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借鉴元件组合模型的建模方法,将含分数阶导数的软体元件与虎克体串联,引入能反映应力水平和时间影响的损伤变量,提出一种四元件非线性蠕变损伤模型,并给出该模型的本构方程和蠕变方程。在应力水平较低时,模型能够有效地描述岩石的衰减蠕变和稳定蠕变;当应力水平超过岩石的长期强度时,能够反映加速蠕变特性。利用蠕变试验数据对所提出的模型进行辨识,结果表明该模型不但能够很好地描述蠕变曲线中衰减蠕变阶段、稳态蠕变阶段和加速蠕变阶段,而且可以在保证拟合精度的条件下减少模型中的参数,为非线性蠕变模型研究提供了一种新的思路。
By referring to the modeling method of component combination model, the software component with fractional derivative is connected in series with Hooke body, and the damage variable which can reflect the influence of stress level and time is introduced. A four-element nonlinear creep damage model is proposed and given Constitutive equation and creep equation of the model. When the stress level is low, the model can effectively describe the decay creep and stable creep of rocks. When the stress level exceeds the long-term strength of rock, it can reflect the accelerated creep characteristics. The creep test data is used to identify the proposed model. The results show that the model can not only describe the decay creep phase, the steady creep phase and the accelerated creep phase in the creep curve well, but also can guarantee the fitting accuracy The parameters in the model are reduced, which provides a new idea for the study of nonlinear creep model.