基于特征正交分解的材料微结构参数化表征模型及等效性能优化设计  

A POD-Based Parameterization Model for Material Microstructure Representation and Its Application to Optimal Design of Material Effective Mechanical Properties

作　　者：郭志文[1] 肖曼玉[1] 夏凉[2,3,4] 

机构地区：[1]西北工业大学理学院数学与应用数学系,西安710129 [2]巴黎东部大学多尺度模拟与仿真实验室(CNRS UMR 8208) [3]华中科技大学机械科学与工程学院 [4]数字制造装备与技术国家重点实验室(华中科技大学),武汉430074

出　　处：《应用数学和力学》2017年第7期727-742,共16页Applied Mathematics and Mechanics

基　　金：国家自然科学基金青年科学基金(11302173);陕西省自然科学基金(2017JQ1037)~~

摘　　要：随着计算能力的不断发展,近年来基于材料微结构图像的材料等效性能数值模拟越来越受到学者们的重视.在此背景下,提出了一种针对材料微结构图像的高效参数化表征模型.通过特征正交分解(proper orthogonal decomposition,POD)对已有材料微结构图像数据进行特征分析,得到近似描述该类材料微结构的特征缩减基.应用移动最小二乘(moving least squares,MLS)法建立特征缩减基映射系数的响应面模型,拟合得到任意给定参量相应的缩减基映射系数.利用拟合缩减基系数可获得任意给定参量对应的微结构图像矩阵.该参数化表征模型被用于表征含椭球夹杂的两相材料(2-phase composite)的二维情形,并进一步应用于这类复合材料宏观等效力学性能的优化设计.With the increasing computing capability, numerical material simulation based on material microstructure images has attracted interest of more and more researchers. Within this context, an efficient numerical material parameterization model was proposed for the represen- tation of material microstructures. ~rst, the eigenvalue analysis of the material microstructure image data was carried out through the proper orthogonal decomposition （POD） to extract a common POD basis. The material microstructure image can be represented as a linear combina- tion of the retained POD basis. Then, response surfaces of the POD projection coefficients with respect to the controlling parameters were built with the method of moving least squares. By means of this numerical parameterization model, the corresponding material microstructure im- age for arbitrary input controlling parameters can be reconstructed. Application of this model was demonstrated in view of a set of 2-phase composite material snapshots. This parameterized material microstructure representation model can also been applied to the optimal design of ma- terial effective mechanical properties.

关 键 词：材料微结构 特征正交分解 响应面 参数化模型 代理模型 均匀化 优化设计 

分 类 号：V214.8[航空宇航科学与技术—航空宇航推进理论与工程]