Numerical study on deformations in a cracked viscoelastic body with the extended finite element method

摘要

Deformations such as crack opening and sliding displacements in a cracked viscoelastic body are numerically investigated by the extended finite element method (XFEM). The solution is carried out directly in time domain with a mesh not conforming to the crack geometry. The generalized Heaviside function is used to reflect the displacement discontinuity across a crack surface while the basis functions extracted from the viscoelastic asymptotic fields are used to manifest the gradient singularity at a crack tip. With these treatments, the XFEM formulations are derived in an incremental form. In evaluating the stiffness matrix, a selective integration scheme is suggested for problems with high Poisson ratios often encountered in viscoelastic materials over different element types in the XFEM. Numerical examples show that the crack opening displacement and crack sliding displacement are satisfactory.