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 引用本文: 王晓明, 田兴兴, 张振, 肖衡. 显式方法模拟类橡胶材料率相关Mullins效应. 力学学报, 待出版.
Wang Xiaoming, Tian Xingxing, Zhang Zhen, Xiao Heng. Explicitly modeling the Mullins effect of rubber-like material with rate dependency. Chinese Journal of Theoretical and Applied Mechanics, in press.
 Citation: Wang Xiaoming, Tian Xingxing, Zhang Zhen, Xiao Heng. Explicitly modeling the Mullins effect of rubber-like material with rate dependency. Chinese Journal of Theoretical and Applied Mechanics, in press.

## EXPLICITLY MODELING THE MULLINS EFFECT OF RUBBER-LIKE MATERIAL WITH RATE DEPENDENCY

• 摘要: 有了加载历史后的类橡胶材料再次加载, 会发生应力软化效应, 也称为Mullins效应. Mullins效应引起的应力-应变滞回圈会随着应变率的变化而发生改变. 首先, 经典的类橡胶材料弹性势通常不考虑耗散, 无法从理论上解释为什么材料有了加载历史以后会产生应力软化现象; 其次, 传统方法通常把应变率作为固定的参数引入到方程, 这样就增加了模型的使用局限性; 最后, 大部分模型仅仅考虑单一的变形模式(比如单轴拉伸), 而真实的材料还可能受到等双轴拉伸、平面应变拉伸等更加复杂的变形模式. 文章基于显式方法构造类橡胶材料弹性势, 用来模拟不同应变率下考虑Mullins效应的应力-应变关系. 首先, 通过研究类橡胶材料在加载-卸载下的应力-应变关系, 构造耗散随着加载历史变化的规律; 其次, 将耗散和应变率作为变量引入到形状特征参数中, 构造3个基准实验新的形函数表达; 最后, 利用对数应变构造3个不变量, 结合前面得到的形函数, 基于Hermite 插值方法得到统一弹性势. 结果表明, 通过统一弹性势可以分别推导得到3个基准实验下的应力-应变关系, 对于率相关Mullins效应的实验数据可以进行精确的匹配与合理的预测. 本研究工作所有的参数通过显式方法给出, 大大减少了计算代价, 为类橡胶材料的工程设计和实际应用提供了重要数据和设计指导.

Abstract: Stress softening, known as Mullins effect, occurs in rubber-like materials during the first and subsequent deformations. The stress-strain hysteresis loops induced by the Mullins effect will change as the strain rate varies. First, classical elastic potential usually does not consider dissipation, and cannot theoretically explain why the material exhibits stress softening after a loading history. Second, when considering the effects of strain rate, traditional methods often introduce it as a fixed parameter into the equation, which greatly increases the limitations of the model. Third, most of models only consider a single deformation mode, for example, uniaxial tension. whereas real materials may also be subjected to more complex deformation modes such as equi-biaxial tension and plane strain tension. A unified elastic potential is proposed to simulate stress-strain relationship with the Mullins effect in different strain rate. First, constructing evolution equation of dissipation by researching stress-strain relationship in loading-unloading process. Second, proposing shape functions of three benchmark tests by introducing dissipation and strain rate into the characteristic parameters. Third, combined with shape function and three invariants, a unified potential is proposed by using Hermite interpolation method. The results show that the stress-strain relationships under three benchmark experiments can be derived by using a unified elastic potential, and the rate-dependent stress-strain experimental data can be accurately matched and reasonably predicted. All the parameters presented in this article can be determined by explicit methods, thus can significantly reducing computational costs. This work provides essential data and design guidance for the engineering design and practical application of rubber-like materials.

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