Use of a two-dimensional finite-element model for studying fracture processes

Abstract

1. A quadrangular singular element was developed for studying the process of brittle fracture of two-dimensional regions. The displacement field in the vicinity of the crack tip was approximated by an interpolation polynomial — a complete cubic simplex. A linear distribution of displacements is retained on the contour, thanks to which continuity of displacements with adjacent linear elements is provided. Possible crack developments are controlled by criteria: maximum tensile stresses, maximum energy flow, and minimum strain energy density. The element is effective in modeling the crack propagation path with consideration of the effect of hydrostatic pressure and has an acceptable accuracy in describing the asymptotics of a crack. The superelement structure of the element permits including Goodman's special element [3] and can be used for studying fractures also in compressed zones. 2. The singular element permits studying the stress-strain state of both surface and underground hydraulic structures jointly with the foundation with consideration of the development of fracture phenomena of materials with accompanying effects of seepage pressure.