On the equivalence between the multiplicative hyper-elasto-plasticity and the additive hypo-elasto-plasticity based on the modified kinetic logarithmic stress rate

Jiao, Yang; Fish, Jacob

doi:10.1016/j.cma.2018.06.017

Cited by 25 publications

(4 citation statements)

References 99 publications

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“…Despite the fact that the energy dissipation effects would be essential for cyclic loading processes, as explained in the foregoing, reasonable forms of the elastic rate equation at finite elasto‐plastic deformations may be investigated in an idealized sense with elastic unstressed states and results are of significance toward clarifying relevant issues concerning the constitutive structure of Eulerian finite elasto‐plasticity with the additive separation of the stretching. This may be the case for the new insights into the relationship between the additive separation of the stretching and the multiplicative separation of the deformation gradient as well as the similarities and differences or pros and cons of different developments of the logarithmic rate, as have been achieved most recently in References 41 and 42.…”

Section: New Elasto‐plasticity Modelmentioning

confidence: 91%

High‐efficiency algorithms for simulating metal failure effects under multiaxial repeated loadings

Zhan

Wang

Bruhns

et al. 2021

Numerical Meth Engineering

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High-efficiency algorithms are proposed for numerically integrating elasto-plastic rate equations for the purpose of simulating metal failure effects under repeated loading conditions. Results are obtained with a newly established elasto-plasticity model which can automatically simulate both low and high cycle fatigue failure effects, with reference to neither damage-like variables nor ad hoc failure criteria. Novelties are incorporated in a few respects. First, multiaxial loading processes with arbitrarily changing principal stresses and axes can be treated in a broad sense beyond usually treated proportional loading cases. Second, by means of the commonly used J 2 -invariant of the deviatoric stress, multiaxial loading cases can be directly treated just as in the uniaxial loading case. Third, high cost in time consumption can be considerably reduced in evaluating both low and high cycle failure effects. Numerical examples are presented for simulating uniaxial and multiaxial fatigue failure effects and simulation results are in good agreement with experimental data. Results show that the computation speed with the new algorithms exceeds 600 times faster than usual integration algorithms.

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Section: New Elasto‐plasticity Modelmentioning

confidence: 91%

High‐efficiency algorithms for simulating metal failure effects under multiaxial repeated loadings

Zhan

Wang

Bruhns

et al. 2021

Numerical Meth Engineering

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“…However, in [63,73], one can find examples that illustrate the difficulties which can be encountered in modeling the multistage deformation processes (including unloading): if the purely elastic cyclic loading is realized upon completion of elastoplastic deformation and unloading, then the stress hysteresis will be observed. In [73,74], the logarithmic spin, called the kinetic logarithmic spin (k-logspin), was improved. The modernized spin makes it possible to meet the conservation conditions in the simulation of multi-stage deformation processes, including unloading, but the consideration is limited to anisotropic material.…”

Section: Analysis Of the Formulations With An Emphasis On Describing Geometric Nonlinearity And Fulfillment Of Thermodynamic Constraintsmentioning

confidence: 99%

Some Issues on Crystal Plasticity Models Formulation: Motion Decomposition and Constitutive Law Variants

2021

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In this paper, kinematic relations and constitutive laws in crystal plasticity are analyzed in the context of geometric nonlinearity description and fulfillment of thermodynamic requirements in the case of elastic deformation. We consider the most popular relations: in finite form, written in terms of the unloaded configuration, and in rate form, written in terms of the current configuration. The presence of a corotational derivative in the relations formulated in terms of the current configuration testifies to the fact that the model is based on the decomposition of motion into the deformation motion and the rigid motion of a moving coordinate system, and precisely the stress rate with respect to this coordinate system is associated with the strain rate. We also examine the relations of the mesolevel model with an explicit separation of a moving coordinate system and the elastic distortion of crystallites relative to it in the deformation gradient. These relations are compared with the above formulations, which makes it possible to determine how close they are. The results of the performed analytical calculations show the equivalence or similarity (in the sense of the response determined under the same influences) of the formulation and are supported by the results of numerical calculation. It is shown that the formulation based on the decomposition of motion with an explicit separation of the moving coordinate system motion provides a theoretical framework for the transition to a similar formulation in rate form written in terms of the current configuration. The formulation of this kind is preferable for the numerical solution of boundary value problems (in a case when the current configuration and, consequently, contact boundaries, are not known a priori) used to model the technological treatment processes.

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“…Two recent works from Jiao and Fish [16,17] investigated extensively the role of the co-rotational framework, pointing out the drawbacks of the most common objective stress rates (i.e. Jaumann, Green-Naghdi and logarithmic).…”

Section: Kinematic Frameworkmentioning

confidence: 99%

Fully implicit numerical integration of the Yoshida-Uemori two-surface plasticity model with isotropic hardening stagnation

Fincato

Tsutsumi

Zilio

et al. 2021

Frattura Ed Integrità Strutturale

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The paper deals with the numerical investigation and implementation of the two-surface plasticity model (or bounding surface model). This plasticity theory allows to describe the deformation behavior under large strain cyclic plasticity and the material stress-strain responses at small-scale re-yielding after large pre-straining. A novel strategy to model the isotropic hardening stagnation is developed within a fully implicit integration scheme in order to speed up the computation and to improve the material description.

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On the equivalence between the multiplicative hyper-elasto-plasticity and the additive hypo-elasto-plasticity based on the modified kinetic logarithmic stress rate

Cited by 25 publications

References 99 publications

High‐efficiency algorithms for simulating metal failure effects under multiaxial repeated loadings

High‐efficiency algorithms for simulating metal failure effects under multiaxial repeated loadings

Some Issues on Crystal Plasticity Models Formulation: Motion Decomposition and Constitutive Law Variants

Fully implicit numerical integration of the Yoshida-Uemori two-surface plasticity model with isotropic hardening stagnation

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