A ϑ method-based numerical simulation of crack growth in linear elastic fracture

Abstract

This paper presents a method for the automatic simulation of quasi-static crack growth in 2D linear elastic bodies with existing cracks. A finite element algorithm, based on the so-called ϑ method, provides the load vs. crack extension curves in the case of stable rectilinear crack propagation. Since the approach is both theoretically general and simple to be performed from a computational point of view, it appears very suitable for the extension to curvilinear crack propagation in nonlinear materials.

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“…Fortino and Bilotta 44 presented an algorithm to determine the amount of crack growth in 2D problems with stable rectilinear crack growth. Formica et al 45 developed a crack growth formulation based on the so‐called Destuynder–Djaoua method 46, in which the crack length increment is related to the given load parameter. However, more developments are necessary for the general case of curvilinear crack growth in multiple cracked bodies since the crack growth path is not known a‐priori .…”