显式模拟类橡胶材料Mullins效应滞回圈

EXPLICIT MODELING THE HYSTERESIS LOOPS OF THE MULLINS EFFECT FOR RUBBER-LIKE MATERIALS

通过显式、直接的方法提出一个多轴可压缩应变能函数,用来模拟类橡胶材料在加载-卸载作用下,由于Mullins效应而产生的应力-应变滞回圈.本文的创新点在于将表征能量耗散的变量引入到应变能函数.新的弹性势具有以下两个特点:第一,在加载情况下,新引入的变量不会对弹性势产生任何影响,因此,只要给出合适的形函数显式表达,3个基准实验,包括单轴拉伸和压缩,等双轴拉伸和压缩,以及平面应变,都可精确模拟;第二,新引入的变量在卸载情况下将被激活.在不同的卸载应力下,变量将发生改变,从而影响弹性势,使其最终产生不同的应力-应变关系卸载曲线,与对应的加载曲线共同构成应力-应变滞回圈.通过对Mullins效应实验数据进行分析和研究,得出了卸载形函数在不同卸载应力下变化的规律,并预测不同卸载应力下的应力-应变关系.最后,我们将得到精确匹配实验数据的数值模拟结果,从而证明本文方法不仅可以精确匹配至少3个基准实验,还可以模拟和预测类橡胶材料在加载-卸载作用下由于Mullins效应而产生的滞回圈.

A multi-axial compressible strain energy function is propose to simulate the stress-strain hysteresis loops,which produced by the Mullins effect for rubber-like materials subjected to loading-unloading cycle by a direct, explicit method. The novelty of this paper is to introduce a new variable, which captures the property of dissipation into the potential, and give out a new multi-axial strain energy function. Two properties are incorporated into the new potential:Firstly, the new variable may not affect the potential in the process of loading. Therefore, we can exactly simulate the three benchmark tests, including uniaxial tension and compression, equal-axial tension and compression, and plane strain, by explicitly giving out the appropriate formulations of shape functions;Secondly, the new variable may become active in the process of unloading. The variable may affect the potential by changing with the unloading stress, and produce different stress-strain curves in the unloading process. As a result, the hysteresis loops may be produced in the loading-unloading cycles. We give out the change rules of the shape functions in the unloading process, and predict the stress-strain relation with different unloading stress by analysis the classical test data of the Mullins effects. Numerical results for model validation are in good accord with the three benchmark tests, and the experiments with hysteresis loops producing from the Mullins effect at the end of this paper.