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在分数阶黏弹性模型的基础上,根据Mittag-Leffler函数的性质及Laplace变换公式推导了磁流变弹性体的蠕变柔量和应力松弛模量的表达式;利用流变仪分别测试了磁流变弹性体的蠕变和松弛行为,研究了磁场和应变对蠕变柔量和应力松弛模量的影响,并对分数阶黏弹性模型拟合结果进行了验证。结果表明:外部磁场可以约束硅橡胶基磁流变弹性体的蠕变行为、增大聚氨酯橡胶基磁流变弹性体的松弛模量,其松弛行为具有明显的应变依赖性;分数阶黏弹性模型的拟合精度较高,能够很好地表征磁流变弹性体的蠕变和松弛行为。
Based on the fractional viscoelastic model, the expressions of creep compliance and stress relaxation modulus of MRF are deduced according to the properties of Mittag-Leffler function and Laplace transformation formula. The creep and relaxation behaviors of rheological elastomers were studied. The effects of magnetic field and strain on creep compliance and stress relaxation modulus were studied. The results of fractional viscoelastic model fitting were also validated. The results show that the external magnetic field can constrain the creep behavior of silicone rubber-based magnetorheological elastomers, and increase the relaxation modulus of polyurethane rubber-based magnetorheological elastomers with obvious strain dependence. The fractional viscoelastic model The fitting accuracy is high, which can well characterize the creep and relaxation behaviors of MRFs.