含V型缺口分数阶黏弹性复合材料反平面界面断裂的辛方法

This paper presents a symplectic method for the anti-plane fracture analysis of an interface V-notch in fractional viscoelastic composite media. The fractional Kelvin Zener model is used to describe the viscoelastic characteristics of materials. With the help of Laplace transform,the fundamental equations of an anti-plane viscoelastic fracture problem in time domain arc transformed into frequency domain. By introducing the dual generalized stress variables, the Hamiltonian system is established. Then the eigenvalues and eigensolutions of the Hamiltonian dual equation are obtained by the method of separation of variables, and the unknown coefficients of the symplectic series are determined by the symplectic adjoint orthogonal relationship and the outer boundary conditions. In this way, the analytical expression of the anti-plane stress/strain intensity factor of the viscoelastic media with a V-notch is derived obtained. Finally,the intensity factor in time domain is found by inverse Laplace transform. In numerical examples,the accuracy of the presented method is verified,and the effects of fractional order parameters, notch angle and external load on the stress/strain intensity factor are revealed.