A comparative analysis of two formulations for non linear hardening plasticity models: Application to shakedown analysis
A comparative analysis of two formulations for non linear hardening plasticity models: Application to shakedown analysis
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DOI：
10.1016/j.euromechsol.2015.03.001
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发表时间：
2015-09
影响因子：
4.1
通讯作者：
C. Bouby;D. Kondo;G. Saxcé
中科院分区：
文献类型：
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作者：
C. Bouby;D. Kondo;G. Saxcé
本文主要对比分析了两种具有非线性硬化规律的塑性模型，即Armstrong模型和Frederick模型，以及最近在广义标准材料（GSM）框架下提出的一种修正方法。我们首先适当地利用双势理论对这两个模型进行了详细的数学分析。这为GSM模型提供了双势的封闭形式表达式。此外，首次证明了Armstrong和Frederick模型不承认凸势；该结果证实了该模型的非关联框架的必要要求。然后，对于改进的模型，利用上述基于双电位的工具，我们对薄壁管在恒张力和交变循环扭转下进行了安定分析。通过将所得结果与数值求解相应安定界问题所得数据进行比较，验证了所得结果的准确性。最后，对两种模型的预测结果进行了比较，说明了两种模型的显著差异。
The paper is mainly devoted to a comparative analysis of two plasticity models with a nonlinear hardening law, namely the Armstrong and Frederick model, and a recent modification proposed in literature in the framework of Generalized Standard Materials (GSM). We first provide a detailed mathematical analysis of the two models by appropriately resorting to the bipotential theory. This delivers for the GSM model a closed form expression of a bipotential. Moreover, it is demonstrated for the first time that the Armstrong and Frederick model does not admit a convex potential; this result confirms the necessary requirement of a non associated framework for this model. Then, for the modified model, making use of the above bipotential-based tools, we carry out a shakedown analysis of a thin walled tube under constant tension and alternating cyclic torsion. The accuracy of the obtained results is checked by comparing them to data obtained by numerical solving the corresponding shakedown bounds problems. Finally, the predictions of the two models are compared and illustrated their significant differences.