人颅骨粘弹性的分数阶模型研究

Study on A Fractional Model of Viscoelasticity of Human Cranial Bone

利用Riemann_Liouville的分数阶微积分算子及理论 ,将标准的整数阶St.Venant力学模型推广至它的分数阶形式 ;根据Boltzmann迭加原理 ,应用离散化求逆Laplace变换的方法以及H_Fox函数 ,得出了分数阶St.Venant模型的应力松弛函数和蠕变函数的解析表达式 ,并分别与现有的人颅骨粘弹性实验数据相拟合。结果表明 ,分数阶的St.Venant模型比标准的整数阶St.Venant模型能够更有效地刻画人颅骨的粘弹性的应力～应变本构特性。

In this paper, the standard St. Venant model with integer order was generalized by applying the Riemann-Liouville fractional calculus operators and its theory. The analytical expressions of the stress relaxation function and creep function for the obtained fractional St. Venant model were given by using the Boltzmann superposition principle and discrete inverse Laplace transform method. H-Fox functions played a dominant role in solving the problem. The analytical solutions of the fractional model were fitted with the experimental data for viscoelasticity of human cranial bone. The results showed that the fractional St. Venant model was more efficient than the standard St. Venant model with integer order in describing the stress - strain constitutive relations for the viscoelasticity of human cranial bone.