Use of modified standard 20-node isoparametric brick elements for representing stress/strain fields at a crack tip for elastic and perfectly plastic material

The analysis of defects in engineering structures and components has to take into account the singular strain field at the crack tip. The problems encountered in such analyses have unique geometries, have some non-linear elastic plastic behaviour and are three-dimensional in nature. Two-dimensional fracture mechanics analysis methods have been developed and proved by other researchers to show that 8-noded collapsed finite elements have the required singular strain fields for both the elastic and perfectly plastic material conditions. This paper proves the conditions under which three-dimensional collapsed elements represent the stress/strain fields at a crack tip required for elastic and perfectly plastic material.