An interpretation of subloading tij model in the context of conventional elastoplasticity theory
An interpretation of subloading tij model in the context of conventional elastoplasticity theory
复制标题
传统弹塑性理论背景下的次加载 tij 模型解释
DOI：
10.3208/sandf.45.4_61
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发表时间：
2005
影响因子：
3.7
通讯作者：
T. Nakai
中科院分区：
文献类型：
--
作者：
D. Pedroso;M. Farias;T. Nakai
最近提出了一种称为次加载 tij 的各向同性硬化弹塑性模型（Nakai 和 Hinokio，2004）。子加载 tij 模型与传统模型的三个特点不同：（a）使用由张量 tij 给出的修改应力空间； (b) 将塑性应变增量分成两个分量，以及 (c) 基于次加载概念使用两个屈服面。相对于著名的 Cam-clay 模型，这三个特征极大地提高了模型的预测能力。然而，模型的制定和实现变得有点复杂。在本文中，应力和应变演化以及控制模型屈服面大小的内部变量演化的基本方程被重新表述，以类似于任何传统弹塑性模型的方程。这显着促进了模型的相应微分方程组的数值积分（显式或隐式）。本公式还确定了每个概念的物理含义，并清楚地表明它们在弹塑性本构张量的推导中的作用。该模型最初制定时没有考虑塑性应变增量分裂，以强调采用次加载概念的效果。然后使用不同的方法考虑塑性分裂，该方法允许以更简单的方式编写本构张量。所提出的程序已成功测试，并且附录中给出了实现该模型所需的所有导数和算法。作者希望这些过程使其他研究人员更容易按原样实施和使用该模型或使用任何其他模型中的基本概念。
An isotropic hardening elastoplastic model, named subloading tij, has been recently proposed (Nakai and Hinokio, 2004). Three features differentiate subloading tij model from the conventional ones: (a) the use of a modified stress space given by tensor tij; (b) the split of the plastic strain increments in two components and (c) the use of two yield surfaces based on the concept of subloading. These three characteristics greatly improve the prediction capabilities of the model, with respect to those of the well-known Cam-clay model. However, the model formulation and implementation becomes a little more complex. In this paper the basic equations for the evolution of stresses and strains and for the evolution of the internal variables that control the size of the yield surfaces of the model are reformulated in such a way as to resemble those of any conventional elastoplastic model. This facilitates significantly the numerical integration (explicit or implicit) of the corresponding system of differential equations of the model. The present formulation also identifies the physical meaning of each concept and clearly shows where they intervene in the deduction of the elastoplastic constitutive tensors. The model is initially formulated without taking into account the plastic strain increment split, in order to emphasize the effect of adopting the subloading concept. Then the plastic split is considered using a different approach that allows writing the constitutive tensors in a simpler manner. The procedures proposed were successfully tested and all derivatives and algorithms necessary to implement the model are given in the appendices. The authors hope that these procedures make it easier for other researchers to implement and use the model as it is or to use the basic concepts in any other model.