ANALYSIS OF DYNAMIC CONTACT OF CRACKS IN VISCOELASTIC MEDIA

A novel single-step method is proposed for the analysis of dynamic response of contactable crack in viscoelastic media. In the method, a two-level algorithm is employed for dealing with a non-linear boundary condition caused by the dynamic contact of crack surfaces. At the first level, an explicit method is adopted to calculate nodal displacements of the global viscoelastic system without considering the effect of dynamic contact of cracks and at the second level, by introducing the contact condition of crack surfaces, a group of equations of smaller order is derived to calculate dynamic contact forces on the crack surfaces. The method is very convenient and efficient for the analysis of problems of dynamic contact. The accuracy and the stability condition of the method are also discussed in the paper. It is shown that the accuracy of the method is of the second order and the numerical stability condition is wider than that of other explicit methods, such as the predictor-corrector method and the explicit difference methods in which a backward difference form is used for the velocity term of the equation. Numerical results are obtained for the impact of a thick plate with an infinite crack. The results demonstrate that when damping exists, the high-frequency oscillation in the solution of contact force is reduced and the opening of crack faces becomes smaller.