Crack problems in a viscoelastic medium using enriched finite element method

Abstract

Crack problems in 2-D and 3-D linear viscoelastic media are numerically investigated using the enriched finite element method (enriched FEM). In the same spirit as for the enriched elements, the viscoelastic crack-tip asymptotic displacement field is obtained by using the viscoelastic–elastic correspondence principle and is transformed into the polynomial displacement field of regular elements. Thereby, the time-dependent unknowns in the asymptotic displacement field related to the crack strain energy release rate are introduced as the additional degree of freedoms (DOFs) of enriched elements. With these treatments, the incremental enriched FEM formulations in time domain are derived according to the Boltzmann superposition principle. The present method shows that the time-dependent strain energy release rate can be easily obtained from the extra DOFs. Several illustrative examples are given and good agreement between the present results and those from analytical and other numerical methods is confirmed. The method developed in this paper is capable of solving crack problems in viscoelastic media with complicated geometry, loading and constraint conditions.