基于渐近均匀化法的黏弹性复合材料时域本构模型研究

doi:10.19936/j.cnki.2096-8000.20250828.002

复合材料科学与工程 ›› 2025, Vol. 0 ›› Issue (8): 8-14.DOI: 10.19936/j.cnki.2096-8000.20250828.002

基于渐近均匀化法的黏弹性复合材料时域本构模型研究

武顺心^1,2, 朱水文^1,2*

1.湖北汽车工业学院汽车工程学院,十堰 442002;
2.汽车动力传动与电子控制湖北省重点实验室,十堰 442002

收稿日期:2024-08-05 出版日期:2025-08-28 发布日期:2025-09-23
通讯作者: 朱水文(1978—),男,博士,讲师,硕士生导师,主要从事复合材料及汽车轻量化方面的研究,swzhu@huat.edu.cn。
作者简介:武顺心(1999—),男,在读硕士,主要从事复合材料均匀化及相关方面的研究。
基金资助:
湖北汽车工业学院博士基金(BK202213);汽车动力传动与电子控制湖北省重点实验室开放基金(ZDK12023B09);湖北省教育厅项目(B2023076)

Time-domain constitutive modeling of viscoelastic composites based on asymptotic homogenization method

WU Shunxin^1,2, ZHU Shuiwen^1,2*

1. School of Automotive Engineering, Hubei University of Automotive Technology, Shiyan 442002, China;
2. Hubei Key Laboratory of Automotive Power Train and Electronic Control, Shiyan 442002, China

Received:2024-08-05 Online:2025-08-28 Published:2025-09-23

摘要/Abstract

摘要： 本文旨在建立一种高效、准确的黏弹性复合材料宏观本构关系建模方法。通过结合渐近均匀化理论和特征位移法,建立了微观结构与宏观响应之间的定量关系。采用降阶均匀化方法求解特征位移,有效提高了计算效率,并直接得到了时域中的宏观本构关系。将得到的本构关系以用户自定义材料子程序(UMAT)的形式嵌入有限元软件ABAQUS中,并通过与Digimat的对比验证了模型的可靠性。数值结果表明,纤维体积分数和黏弹性衰减比对复合材料的应力松弛行为具有显著影响。随着纤维体积分数的增加,复合材料的初始应力值和应力松弛速率均增大;而衰减比的增大则导致应力松弛速率减慢。研究表明,该方法能够准确预测黏弹性复合材料的时域力学响应,为复合材料的设计和优化提供了有力的理论支撑。

关键词: 渐近均匀化, 黏弹性, 体积分数, 应力松弛, 宏观-微观, 复合材料

Abstract: The aim of this paper is to establish an efficient and accurate method for modeling the macroscopic constitutive relationship of viscoelastic composites. By combining the asymptotic homogenization theory and the eigen-displacement method, a quantitative relationship between the microstructure and the macroscopic response is established. The reduced-order homogenization method is used to solve the characteristic displacement, which effectively improves the computational efficiency and directly obtains the macroscopic ontological relationship in the time domain. The obtained ontological relationship is embedded into the finite element software ABAQUS in the form of a user-defined material subroutine (UMAT), and the reliability of the model is verified by comparison with Digimat. The numerical results show that the fiber volume fraction and viscoelastic decay ratio have a significant effect on the stress relaxation behavior of the composites. As the fiber volume fraction increases, both the initial stress value and the stress relaxation rate of the composites increase; while the increase in the decay ratio leads to a slower stress relaxation rate. It is shown that the method can accurately predict the time-domain mechanical response of viscoelastic composites, which provides a strong theoretical support for the design and optimization of composites.

Key words: asymptotic homogenization, viscoelasticity, volume fraction, stress relaxation, macro-micro, composites

中图分类号:

TB332

武顺心, 朱水文. 基于渐近均匀化法的黏弹性复合材料时域本构模型研究[J]. 复合材料科学与工程, 2025, 0(8): 8-14.

WU Shunxin, ZHU Shuiwen. Time-domain constitutive modeling of viscoelastic composites based on asymptotic homogenization method[J]. COMPOSITES SCIENCE AND ENGINEERING, 2025, 0(8): 8-14.

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基于渐近均匀化法的黏弹性复合材料时域本构模型研究

Time-domain constitutive modeling of viscoelastic composites based on asymptotic homogenization method

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