Generalized displacement control technique for mode I/II fracture problems using cohesive zone model within a modified element‐free Galerkin framework

Abstract

A modified element‐free Galerkin (EFG) method that combines the Heaviside enrichment and diffraction method is used to study crack propagation problems by employing a cohesive zone model (CZM) with an exponential traction separation law (TSL). The generalized displacement control method (GDCM) is adopted to solve the nonlinearity arising during the damage evolution. The proposed methodology is applied to (1) uncracked three‐point bending (TPB) and (2) adhesively bonded: (a) cracked double cantilever beam (DCB), and (b) end‐notched flexure (ENF) problems. In the passing, a simple 1D study is considered to demonstrate the advantage of level‐set enrichment coupled with CZM. Several parametric studies have been carried out on the EFG method and GDCM (reference and incremental load parameter). The results obtained by the proposed methodology agree well with the experimental/reference results. Specific advantages of GDCM on computational time, number of iterations, and ability to capture snapback vis‐à‐vis the popular Newton–Raphson technique are presented.