A pseudo-ODE modelling trick for the direct method of lines computation of important fracture mechanics parameters

Abstract

A novel introduction in fracture mechanics of pseudo-ordinary differential equations (ODEs) corresponding to the stress intensity factors (SIFs), augments the under-determined system of ODEs produced by the method of lines (MOL) solution of the equations of elasticity, in the presence of cracks. With this modelling "trick", which is natural to MOL, the SIFs are obtained directly, as part of the solution unknowns, thus avoiding the uncertainties associated with other indirect methods.