Efficient treatment of stress singularities in poroelastic wave based models using special purpose enrichment functions

The Finite Element Method is the most commonly used prediction technique to model the harmonic behavior of poroelastic materials. A major disadvantage of this method is its practical frequency limitation in that the computational efforts become prohibitively large at higher frequencies. A recently developed Wave Based Method is an efficient alternative deterministic prediction technique which aims at relaxing this frequency limitation by using exact solutions of the governing equations to approximate the field variables. This paper discusses the application of the Wave Based Method for the particular case that stress singularities are present in corners of the poroelastic domain. Based on an asymptotic analysis, the paper derives a criterion to predict the presence of stress singularities and proposes a suitable set of enrichment functions to extend the conventional set of expansion functions. The beneficial effect of incorporating these functions on the convergence of the Wave Based Method is illustrated by means of a numerical validation study.