具有三尺度微结构的非线性随机异质材料的统计高阶还原模型

IF 3.4 3区 材料科学 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY
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引用次数: 0

摘要

建立了一种有效的统计高阶三尺度还原均质化(SHTRH)方法,用于分析具有多种微观构型的非线性随机异质材料。首先,给出了基于微尺度和微尺度区域的各种单元函数,并通过柯尔莫哥洛夫强大数定律计算了两个预期均质化系数。此外,还提出了非线性均质化方程,并利用高阶单元解和均质化解推导出相应的位移和应力求解的降阶多尺度系统。新的统计多尺度方法的主要特点是:(i) 建立了新的简化模型,以较低的成本解决随机复合材料的非弹性问题;(ii) 高阶均质化解不需要随机问题宏观解的高阶连续性;(iii) 开发了用于分析具有三尺度结构的非线性随机复合材料的统计高阶多尺度算法。最后,该算法的有效性和正确性通过几种具有多尺度配置的超弹性、塑性和损伤周期/随机复合材料得到了证实。计算结果表明,所提出的 SHTRH 方法有助于分析宏观非线性性能,并能有效捕捉随机异质复合材料的微观和中观信息。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A statistical high-order reduced model for nonlinear random heterogeneous materials with three-scale micro-configurations

An effective statistical higher-order three-scale reduced homogenization (SHTRH) method is established to analyze the nonlinear random heterogeneous materials with multiple micro-configurations. Firstly, the various unit cell functions based on the microscale and mescoscale regions are given, and two expected homogenization coefficients are computed through Kolmogorov's strong laws of large number. Further, the nonlinear homogenized equations are formulated, and the corresponding reduced-order multiscale systems for displacement and stress solutions are derived by using the high-order unit cell solutions and homogenized solutions. The key features of the new statistical multiscale methods are (i) the novel reduced models established to solve the inelastic problems of random composites at a fraction of cost, (ii) the high-order homogenized solutions which do not need high-order continuity for the macro solutions of the random problems and (iii) the statistical high-order multiscale algorithms developed for analyzing the nonlinear random composites with three-scale structures. Finally, the effectiveness and correctness of the algorithm are confirmed according to several hyperelastic, plasticity and damage periodic/random composites with multiple-scale configurations. The computation shows that the proposed SHTRH methods are useful for analyzing the macroscopic nonlinear performance, and can efficiently catch the microscopic and mesoscopic information for the random heterogeneous composites.

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来源期刊
Mechanics of Materials
Mechanics of Materials 工程技术-材料科学:综合
CiteScore
7.60
自引率
5.10%
发文量
243
审稿时长
46 days
期刊介绍: Mechanics of Materials is a forum for original scientific research on the flow, fracture, and general constitutive behavior of geophysical, geotechnical and technological materials, with balanced coverage of advanced technological and natural materials, with balanced coverage of theoretical, experimental, and field investigations. Of special concern are macroscopic predictions based on microscopic models, identification of microscopic structures from limited overall macroscopic data, experimental and field results that lead to fundamental understanding of the behavior of materials, and coordinated experimental and analytical investigations that culminate in theories with predictive quality.
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