On the introduction of return mapping schemes in elasto-plastic finite element simulations for isotropic and kinematic hardening

In this study, suitable distinct stress integration algorithms for advanced anisotropic models with mixed hardening, and their implementation in finite element codes, are discussed. The constitutive model studied in the present work accounts for advanced (non-quadratic) anisotropic yield criteria, namely, the Barlat et al. 2004 model with 18 coefficients (Yld2004-18p), combined with a mixed isotropic-nonlinear kinematic hardening law. This phenomenological model allows for an accurate description of complex plastic yielding anisotropy and Bauschinger effects, which are essential for a reliable prediction of deep drawing and springback results using numerical simulations.In the present work distinct algorithm classes are analysed: (i) a semi-explicit algorithm that accounts for the sub-incrementation technique; (ii) the cutting-plane approach (semi-implicit integration); and (iii) the fully-implicit multi-stage return mapping procedure, based on the control of the potential residual. The numerical performance of the developed algorithms is inferred by benchmarks in sheet metal forming processes. The quality of the solution is assessed and compared to reference results. In the end, an algorithmic and programming framework is provided, suitable for a direct implementation in commercial Finite Element codes, such as Abaqus (Simulia) and Marc (MSC-Software) packages.

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On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems

Acta Mechanica ◽

10.1007/s00707-021-03069-3 ◽

2021 ◽

Author(s):

Cyprian Suchocki

Keyword(s):

Finite Element ◽

Kinematic Hardening ◽

Constitutive Models ◽

Small Strain ◽

Cyclic Plasticity ◽

Isotropic Hardening ◽

Mapping Algorithm ◽

Hardening Rule ◽

Return Mapping ◽

Cyclic Plasticity Model

AbstractIn this work the finite element (FE) implementation of the small strain cyclic plasticity is discussed. The family of elastoplastic constitutive models is considered which uses the mixed, kinematic-isotropic hardening rule. It is assumed that the kinematic hardening is governed by the Armstrong–Frederick law. The radial return mapping algorithm is utilized to discretize the general form of the constitutive equation. A relation for the consistent elastoplastic tangent operator is derived. To the best of the author’s knowledge, this formula has not been presented in the literature yet. The obtained set of equations can be used to implement the cyclic plasticity models into numerous commercial or non-commercial FE packages. A user subroutine UMAT (User’s MATerial) has been developed in order to implement the cyclic plasticity model by Yoshida into the open-source FE program CalculiX. The coding is included in the Appendix. It can be easily modified to implement any isotropic hardening rule for which the yield stress is a function of the effective plastic strain. The number of the utilized backstress variables can be easily increased as well. Several validation tests which have been performed in order to verify the code’s performance are discussed.

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Characterising Fatigue Behaviour of Nodular Cast Iron Using Micromechanical Simulations

MATEC Web of Conferences ◽

10.1051/matecconf/201930013002 ◽

2019 ◽

Vol 300 ◽

pp. 13002

Author(s):

Mehul Lukhi ◽

Meinhard Kuna ◽

Geralf Hütter

Keyword(s):

Finite Element ◽

Cast Iron ◽

Volume Fraction ◽

Cell Model ◽

Kinematic Hardening ◽

Nodular Cast Iron ◽

Fatigue Behaviour ◽

Cyclic Stress ◽

Finite Element Simulations ◽

Final Failure

Elastic-plastic porous materials experience an increase in the mean void volume fraction when they are subjected to cyclic loading. This behavior is known both from the experiments and simulations in the literature. The authors have first time used this mechanism for the evaluation of the fatigue life in nodular cast iron. In this contribution, the stress-life approach is presented for the characterization of fatigue failure. For this purpose, micromechanical finite-element simulations are carried out using the axisymmetric cell model. The cell model having isotropic/non-linear kinematic hardening behavior is subjected to fully reversed cyclic stress controlled loading. The finite element simulations are carried out cycle by cycle until the final failure of the cell model. The numbers of cycles to failure are extracted from the simulations. The stress-life curves are shown for spherical and elliptical graphite particle cell models. The results of the micromechanical simulations are in qualitative agreement with the typical experimental stress-life curves.

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Strain Localization during Equal-Channel Angular Pressing analyzed by Finite Element Simulations

10.20944/preprints201712.0143.v1 ◽

2017 ◽

Author(s):

Tobias Daniel Horn ◽

Christian Bert Silbermann ◽

Philipp Frint ◽

Martin Franz-Xaver Wagner ◽

Jörn Ihlemann

Keyword(s):

Finite Element ◽

Strain Hardening ◽

Equal Channel Angular Pressing ◽

Strain Localization ◽

Kinematic Hardening ◽

Microstructural Analysis ◽

Finite Element Simulations ◽

Localized Deformation ◽

Angular Pressing ◽

Special Cases

Equal-Channel Angular Pressing (ECAP) is a method used to introduce severe plastic deformation into a metallic billet without changing its geometry. In special cases strain localization occurs and a pattern consisting of regions with high and low deformation (so-called shear and matrix bands) can emerge. This paper studies this phenomenon numerically adopting two-dimensional finite element simulations of one ECAP pass. The mechanical behavior of aluminum is modeled using phenomenological plasticity theory with isotropic or kinematic hardening. The effects of the two different strain hardening types are investigated numerically by systematic parameter studies: While isotropic hardening only causes minor fluctuations in the plastic strain fields, a material with high initial hardening rate and sufficient strain hardening capacity can exhibit pronounced localized deformation after ECAP. The corresponding finite element simulation results show a regular pattern of shear and matrix bands. This result is confirmed experimentally by ECAP-processing of AA6060 material in a severely cold worked condition, where microstructural analysis also reveals the formation of shear and matrix bands. Excellent agreement is found between the experimental and numerical results in terms of shear and matrix band width and length scale. The simulations provide additional insights regarding the evolution of the strain and stress states in shear and matrix bands.

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