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

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.

Automated summary

The extended approach blends isogeometric analysis and the first-order local maximum entropy for accurate parametrization and improved estimation, enforcing compatibility and eliminating discontinuity effects through techniques such as shifting and blending. Several examples demonstrate the viability, including straight and curved crack propagation.