利用分数阶导数模型研究有记忆的固体材料

Toward a model for solid materials with memory by use of the fractional-order derivatives

对一类带有不同分数阶导数的黏弹性材料本构方程进行了讨论,其解通过拉普拉斯变换得到,可用H-Fox函数表示,且解与实验数据拟合较好。在频率域模型的行为方面,损耗角正切的极限由应变和应力时间导数阶的差决定。

A constitutive equation on viscoelastic materials with different fractional order derivatives is discussed, and its solution is obtained by using Laplace transform techniques and can be expressed in terms of H-Fox functions. The so-lution is consistent with the experimental data. The model behavior in the frequency domain is also discussed, the limit of the loss tangent is governed by the difference between the order of time derivatives of strain and stress.