A fictitious crack XFEM with two new solution algorithms for cohesive crack growth modeling in concrete structures

Abstract

Purpose – The purpose of this paper is to achieve numerical simulation of cohesive crack growth in concrete structures. Design/methodology/approach – The extended finite element method (XFEM) using four-node quadrilateral element associated with the fictitious cohesive crack model is used. A mixed-mode traction-separation law is assumed for the cohesive crack in the fracture process zone (FPZ). Enrichments are considered for both partly and fully cracked elements, and it thus makes the evolution of crack to any location inside the element possible. In all. two new solution procedures based on Newton-Raphson method, which differ from the approach suggested by Zi and Belytschko (2003), are presented to solve the nonlinear system of equations. The present formulation results in a symmetric tangent matrix, conveniently in finite element implementation and programming. Findings – The inconvenience in solving the inversion of an unsymmetrical Jacobian matrix encountered in the existing approach is avoided. Numerical results evidently confirm the accuracy of the proposed approach. It is concluded that the developed XFEM approach is especially suitable in simulating cohesive crack growth in concrete structures. Research limitations/implications – Multiple cracks and crack growth in reinforced concretes should be considered in further studies. Practical implications – The research paper presents a very useful and accurate numerical method for engineering application problems that has ability to numerically simulate the cohesive crack growth of concrete structures. Originality/value – The research paper provides a new numerical approach using two new solution procedures in solving nonlinear system of equations for cohesive crack growth in concrete structures that is very convenient in programming and implementation.