期刊论文详细信息
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES 卷:46
Towards variational constitutive updates for non-associative plasticity models at finite strain: Models based on a volumetric-deviatoric split
Article
Mosler, J.1  Bruhns, O. T.2 
[1] GKSS Forschungszentrum Geesthacht GmbH, Inst Mat Res, D-21502 Geesthacht, Germany
[2] Ruhr Univ Bochum, Inst Mech, D-44780 Bochum, Germany
关键词: Variational principles;    Energy minimization;    Variational constitutive updates;    Non-associativity;   
DOI  :  10.1016/j.ijsolstr.2008.12.008
来源: Elsevier
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【 摘 要 】

In this paper, an enhanced variational constitutive update suitable for a class of non-associative plasticity theories at finite strain is proposed. in line with classical numerical formulations for plasticity models, such as the by now established return-mapping algorithm, variational constitutive updates represent a numerical method for computing the unknown state variables. However, in contrast to conventional algorithms, variational constitutive updates are fully variational, i.e., all unknown variables follow jointly from minimizing a certain potential. In addition to the physical and mathematical elegance of these variational schemes, they show several practical advantages as well. For instance, numerically efficient and robust optimization schemes can be directly employed for solving the resulting minimization problem. Since mathematically, plasticity is a non-smooth problem and often, it leads to highly singular systems of equations as known from single crystal plasticity, a robust implementation is of utmost importance. So far, variational constitutive updates have been developed for different classes of standard dissipative solids, i.e., solids characterized by associative evolution equations and flow rules. in the present paper, this framework is extended to a certain class of non-associative plasticity models at finite strain. All models failing into this class show a volumetric-deviatoric split of the Helmholtz energy and the yield function. Typical prototypes are Drucker-Prager or Mohr-Coulomb models playing an important role in soil mechanics. The efficiency and robustness of the resulting algorithmic formulation is demonstrated by means of selected numerical examples. (C) 2008 Elsevier Ltd. All rights reserved.

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