On boundary conditions for homogenization of volume elements undergoing localization
On boundary conditions for homogenization of volume elements undergoing localization
复制标题
局部化体积元均匀化的边界条件
DOI：
10.1002/nme.5597
复制
发表时间：
2017
影响因子：
2.9
通讯作者：
V. Ulbricht
中科院分区：
文献类型：
--
作者：
J. Goldmann;J. Brummund;V. Ulbricht
本文提出了一种周期性边界条件的自适应算法，称为镶嵌边界条件。而周期性边界元限制应变局部化区域服从微观结构的周期性，所提出的镶嵌边界元调整周期框架，以满足局部化区域。因此，允许任意的显影局部区域。尽管如此，该公式本质上不易受到虚假定位的影响。此外，修改的Hough变换推导出，这构成了一个无偏的标准检测的定位区域。推导出的配方的行为证明了各种例子，并与其他BC相比。由此表明，镶嵌BC导致的有效应力的局部化方向上的合理的依赖。此外，随着代表性体积单元的尺寸的增加，刚度值的良好收敛被示出，以及在使用应变软化材料时的有益特性。
This paper presents an adaption of periodic boundary conditions (BC), which is termed tessellation BC. While periodic BC restrict strain localization zones to obey the periodicity of the microstructure, the proposed tessellation BC adjust the periodicity frame to meet the localization zone. Thereby, arbitrary developing localization zones are permitted. Still the formulation is intrinsically unsusceptible against spurious localization. Additionally, a modification of the Hough transformation is derived, which constitutes an unbiased criterion for the detection of the localization zone. The behavior of the derived formulation is demonstrated by various examples and compared with other BC. It is thereby shown that tessellation BC lead to a reasonable dependence of the effective stress on the localization direction. Furthermore, good convergence of stiffness values with increasing size of the representative volume element is shown as well as beneficial characteristics in use with strain softening material.