EXPLICITLY MODELING PERMANENT SET AND ANISOTROPY PROPERTY INDUCED BY STRESS SOFTENING FOR RUBBER-LIKE MATERIALS
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摘要: 类橡胶材料在经过初次加载后会产生应力软化现象, 也就是Mullins效应. 实验证明应力软化现象会导致材料产生不可恢复变形, 同时引入各向异性特征. 本文基于对数应变构造一个多轴可压缩应变能函数, 先引入耗散来表征应力软化现象, 再引入依赖耗散大小的不可恢复变形量以及各向异性特征量, 使得新模型既可以表征Mullins效应, 又能模拟应力软化作用下产生的不可恢复变形和各向异性特征. 本文在各向同性形函数的基础上, 通过球坐标系的思想, 进一步发展并提出了一个任意方向适用的各向异性形函数. 新模型在材料尚未发生软化(耗散为0)的情况下, 表现出各向同性; 一旦发生应力软化(耗散大于0), 则变为各向异性. 随着加载−卸载循环的累积, 耗散逐渐变大, 不可恢复变形也随之变大直到达到一个稳定的值, 各向异性特性也逐渐变得明显. 新方法得到的结果可以精确匹配经典的实验数据, 并预测不同方向的应力软化现象以及由此产生的不可恢复变形和各向异性特征.Abstract: Stress softening, known as the Mullins effect, is observed in rubber-like materials after initial loading cycles. Experimental observations have shown that the Mullins effect leads to a permanent set and induces anisotropic properties. A multi-axial, compressible strain energy function based on the Hencky strain is proposed to account for the stress softening and simulate the permanent set and anisotropic properties by introducing two variables, separately characterizing the permanent set and anisotropic properties, which are dependent on dissipation. A comprehensive, explicit shape function is proposed by using the spherical coordinate system to make the model effective in arbitrary direction. The new model exhibits isotropic properties when it not yet induced stress softening, and becomes anisotropy when the Mullins effect occurs. The residual strain increases and reach a fixed value as the loading-unloading cycles proceeds, and the anisotropy becomes more obvious. The simulation results are shown good accord with the classical experimental data and successfully forecast the permanent set and anisotropic properties induced by stress softening.
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Key words:
- tress softening /
- permanent set /
- anisotropy /
- dissipation /
- shape function
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图 2 六面体橡胶块三维受力示意图
Figure 2. Schematic of hexahedral rubber block with three-dimensional force
图 4 任意方向受力的球坐标示意图
Figure 4. Schematic of loading in arbitrary direction by Spherical coordinate system
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