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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Armbruster, Dieter / Chen, Xi / Bessaih, Hakima / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi

IMPACT FACTOR 2017: 1.162

CiteScore 2017: 1.41

SCImago Journal Rank (SJR) 2017: 0.382
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Mathematical Citation Quotient (MCQ) 2017: 0.12

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Volume 19, Issue 7-8


Return Mapping Algorithms (RMAs) for Two-Yield Surface Thermoviscoplastic Models Using the Consistent Tangent Operator

Grégory Antoni / Frédéric Lebon / Thierry Désoyer
Published Online: 2018-09-19 | DOI: https://doi.org/10.1515/ijnsns-2017-0073


The return mapping algorithms (RMAs) presented here are designed for use with pressure-dependent thermoviscoplastic constitutive models involving irreversible effects associated with solid–solid phase transformations. During the volume solid–solid phase transformations occurring under mechanical loads, an “anomalous” plasticity, the so-called “TRansformation Induced Plasticity” (TRIP), is generated at much lower stress levels than those related to the yield stress of the material in the context of the classical plasticity. TRIP mechanisms are superimposed on the classical plasticity which is liable to occur in the case of metallic materials. Based on a non-standard generalized material framework, two different models are presented in which an “associative” plastic flow is introduced in the context of classical plasticity and a “non-associative” flow rule in the context of TRIP-like plasticity. In this paper, a complete algorithmic treatment of these two rate-dependent constitutive models is therefore proposed with the associated consistent tangent operator for dealing the quasi-surface irreversible solid–solid transformations which can appear in metal alloys during specific thermomechanical solicitations. The predictive abilities of the presented numerical procedure for modelling this kind of the irreversible solid–solid transformations involving two plasticity processes are tested and assessed by performing a two-dimensional finite-element analysis on some numerical examples.

Keywords: transformation-induced plasticity,quasi-surface irreversible solid–solid phase transformations,return mapping algorithms,consistent tangent operator,finite-element analysis


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About the article

Received: 2017-03-23

Accepted: 2018-08-10

Published Online: 2018-09-19

Published in Print: 2018-12-19

Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 19, Issue 7-8, Pages 681–697, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2017-0073.

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