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

In 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.

Viscoplastic Parametric Analysis of Cylindrical Specimen Under Cyclic Behaviour

The present study tries to present a cyclic hardening model with the aim to simulate quantitatively the material response under strain controlled cyclic loading in tension-compression, of specified axial deformation. A numerical study was carried out to investigate the cyclic constitutive behaviour of alloy Indium under viscoplastic deformation. The analysis was performed under prescribed symmetric strain-controlled cyclic loading. The model contains both isotropic and kinematic hardening components, while the analysis were performed using Comsol Multiphysics for only 60 seconds duration. The kinematic hardening was described by using multiple back stresses. Multiple back stresses can provide a smoother transition between the elastic and plastic deformation, and it improves the general shape of the hysteresis loop. Two cases (geometries) have been examined in this study. From the material model and finite element cyclic plasticity model results, it is found that for the same parameters, but different dimensions there is difference on the stress-strain curves as well as on the von Mises stresses.

Strain Range Dependent Cyclic Hardening of 08Ch18N10T Stainless Steel—Experiments and Simulations

This paper describes and presents an experimental program of low-cycle fatigue tests of austenitic stainless steel 08Ch18N10T at room temperature. The low-cycle tests include uniaxial and torsional tests for various specimen geometries and for a vast range of strain amplitude. The experimental data was used to validate the proposed cyclic plasticity model for predicting the strain-range dependent behavior of austenitic steels. The proposed model uses a virtual back-stress variable corresponding to a cyclically stable material under strain control. This internal variable is defined by means of a memory surface introduced in the stress space. The linear isotropic hardening rule is also superposed. A modification is presented that enables the cyclic hardening response of 08Ch18N10T to be simulated correctly under torsional loading conditions. A comparison is made between the real experimental results and the numerical simulation results, demonstrating the robustness of the proposed cyclic plasticity model.

Modelling the Strain Range Dependent Cyclic Hardening of SS304 and 08Ch18N10T Stainless Steel with a Memory Surface

This paper deals with the development of a cyclic plasticity model suitable for predicting the strain range dependent behavior of austenitic steels. The proposed cyclic plasticity model uses the virtual back-stress variable corresponding to a cyclically stable material under strain control. This new internal variable is defined by means of a memory surface introduced in the stress space. The linear isotropic hardening rule is also superposed. First, the proposed model was validated on experimental data published for the SS304 material (Kang et al. Constitutive modeling of strain range dependent cyclic hardening. Int J Plast 19 (2003) 1801–1819). Subsequently, the proposed cyclic plasticity model was applied to own experimental data from uniaxial tests realized on 08Ch18N10T at room temperature. The new cyclic plasticity model can be calibrated by the relatively simple fitting procedure that is described in the paper. A comparison between the results of a numerical simulation and the results of real experiments demonstrates the robustness of the proposed approach.

Automated calibration of advanced cyclic plasticity model parameters with sensitivity analysis for aluminium alloy 2024-T351

The plasticity models in finite element codes are often not able to describe the cyclic plasticity phenomena satisfactorily. Developing a user-defined material model is a demanding process, challenging especially for industry. Open-source Code_Aster is a rapidly expanding and evolving software, capable of overcoming the above-mentioned problem with material model implementation. In this article, Chaboche-type material model with kinematic hardening evolution rules and non-proportional as well as strain memory effects was studied through the calibration of the aluminium alloy 2024-T351. The sensitivity analysis was performed prior to the model calibration to find out whether all the material model parameters were important. The utilization of built-in routines allows the calibration of material constants without the necessity to write the optimization scripts, which is time consuming. Obtaining the parameters using the built-in routines is therefore easier and allows using the advanced modelling for practical use. Three sets of material model parameters were obtained using the built-in routines and results were compared to experiments. Quality of the calibration was highlighted and drawbacks were described. Usage of material model implemented in Code_Aster provided good simulations in a relatively simple way through the use of an advanced cyclic plasticity model via built-in auxiliary functions.