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双势积分算法在非关联材料中的应用

周洋靖 冯志强 彭磊

周洋靖, 冯志强, 彭磊. 双势积分算法在非关联材料中的应用[J]. 应用数学和力学, 2018, 39(1): 11-28. doi: 10.21656/1000-0887.380139
引用本文: 周洋靖, 冯志强, 彭磊. 双势积分算法在非关联材料中的应用[J]. 应用数学和力学, 2018, 39(1): 11-28. doi: 10.21656/1000-0887.380139
ZHOU Yangjing, FENG Zhiqiang, PENG Lei. Application of the Bi-Potential Integration Algorithm to Non-Associated Materials[J]. Applied Mathematics and Mechanics, 2018, 39(1): 11-28. doi: 10.21656/1000-0887.380139
Citation: ZHOU Yangjing, FENG Zhiqiang, PENG Lei. Application of the Bi-Potential Integration Algorithm to Non-Associated Materials[J]. Applied Mathematics and Mechanics, 2018, 39(1): 11-28. doi: 10.21656/1000-0887.380139

双势积分算法在非关联材料中的应用

doi: 10.21656/1000-0887.380139
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,博士生(通讯作者. E-mail: yjzhou1988@qq.com);冯志强(1963—),男,教授,博士生导师(E-mail: feng@ufrst.univevry.fr);彭磊(1990—),男,博士生(E-mail: penglei.swjtu@foxmail.com).

  • 中图分类号: O39|O341

Application of the Bi-Potential Integration Algorithm to Non-Associated Materials

Funds: The National Natural Science Foundation of China(11372260)
  • 摘要: 在双势理论的框架下,根据材料自由能形式,材料可以被划分为显式标准材料和隐式标准材料.以经典的非关联D-P模型为例,对其本构锥体进行了描述,并引入了一对对偶锥体.证明了在对偶锥体的描述下,不仅能满足非关联D-P模型自身本构关系,其应力和塑性应变也能满足隐式流动表达.结合双势理论和D-P模型自身的本构特点,推导出了非关联D-P模型率形式弹性状态下、率形式塑性状态下、增量形式弹性状态下、增量形式塑性状态下和增量形式弹塑性状态下的双势函数,从而得到了非关联D-P模型的双势积分算法.通过数值模拟算例验证了双势积分算法的准确性和稳定性.
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  • 收稿日期:  2017-05-23
  • 修回日期:  2017-05-23
  • 刊出日期:  2018-01-15

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