Stress Intensity Factor Extraction from the Enriched Partition of Unity Solution for a Cracked Linear Elastic Medium

Abstract

The stress intensity factor is a useful tool for predicting material failure and describing the stress states of brittle materials. We present a technique to calculate the stress intensity factor for a linear elasticity problem on a cracked domain with an enriched partition of unity method. We use a particular partition of unity function, which is piecewise polynomial and has wide flat-top region. The flat-top area in the partition of unity function helps the displacements and the stress fields in the vicinity of the crack tip to be accurately represented, even with a coarse background mesh. Among other methods for calculating the stress intensity factor, we find that the direct extraction method is the most accurate and efficient one given a relatively coarse background mesh for the enriched partition of unity method.