Journal of Mechanical Science and Technology 29 (3) (2015) 1131~1143 www.springerlink.com/content/1738-494x DOI 10.1007/s12206-015-0225-8 A new criterion for modeling multiple discontinuities passing through an element using XIGA † I. V. Singh * , G. Bhardwaj and B. K. Mishra Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, 247667 Uttarakhand, India (Manuscript Received June 23, 2014; Revised September 22, 2014; Accepted November 13, 2014) ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Abstract In this paper, a new criterion is proposed for the modeling multiple discontinuities i.e. crack, hole and inclusion passing through an element by XIGA. The modeling of multiple discontinuities passing through an element is done by imposing the additional degrees of freedom at the control points lying inside the influence of elements intersected by the discontinuities. In XIGA, the crack faces are mod- eled by discontinuous Heaviside jump functions, whereas the singularity in stress field at the crack tip is modeled by crack tip enrichment functions. The modeling of holes and inclusions is performed by Heaviside jump function and distance function respectively. The value of stress intensity factor is computed using domain form of interaction integral approach. Few static plane edge crack problems are ana- lyzed in the presence of holes and inclusions to validate the proposed criterion. The results obtained by XIGA are compared with XFEM. Keywords: XIGA; Cracks; Holes; Inclusions; Stress intensity factor ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction The study of structures/components failure is important from the safety and design point of view. The new era of re- search for computational community is the prediction and analysis of component in the presence of defects. Now a day, most of the engineering structures are analyzed by finite ele- ment method (FEM). Although, FEM has got some advan- tages in solving various field problems but it has got few drawbacks in analyzing the problems involving discontinuities such as voids, inclusions and micro-cracks. In order to over- come the problems associated with the FEM, element free Galerkin method [1], reproducing kernel particle method [2] meshless local petrov Galerkin method [3] extended finite element method [4] have been developed. In these methods, the approximation of geometry may introduce some error in the solution since different basis functions are employed for defining the geometry and solution. To remove the error asso- ciated with the geometric discretization, a new approach is developed, known as isogeometric analysis (IGA) [5]. In IGA, the error associated with the domain discretization is totally removed as he employed same basis function i.e. non-uniform rational B-splines (NURBS) for defining the geometry and solution. Since its development, IGA has been successfully applied in the various fields of engineering and sciences e.g. Cottrell et al. [6] employed the IGA for the vibrational analysis of structures. They (Cottrell et al. [7]) further studied the mesh refinement and continuity of IGA. Hughes et al. [8] used the IGA for the analysis of structural vibrations and wave propa- gation, and found that k-type IGA provides better convergence and accuracy in comparison to p-type IGA. Shaw and Roy [9] proposed NURBS based error reproducing kernel method for solving the solid mechanics problems. Wall et al. [10] per- formed the structural shape optimization of 2-D elasticity problems using IGA. Kiendl et al. [11] proposed an iso- geometric formulation for the analysis of thin shell structures with multiple patches. Nagy et al. [12] presented the study of structural sizing and shape optimisation of curved beams structures using isogeometric analysis. Kim et al. [13] ana- lyzed the linear elasticity problems involving complex shapes using IGA. Seo et al. [14] implemented the concept of IGA for structural shape optimization of shells. Qian [15] com- puted the sensitivity of position and weight of NURBS control points in shape optimization using analytical formulas. The IGA was successfully implemented in cohesive zone model- ing [16]. Temizer et al. [17] performed the contact analysis using IGA, and showed that the implementation of IGA in contact treatment provides greater accuracy and higher rate of convergence as compared to FEM. Nguyen-Thanh et al. [18] developed polynomial splines alternative to NURBS based isogeometric analysis that allows for local refinement. Nguyen-Thanh et al. [19] performed isogeometric analysis of * Corresponding author. Tel.: +91 1332 285888, Fax.: +91 1332 285665 E-mail address: ivsingh@gmail.com † Recommended by Chief-in-Editor Maenghyo Cho © KSME & Springer 2015