoulia
Katerina D. Papoulia
Associate Professor
e-mail: papoulia@uwaterloo.ca
Department of Applied Mathematics
,University of Waterloo
,Waterloo, ON, N2L 3G1
, Canada
e-mail: papoulia@uwaterloo.ca
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Amin Eshraghi
Research Associate
e-mail: maeshrag@uwaterloo.ca
e-mail: maeshrag@uwaterloo.ca
Hamid Jahed
Professor
e-mail: hjahedmo@uwaterloo.ca
e-mail: hjahedmo@uwaterloo.ca
Department of Mechanical
and Mechatronics Engineering
,University of Waterloo
,Waterloo, ON, N2L 3G1
, Canada
Katerina D. Papoulia
Associate Professor
e-mail: papoulia@uwaterloo.ca
Department of Applied Mathematics
,University of Waterloo
,Waterloo, ON, N2L 3G1
, Canada
e-mail: papoulia@uwaterloo.ca
1Corresponding author.
Manuscript received July 15, 2012; final manuscript received September 8, 2012; accepted manuscript posted September 29, 2012; published online January 30, 2013. Assoc. Editor: Krishna Garikipati.
J. Appl. Mech. Mar 2013, 80(2): 021028 (11 pages)
Published Online: January 30, 2013
Article history
Received:
July 15, 2012
Revision Received:
September 8, 2012
Accepted:
September 29, 2012
Citation
Eshraghi, A., Jahed, H., and Papoulia, K. D. (January 30, 2013). "Eulerian Framework for Inelasticity Based on the Jaumann Rate and a Hyperelastic Constitutive Relation—Part II: Finite Strain Elastoplasticity." ASME. J. Appl. Mech. March 2013; 80(2): 021028. https://doi.org/10.1115/1.4007724
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