双势理论用于处理非关联材料本构

周洋靖; 冯志强; 宁坡

doi:10.3879/j.issn.1000-0887.2015.08.001

双势理论用于处理非关联材料本构

doi: 10.3879/j.issn.1000-0887.2015.08.001

西南交通大学力学与工程学院, 成都 610031

基金项目: 国家自然科学基金（11372260）

详细信息

作者简介:
周洋靖（1988—），男，四川人，博士生（通讯作者. E-mail: yjzhou1988@qq.com）；冯志强（1963—），男，重庆人，教授，博士生导师（E-mail: feng@ufrst.univ-evry.fr）；宁坡（1990—），男，湖南人，博士生（E-mail: 351528123@qq.com）.

中图分类号: O39;O341
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出版历程
- 收稿日期: 2015-04-28
- 修回日期: 2015-07-06
- 刊出日期: 2015-08-15

The Bi-Potential Theory Applied to Non-Associated Constitutive Laws

School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, P.R.China

Funds: The National Natural Science Foundation of China（11372260）

摘要

摘要: 基于传统塑性力学框架下的显式积分算法和基于Simo-Taylor提出的回退映射隐式积分算法是固体力学中两大经典本构积分算法.以经典的非关联材料模型Drucker-Prager(D-P)模型和Armstrong-Frederick(A-F)模型为例分别回顾了显式积分算法和隐式积分算法.以双势理论为基础，将双势的概念运用到材料的自由能中，将材料分为显式标准材料和隐式标准材料.两种传统积分算法都能有效地处理显式标准材料的本构关系，但在处理隐式标准材料时却存在一定的问题.双势积分算法是建立在双势理论下的本构积分算法，此算法不仅能够处理显式标准材料，对于处理隐式标准材料，也存在一定的优势.通过变分原理推导了双势积分算法解的存在性，运用双势积分算法处理Drucker-Prager模型和Armstrong-Frederick模型，并与经典传统积分算法得到的结果进行对比，验证了双势本构积分算法的稳定性和准确性.
- 双势积分算法 /
- 显式/隐式积分算法 /
- 非关联本构 /
- D-P模型 /
- A-F模型
Abstract: The explicit integration algorithm based on the traditional plastic mechanics framework and the implicit integration algorithm proposed by Simo-Taylor were 2 classic constitutive integration algorithms widely used in solid mechanics. These 2 algorithms were reviewed respectively with the 2 corresponding classic non-associated constitutive models: the Drucker-Prager model and the Armstrong-Frederick model as the examples. Then, according to the bi-potential theory and with the bi-potential concept applied to the material free energy, solid materials were divided into explicit standard materials and implicit standard ones. It was verified that the 2 classic integration algorithms both can effectively deal with explicit standard materials. However, in dealing with implicit standard materials, the orthogonality cannot be guaranteed in a unified form with the classic methods. The bi-potential algorithm has its own advantage in dealing with both explicit and implicit standard materials. The solution existence of the bi-potential integration algorithm was derived based on the variational principle. Furthermore, the results of the bi-potential algorithm and the classic algorithms were compared through calculation of the Drucker-Prager and Armstrong-Frederick models, and the accuracy and stability of the bi-potential algorithm were proved.
- bi-potential integration algorithm /
- explicit/implicit integration algorithm /
- non-associated constitutive law /
- D-P model /
- A-F model

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