Macroscopic criterion for ductile porous materials based on a statically admissible microscopic stress field
Macroscopic criterion for ductile porous materials based on a statically admissible microscopic stress field
复制标题
DOI：
10.1016/j.ijplas.2015.02.012
复制
发表时间：
2015-07
影响因子：
9.8
通讯作者：
W. Shen;A. Oueslati;G. Saxcé
中科院分区：
文献类型：
--
作者：
W. Shen;A. Oueslati;G. Saxcé
利用作者最近提出的应力变分均匀化（SVH）方法，提出了一个具有vonMises型矩阵的多孔韧性材料的宏观判据。本文从刚塑性材料的Hill应力原理出发，利用拉格朗日乘子放松了细观应力场的屈服条件。另一方面，试验应力场是严格静态容许的，允许改进以前的模型，其中孔隙边界上的应力条件仅在平均意义上得到满足。通过解决由此产生的鞍点问题，并执行一个适当的近似的积分发生在它，我们得到一个封闭的形式公式。新的宏观准则的主要特点是在纯剪切载荷情况下获得了更精确的值。我们还推导了宏观流动规则以及孔隙度演化方程。得到的结果进行了充分的讨论，并与现有的模型，可用的数值数据和有限元结果进行比较。
The aim of work is to propose a macroscopic criterion of porous ductile materials with von Mises type matrix using the Stress Variational Homogenization (SVH) recently proposed by the authors. Starting with Hill's stress principle for rigid plastic materials, the yield condition on the microscopic stress field is relaxed by means of Lagrange multiplier. On the other hand, the trial stress field is strictly statically admissible allowing to improve a previous model in which the stress condition on the pore boundary was only satisfied in a mean sense. By solving the resulting Saddle point problem and performing a suitable approximation of the integral occurring in it, we derive a closed form formula. The main feature of the new macroscopic criterion is a more accurate value obtained for the pure shear loading case. We also derive the macroscopic flow rule as well as the porosity evolution equations. The obtained results are fully discussed and compared to existing models, available numerical data and to Finite Elements results.