A homogenization theory of strain gradient single crystal plasticity and its finite element discretization
A homogenization theory of strain gradient single crystal plasticity and its finite element discretization
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DOI：
10.1016/j.ijplas.2006.11.001
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发表时间：
2007-07
影响因子：
9.8
通讯作者：
D. Okumura;Y. Higashi;K. Sumida;N. Ohno
中科院分区：
文献类型：
--
作者：
D. Okumura;Y. Higashi;K. Sumida;N. Ohno
在这项研究中，均匀化理论的基础上的Gurtin应变梯度公式和有限元离散化的周期性材料的宏观响应的调查的尺寸效应。为了导出由宏观应力关系、弱形式的应力平衡和弱形式的微力平衡组成的均匀化方程，Y周期性被用作单位单元边界处的附加边界条件以及标准边界条件。然后，应用切线模量法，从均匀化方程得到一组有限元方程。通过对一个复合材料模型的分析，验证了该有限元离散方法的计算稳定性和有效性。此外，一个模型多晶体进行了分析，研究晶粒尺寸依赖的多晶体塑性。在分析中，微观夹紧，微观自由，和无缺陷的条件被认为是在晶界的附加边界条件，并讨论了它们的影响。
In this study, a homogenization theory based on the Gurtin strain gradient formulation and its finite element discretization are developed for investigating the size effects on macroscopic responses of periodic materials. To derive the homogenization equations consisting of the relation of macroscopic stress, the weak form of stress balance, and the weak form of microforce balance, the Y-periodicity is used as additional, as well as standard, boundary conditions at the boundary of a unit cell. Then, by applying a tangent modulus method, a set of finite element equations is obtained from the homogenization equations. The computational stability and efficiency of this finite element discretization are verified by analyzing a model composite. Furthermore, a model polycrystal is analyzed for investigating the grain size dependence of polycrystal plasticity. In this analysis, the micro-clamped, micro-free, and defect-free conditions are considered as the additional boundary conditions at grain boundaries, and their effects are discussed.