Stochastic Hierarchical Multiscale Analysis and Design of Heterogeneous Material Property

• 作 者: WeiChen[1]HongyiXu[1]M.StevenGreene[2]HuaDeng[1]CatherineBrinson[3]
• 机 构: Department of Mechanical Engineering, Northwestern University, Evanston, IL, 60208, USA
• 出 处: 7th China-Japan-Korea Joint Symposium on Optimization of Str
• 发表日期: 2012年期

　　Multiscale modeling of material system aims to map microstructure to material property.Complexity created by microstructures randomness poses a huge challenge due to the high computational costs.An image-based, hierarchical multiscale stochastic modeling methodology is developed to capture key microstructure features with sufficient accuracy but maintaining a reasonable computational cost.Filled elastomer material is chosen in the study to analyze its damping property.A two-step approach is proposed for relieving the computational burden.(1) Hierarchical multiscale decomposition: the material system is decomposed into two length scales: RVE (representative volume element) scale and SVE (statistical volume element) scale, which are chosen to describe the macro material property and detailed microstructure respectively.Instead of applying direct numerical simulation (DNS) on RVE size microstructure, finite element analysis (FEA) is carried out on SVE scale microstructures.Material property on RVE level is obtained by upscaling from SVE level in a hierarchical manner.(2) Clustering and stochastic modeling for SVE microstructures and property.Using clustering method, SVE microstructure samples with similar microstructure features are grouped into the same cluster to reduce uncertainty in predicting property.To further relieve the computational cost, the minimum sample size for each SVE cluster is determined based on key statistics of the samples via hypothesis testing.Two hypothesis testing methods, bootstrapping hypothesis testing and t-testing, are employed and compared.Properties of SVE microstructures are predicted by random field models with dimension reduction.The capability and efficiency of the two-step approach is demonstrated by comparative studies using different clustering strategies, as well as different sample sizes of SVE simulations.It is shown that the proposed method can effectively cut down redundant simulations while keeping reasonable accuracy for stochastic analysis of microstructure-property relations.