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Time integration scheme for elastoplastic models based on anisotropic strain‐rate potentials
Author(s) -
Rabahallah Meziane,
Balan Tudor,
Bouvier Salima,
Teodosiu Cristian
Publication year - 2009
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2640
Subject(s) - anisotropy , tangent , plasticity , tangent modulus , strain rate , robustness (evolution) , yield (engineering) , quadratic equation , algorithm , mathematics , materials science , computer science , modulus , geometry , physics , composite material , biochemistry , chemistry , quantum mechanics , gene
Abstract Modelling of plastic anisotropy requires the definition of stress potentials (coinciding with the yield criteria in case of the associated flow rules) or, alternatively, plastic strain‐rate potentials. The latter approach has several advantages whenever material parameters are determined by means of texture measurements and crystal plasticity simulations. This paper deals with a phenomenological description of anisotropy in elastoplastic rate‐insensitive models by using strain‐rate potentials. A fully implicit time integration algorithm is developed in this framework and implemented in a static‐implicit finite element code. Algorithmic details are discussed, including the derivation of the consistent (algorithmic) tangent modulus and the numerical treatment of the yield condition. Typical sheet forming applications are simulated with the proposed implementation, using the recent non‐quadratic strain‐rate potential Srp2004‐18p. Numerical simulations are carried out for materials that exhibit strong plastic anisotropy. The numerical results confirm that the presented algorithm exhibits the same generality, robustness, accuracy, and time efficiency as state‐of‐the‐art yield criterion‐based algorithms. Copyright © 2009 John Wiley & Sons, Ltd.