Implicit iterative finite element scheme for a strain gradient crystal plasticity model based on self-energy of geometrically necessary dislocations
Implicit iterative finite element scheme for a strain gradient crystal plasticity model based on self-energy of geometrically necessary dislocations
复制标题
基于几何必要位错自能的应变梯度晶体塑性模型的隐式迭代有限元方案
DOI：
10.1016/j.commatsci.2011.08.029
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发表时间：
2012
影响因子：
3.3
通讯作者：
N. Ohno
中科院分区：
文献类型：
--
作者：
R. Kametani;K. Kodera;D. Okumura;N. Ohno
在这项研究中，一个隐式迭代有限元计划开发的应变梯度理论的单晶塑性占的自能的几何必要位错（GNDs）。这种应变梯度理论属于粘塑性单晶的Gurtin框架。GND的自能给出了高能高阶应力的特定形式。得到了求解均匀化方程组的隐式有限元方程。将该方法用于分析模型药柱，并与Ohno和Okumura（2007）[4]推导的分析估计值进行了比较。讨论了格式的计算效率和增量稳定性。此外，它表明，开发的计划是可用的，适用于不同类型的高阶应力，包括能量和耗散项。
In this study, an implicit iterative finite element scheme is developed for the strain gradient theory of single-crystal plasticity that accounts for the self-energy of geometrically necessary dislocations (GNDs). This strain gradient theory belongs to the Gurtin framework for viscoplastic single-crystals. The self-energy of GNDs gives a specific form of energetic higher-order stresses. An implicit finite element equation is obtained for solving a set of homogenization equations. The developed scheme is employed to analyze a model grain, and is verified by comparison with the analytical estimation derived by Ohno and Okumura (2007) [4]. The computational efficiency of the scheme and the incremental stability are discussed. Furthermore, it is shown that the developed scheme is available and applicable to different types of higher-order stresses including energetic and dissipative terms.