A comparative study of cluster-based methods at finite strain  

有限应变问题基于聚类的方法之比较研究

作　　者：Yang Yang Lei Zhang Shaoqiang Tang 杨洋;张磊;唐少强(MoE Key Laboratory of High Energy Density Physics Simulations(HEDPS)and State Key Laboratory of Turbulence and Complex Systems(LTCS),College of Engineering,Peking University,Beijing 100871,China)

机构地区：[1]MoE Key Laboratory of High Energy Density Physics Simulations(HEDPS)and State Key Laboratory of Turbulence and Complex Systems(LTCS),College of Engineering,Peking University,Beijing 100871,China

出　　处：《Acta Mechanica Sinica》2022年第4期104-115,I0003,共13页力学学报（英文版）

基　　金：the National Natural Science Foundation of China(Grant Nos.11832001,11521202,and 11890681)。

摘　　要：Virtual clustering analysis(VCA)is a reduced-order method for numerical homogenization.We formulate VCA for finite strain problems,illustrate its implementation,and provide numerical codes for free download and perusal.Comparison for four test examples shows that both VCA and Self-consistent clustering analysis(SCA)excellently approximate FFT-based direct numerical simulation(DNS)results,yet at much reduced numerical expenses.VCA is actually even faster in the online stage.虚拟聚类分析(VCA)是一种数值均匀化的降阶方法.我们给出了有限应变问题的VCA算法.说明了它的实现,并提供了免费下载和阅读的代码.四个测试实例的比较表明,VCA和自洽聚类分析(SCA)都很好地逼近了基于FFT的直接数值模拟(DNS)结果.且计算代价大大降低.与SCA相比,VCA在线上阶段更为快捷.

关 键 词：Virtual clustering analysis Finite strain HOMOGENIZATION Machine learning 

分 类 号：O343[理学—固体力学]