基于分数阶微积分的岩石非线性蠕变损伤力学模型

Mechanical Model of Rock Nonlinear Creep Damage Based on Fractional Calculus

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 means of classic element combination modeling,a new mechanical model of nonlinear creep damage is put forward containing component of fractional calculus and a damage variable for reflecting stress level and times,it also gives the constitutive and creep equations of the model.In lower stress level,the model can be effectively used to describe the rock characteristics,such as the attenuation creep and stabilization creep,moreover,if the stress level beyond the long-term strength of rocks,it can be used to reflect the accelerated creep characteristics.Comparison between the results obtained from the creep damage model and the creep test data shows that this model is not only able to describe the attenuation creep phase,the stabilization creep phase and the speed-up creep phase of the creep curve,but also to reduce the number of parameter in the creep model under the condition that the fitting precision is guaranteed.It provides a new idea for nonlinear creep model research.