Extended isogeometric analysis for simulation of stationary and propagating cracks

Abstract

SUMMARYA novel approach based on a combination of isogeometric analysis (IGA) and extended FEM is presented for fracture analysis of structures. The extended isogeometric analysis is capable of an efficient analysis of general crack problems using nonuniform rational B-splines as basis functions for both the solution field approximation and the geometric description, and it can reproduce crack tip singular fields and discontinuity across a crack. IGA has attracted a lot of interest for solving different types of engineering problems and is now further extended for the analysis of crack stability and propagation in two-dimensional isotropic media. Concepts of the extended FEM are used in IGA to avoid the necessity of remeshing in crack propagation problems and to increase the solution accuracy around the crack tip. Crack discontinuity is represented by the Heaviside function and isotropic analytical displacement fields near a crack tip are reproduced by means of the crack tip enrichment functions. Also, the Lagrange multiplier method is used to impose essential boundary conditions. Moreover, the subtriangles technique is utilized for improving the accuracy of integration by the Gauss quadrature rule. Several two-dimensional static and quasi-static crack propagation problems are solved to demonstrate the efficiency of the proposed method and the results of mixed-mode stress intensity factors are compared with analytical and extended FEM results.

Vibration analysis of cracked FGM plates using higher-order shear deformation theory and extended isogeometric approach

“…We exploit cubic basis functions for almost numerical examples, except a circular plate problem that quadratic basis functions are also used. Herein, present method employes a full integration of ( 1) ( 1) p q + × + Gauss points for the standard elemtents and a subtriangles technique [38] for the enriched elements. The results, unless specified otherwise, are normalized as …”

“…In addition, to capture the discontinuous phenomenon in the cracked FGM plates, the enrichment functions through the partition of unity method (PUM) originated by Belytschko and Black [37] are incorporated with NURBS basic functions to create a novel method as so-called eXtended Isogeometric Analysis (XIGA). XIGA has then been applied to stationary and propagating cracks in 2D [38], plastic collapse load analysis of cracked plane structures [39] and cracked plate/shell structures [40]. Herein, our study focuses on investigating the vibration of the cracked FGM plate with an initial crack emanating from an edge or centrally located.…”

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

“…Moreover, for complex crack patterns with slightly deviating angles between the crack branches, it is expected that the mesh will be extremely distorted. De Luycker et al [259], Ghorashi et al [260] and recently Tambat and Subbarayan [261] combined XFEM with isogeometric analysis (XIGA) allowing crack growth without remeshing also in the context of IGA.…”

Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth

“…In its original, finite element based form, IGA does not completely suppress the need to create a mesh, as the CAD data provides only a 'shell' for the component, but gives no information about the parametrization of the interior of the volume which it encloses. Although the finite element version of IGA was used for fracture analysis [58][59][60][61]. This motivated the inception of a boundary element version of IGA for elasticity problems in [62][63][64].…”