Isogeometric Phase-Field Methods for Modeling Fracture in Shell Structures

Abstract

The simulation of the fracture of engineering structures is a challenging topic that requires accurate and efficient numerical models. This thesis focuses on the modeling of brittle and ductile fracture in thin shell structures employing the phase-field approach. A rotation-free isogeometric Kirchhoff-Love shell model is therefore adopted and combined with brittle and ductile phase-field fracture for-mulations. For the modeling of complex structures, a penalty-based approach is employed for coupling the structural and phase-field behaviors in correspondence of patch interfaces. All the penalty parameters involved in the model are con-trolled by a single dimensionless penalty coefficient, independently of the type and setup of the problem. The efficiency of the solution algorithm is improved by adopting a predictor-corrector algorithm for adaptive local refinement of the mesh based on Locally Refined Non Rational B-Splines, an adaptive time-stepping scheme, and a strongly coupled staggered solution scheme for the solution of the nonlinear system of equations. The presented formulation is qualitatively and quantitatively evaluated through several numerical tests and validated against experimental benchmarks involving complex shell geometries, thus opening for the application of the model to real-world structures.