Crack propagation analysis using Phase-Field model in the framework of Isogeometric analysis and Finite Cell Method

Crack propagation analysis using Phase-Field model in the framework of Isogeometric analysis and Finite Cell Method

Pundir, M.

Turteltaub, S.R. (mentor)

Aerospace Engineering

Aerospace Structures & Materials

2016-05-31

Fracture mechanics based computational methods are becoming increasingly important to study the structural integrity and failure of materials and structures used in engineering applications. One challenging aspect for computational methods is the analysis of crack nucleation and propagation in complex geometries or in materials with inhomogeneities at microstructural level as found in composite materials. To address this challenge, the present work combines three key ingredients namely, (i) the Finite Cell Method (FCM), (ii) Isogeometric Analysis (IgA) and (iii) Phase-Field model. The Finite Cell Method (FCM) has emerged as a promising computational method in order to simplify the modelling of complex geometries. FCM combined with a higher-order finite element method such as IgA has been implemented in numerous field of structural analysis. Within this context, the IgA-FCM framework isi extended to fracture mechanics through incorporation of a Phase-Field model. Phase-Field model, based on variational formulation of a brittle fracture, is used to study the nucleation and the propagation of cracks around voids and inclusions under quasi-static conditions. The ability of Phase-Field model to reconstruct fracture mechanics problems as coupled partial differential equations makes it easy to implement in the IgA-FCM framework. Due to the computationally demanding nature of the Phase-Field model, hierarchical sub-division of Non-Uniform Rational B-spline (NURBs) basis functions is implemented to achieve local refinement in IgA framework. A novel algorithm to implement hierarchical refinement in IgA-FCM framework is presented which is capable of simultaneously implementing element-based local refinement for stable crack propagation as well as Gauss Quadrature based local refinement for better integration around voids and material interfaces. For establishing the feasibility of IgA-FCM in Phase-field modelling, numerous numerical simulations such as crack nucleation around voids, inclusions and crack propagation in presence of voids, soft and hard inclusions were performed for two-dimensional cases. For relatively simple numerical cases considered in this project, modelling of voids and inclusions as fictitious domain resulted in expected crack behaviour such as crack nucleation at high stress location, curvilinear crack influenced by varying stress state in presence of inclusions. With these numerical simulations, it is shown that the IgA-FCM-Phase-Field framework can be effectively applied for fracture mechanics problems involving complex features.

fracture mechanics
isogeometric analysis
phase-field model
finite-cell method
finite element analysis
voids
inclusions
crack

http://resolver.tudelft.nl/uuid:d8b5b782-b329-464d-9210-89bb30494167

Student theses

master thesis

(c) 2016 Pundir, M.