Non-conforming multipatches for NURBS-based finite element analysis of higher-order phase-field models for brittle fracture

TL;DR

This paper introduces a NURBS-based isogeometric method with a non-conforming mesh and a novel VUKIMS technique for efficient higher-order phase-field modeling of brittle fracture, reducing computational cost and complexity.

Contribution

It presents the VUKIMS method for local mesh refinement in multi-patch NURBS models, enhancing efficiency and simplicity in phase-field fracture simulations.

Findings

VUKIMS reduces variable numbers compared to other local refinement methods.

Cubic NURBS elements balance accuracy and computational cost effectively.

The approach handles complex crack patterns with high precision.

Abstract

This paper proposes an effective computational tool for brittle crack propagation problems based on a combination of a higher-order phase-field model and a non-conforming mesh using a NURBS-based isogeometric approach. This combination, as demonstrated in this paper, is of great benefit in reducing the computational cost of using a local refinement mesh and a higher-order phase-field, which needs higher derivatives of basis functions. Compared with other approaches using a local refinement mesh, the Virtual Uncommon-Knot-Inserted Master-Slave (VUKIMS) method presented here is not only simple to implement but can also reduce the variable numbers. VUKIMS is an outstanding choice in order to establish a local refinement mesh, i.e. a non-conforming mesh, in a multi-patch problem. A phase-field model is an efficient approach for various complicated crack patterns, including those with or without an initial crack path, curved cracks, crack coalescence, and crack propagation through holes. The paper demonstrates that cubic NURBS elements are ideal for balancing the computational cost and the accuracy because they can produce accurate solutions by utilising a lower degree of freedom number than an extremely fine mesh of first-order B-spline elements.