X‐IGALME: Isogeometric analysis extended with local maximum entropy for fracture analysis

Abstract

An extended approach is developed by blending isogeometric analysis and the first-order local maximum entropy for the standard and the enhanced fields, respectively. Isogeometric analysis facilitates the accurate parametrization of the geometry in general, particularly the exact geometric parametrization of the conic curves and quadratic surfaces using NURBS. On the other hand, the local maximum entropy leads to an improved estimate for the enhanced part due to its infinite continuity. Moreover, local maximum entropy paves the way to a nonelementwise crack propagation owing to its meshfree characteristic. To enforce compatibility, the shifting technique is amended for the meshfree enhanced part to localize the effect of the Heaviside function to a narrow region around the crack. Next, a blending technique is exploited to remove the effect of the discontinuity in front of the crack tip. The viability of the approach is illustrated at the hand of several examples comprising straight and curved crack propagation.

Extended isogeometric analysis of a progressively fracturing fluid‐saturated porous medium

“…60 The consequences of an incomplete enforcement were also observed in a study on geometric nonlinearity. 61 More recently, IGA was extended with a local maximum entropy (LME), coined X-IGALME, 62 in order to blend finite element and meshfree methods. This approach yields some outstanding features, in particular the singularity-free property of X-IGALME regardless of the crack location within the mesh, which is a major issue in element-based extended approaches 63 Herein, we adopt XIGA to model fracturing in a fully saturated porous media.…”

An extended isogeometric collocation method for fracture analysis

“…It is noted that the term extended FEA is adopted to encompass a wider family, including extended isogeometric FEA. 16,17,[31][32][33] Where used, the eXtended Finite Element Method (XFEM) denotes extended FEA that adopts Lagrange polynomials as the set of basis functions. [34][35][36] Therefore, we strictly avoid using these terms interchangeably.…”

Floating Isogeometric Analysis

“…The efficiency and stability of mesh-based computations and the flexibility of meshless methods have motivated some hybrid approaches, aiming to benefit from the complementing advantages of both settings, see e.g. [13][14][15][16][17].…”