基于自洽聚类的陶瓷基复合材料多尺度损伤演化并发计算方法

A concurrent computational method for multiscale damage evolution in ceramic matrix composites based on self-consistent clustering

摘要

陶瓷基复合材料结构的力学性能在很大程度上取决于细观尺度的损伤演化特征，材料失效本质上源于微观组织的损伤萌生与扩展。为了准确表征复合材料的细观损伤行为，基于参数跨尺度传递的多尺度分析方法已被广泛应用于复合材料力学性能研究中。然而，传统多尺度方法存在计算效率低、计算量随尺度嵌套呈几何级增长等问题，难以满足工程应用的实时性需求。为此，本工作提出一种基于自洽聚类分析的并发多尺度建模方法。该方法利用聚类分析对细观应力/应变场进行降阶处理，通过获得均匀化后的响应结果替代完整的细观有限元计算，从而显著提高多尺度计算效率。数值结果表明，在单向复合材料与编织复合材料算例中，该方法在计算误差小于 4% 的情况下，整体计算效率提升约一个数量级（约提高 10～15 倍）。该方法在保持较高计算精度的同时，能有效降低计算成本，为复合材料结构的高效损伤分析与寿命预测提供新的思路和技术手段。

Abstract

The mechanical properties of ceramic matrix composite structures are predominantly influenced by their micro-scale damage evolution features，given that material failure fundamentally stems from the initiation and progression of microstructural damage. To precisely characterize the micro-damage behavior of composites，multi-scale analysis methods grounded in parameter cross-scale transfer have been extensively employed in the study of composite mechanical properties. Nevertheless，traditional multiscale methods are plagued by low computational efficiency and a geometric increase in computational effort with nested scales，rendering them ill-suited for real-time engineering applications. To tackle this issue，this work puts forward a concurrent multiscale modeling method based on self-consistent clustering analysis. This method utilizes clustering to reduce the dimensionality of the microscale stress/strain field. It substitutes full-scale microscale finite element computations with homogenized response results，thereby substantially enhancing the efficiency of multiscale computations. Numerical results reveal that for both unidirectional and woven composite material cases，the proposed method achieves an overall improvement in computational efficiency of approximately one order of magnitude (10-15 times faster) while keeping computational errors below 3%. By effectively cutting down on computational costs while maintaining high accuracy，this approach provides new insights and technical means for efficient damage analysis and life prediction of composite structures.

关键词

陶瓷基复合材料 / 自洽聚类分析 / 多尺度建模 / 降阶计算

Key words

ceramic matrix composites / self-consistent clustering analysis / multiscale modeling / reduced order calculation

参考文献

[1] Han X X，Xu C H，Xie W H，et al. Multiscale computational homogenization of woven composites from microscale to mesoscale using data—driven self—consistent clustering analysis[J].Composite Structures，2019，220：760-768.

[2] Ciampaglia A. Data driven statistical method for the multiscale characterization and modelling of fiber reinforced composites[J].Composite Structures，2023，320：117215.

[3] Rayen B N，Vachon—Joannette P，Lombarkia R，et al. Implementation of three—scale bridging for fast homogenization of woven composite through clustering—based reduced order modeling[C]//Proceedings of the 13th Canada—Japan Workshop on Composites （CJWC13），2023.

[4] Han X X，Gao J Y，Fleming M，et al. Efficient multiscale modeling for woven composites based on self—consistent clustering analysis[J].Computer Methods in Applied Mechanics and Engineering，2020，364：112929.

[5] Yu C，Kafka O L，Liu W K. Multiresolution clustering analysis for efficient modeling of hierarchical material systems[J].Computational Mechanics，2021，67（5）：1293-1306.

[6] Liu Z L，Bessa M A，Liu W K. Self—consistent clustering analysis：an efficient multi—scale scheme for inelastic heterogeneous materials[J].Computer Methods in Applied Mechanics and Engineering，2016，306：319-341.

[7] Yu C，Kafka O L，Liu W K. Self—consistent clustering analysis for multiscale modeling at finite strains[J].Computer Methods in Applied Mechanics and Engineering，2019，349：339-359.

[8] Wu S Y，Guo L C，Li Z X，et al. A concurrent multiscale scheme FFT—SCA for meso—micro damage evolution of 3D woven composites independent of mesoscopic material parameters[J].Composites Science and Technology，2025，261：111021.

[9] Gao J Y，Mojumder S，Zhang W Z，et al. Concurrent n—scale modeling for non—orthogonal woven composite[J].Computational Mechanics，2022，70（4）：853-866.

[10] Liu T R，Yang Y，Bacarreza O R，et al. An extended full field self—consistent cluster analysis framework for woven composite[J].International Journal of Solids and Structures，2023，281：112407.

[11] Liu Z L，Wu C T，Koishi M. A deep material network for multiscale topology learning and accelerated nonlinear modeling of heterogeneous materials[J].Computer Methods in Applied Mechanics and Engineering，2019，345：1138-1168.

[12] Moulinec H，Suquet P. A numerical method for computing the overall response of nonlinear composites with complex microstructure[J].Computer Methods in Applied Mechanics and Engineering，1998，157（1/2）：69-94.

[13] Feyel F， Chaboche J L. FE 2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials[J].Computer Methods in Applied Mechanics and Engineering，2000，183（3/4）：309-330.

[14] Liu Z L，Fleming M，Liu W K. Microstructural material database for self—consistent clustering analysis of elastoplastic strain softening materials[J].Computer Methods in Applied Mechanics and Engineering，2018，330：547-577.

[15] Matouš K，Geers M G D，Kouznetsova V G，et al. A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials[J].Journal of Computational Physics，2017，330：192-220.

[16] Mura T. Micromechanics of defects in solids[M]. Dordrecht：Springer，1987.

[17] Brisard S，Dormieux L. FFT—based methods for the mechanics of composites：a general variational framework[J].Computational Materials Science，2010，49（3）：663-671.

[18] Liu Z L，Kafka O L，Yu C，et al. Data—driven self—consistent clustering analysis of heterogeneous materials with crystal plasticity[M]//Advances in Computational Plasticity. Cham：Springer，2017：221-242.

[19] Belytschko T，Liu W K，Moran B. Nonlinear finite elements for continua and structures[M]. Chichester：John Wiley，2000.

[20] Kovachki N，Liu B，Sun X S，et al. Multiscale modeling of materials：computing，data science，uncertainty and goal—oriented optimization[J].Mechanics of Materials，2022，165：104156.

[21] Raju K，Tay T E，Tan V B C. A review of the FE 2 method for composites[J].Multiscale and Multidisciplinary Modeling，Experiments and Design，2021，4（1）：1-24.

[22] Bishara D，Xie Y X，Liu W K，et al. A state—of—the—art review on machine learning—based multiscale modeling，simulation，homogenization and design of materials[J].Archives of Computational Methods in Engineering，2023，30（1）：191-222.

[23] Cui Y H，Zhang Z L. A novel concurrent multiscale method based on the coupling of Direct FE 2 and CPFEM[J].Thin—Walled Structures，2025，206：112610.

[24] Li H L，Sharif Khodaei Z，Aliabadi M H. FFT—based homogenisation for efficient concurrent multiscale modelling of thin plate structures[J].Computational Mechanics，2025，75（2）：637-653.

[25] 韩新星. 基于聚类分析的编织复合材料多尺度计算方法研究[D]. 哈尔滨：哈尔滨工业大学，2020.

[26] Han X X. Multiscale computational method of woven composites based on clustering analysis[D]. Harbin：Harbin Institute of Technology，2020.

基金资助

国家自然科学基金(52505144)

国家科技重大专项(Y2022-IV-0002-0019)

中国博士后科学基金(2024M764101，GZC20252715)

中国科学技术协会青年人才托举工程(YESS20241007AE)

北京市自然科学基金(3252007)

中国太行国家实验室项目(THL-K-25-050)

中央高校基本科研业务费专项资金()