Adaptive phase field analysis with dual hierarchical meshes for brittle fracture
Adaptive phase field analysis with dual hierarchical meshes for brittle fracture
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DOI：
10.1016/j.engfracmech.2019.106608
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发表时间：
2019-09
影响因子：
5.4
通讯作者：
S. Goswami;C. Anitescu;T. Rabczuk
中科院分区：
文献类型：
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作者：
S. Goswami;C. Anitescu;T. Rabczuk
提出了一种新的基于双网格的自适应相场方法来求解断裂问题。顾名思义，所提出的格式使用两个不同特征单元尺寸(H)的网格进行求解，弹性场采用较粗的网格，相场采用较细的网格。为了便于网格之间的信息交换，提出了一种高效的数据传输算法。通过使用分层T网格上的多项式样条(PHT-Splines)实现自适应h-精化方案，提高了公式的效率。提出的数据传输算法利用了PHT-Spline固有的层次性和局部化特性，并实现了自适应。已经为两个网格提出了独立的精化策略。为了说明该方法的性能，文中给出了六个数值算例。对于大多数例子，对于两个网格的单元大小的不同组合，已经报告了临界负载和计算效率(以CPU时间为单位)。结果表明，当弹性网格h=0.5 L 0，相场网格h=0.2 5 L 0时，所得结果与传统相场模型h=0.2 5，L 0，L 0表示长度尺度参数所得到的结果相同.此外，在较粗的网格上进行弹性分析，使得所提出的方法比传统方法更快、更便宜，这表明该方法在其他相场问题中具有潜在的应用前景。
We present a novel dual-mesh based adaptive phase field method for solving fracture problems. As the name suggests, the proposed scheme is solved using two meshes with different characteristic element sizes (h); a coarser mesh for the elastic field and a finer mesh for the phase field. To facilitate the exchange of information between the meshes, an efficient data transfer algorithm is proposed. The efficiency of the formulation is enhanced by implementing an adaptive h-refinement scheme using polynomial splines over hierarchical T-meshes (PHT-splines). The inherent hierarchical nature of PHT-Splines andtheir localization property is exploited in the proposed data transfer algorithm as well as in implementing adaptivity. Independent refinement strategies have been proposed for both meshes. To illustrate the performance of the proposed approach, six numerical examples have been presented. For most examples, the critical load and computational efficiency (in terms of CPU time) have been reported for different combinations of element sizes of both meshes. The present work concludes that the proposed approach with h= 0.5 l 0 for the elastic mesh and h= 0.25 l 0 for the phase field mesh yields results as accurate as results obtained from the conventional phase field model with h= 0.25 l 0, where l 0 denotes length scale parameter. Moreover, the elastic analysis being performed on a coarser mesh makes the proposed approach faster and cheaper than the conventional approach, indicating potential for future applications in other phase field problems.