Linear elastic fracture mechanics via the Material Point Method: a phase field approach

Kakouris, Emmanouil G. (2019) Linear elastic fracture mechanics via the Material Point Method: a phase field approach. PhD thesis, University of Nottingham.

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Abstract

Fracture is one of the main failure mechanisms of materials and structural components. During the past thirty years, various methods have been introduced to simulate crack initiation and growth. These include the introduction of Element Deletion Method and re-meshing strategies within the standard Finite Element Method (FEM), cohesion based Finite Element strategies and the extended Finite Element Method. Very recently, a new method for crack propagation, namely the phase field method has been introduced; phase field models have been proven very robust in accurately predicting complex crack behavior while at the same time avoiding standard re-meshing or enriching techniques.

To this point, phase field modelling has extensively been applied within a Finite Element framework while very little research and applications have been demonstrated with particle methods. However, treating the crack propagation problem using a grid based method is a challenging and computationally taxing task. The reliability and robustness of the Finite Element Method and in general mesh-based methods depends on the quality of the mesh itself. In this work, the phase field method is re-formulated and treated using an attractive Particle-In-Cell (PIC) scheme, namely the Material Point Method (MPM). In this approach, the coupled continuum/phase field governing equations are defined at a set of material points and interpolated at the nodal points of an Eulerian, i.e. non-deforming, mesh. The accuracy of the simulated crack path is thus decoupled from the quality of the underlying Finite Element mesh and relieved from corresponding mesh distortion errors.

This framework is then generalized for the case of anisotropic brittle fracture by introducing an anisotropic crack density functional. The anisotropic crack density functional gives rise to a family of phase field models, both second and fourth order, able to address brittle fracture simulation in anisotropic media. The proposed method is further extended into dynamic brittle fracture using both isotropic and anisotropic phase field models. Frictional contact problems involving phase field fracture are also examined and their post-fracture contact response is investigated. On the proposed model, the local contact features are naturally handled using the Eulerian mesh and the damage evolution emerges without the need to numerically track discontinuities in the displacement field e.g. with jump and tip enrichment functions as well as complex crack paths can be obtained without any additional ad hoc rules. These advantages make the derived model a robust computational tool when arbitrary crack paths occur at impact-fracture problems.

Following, the proposed model is used to efficiently simulate crack paths induced from rocking response. The accuracy of the method is examined and verified based on existing analytical rocking response models; the method is then further extended into rocking system dynamics involving phase field fracture. Merits and drawbacks of the proposed formulation are examined using a set of benchmark tests. The influence of impact velocity, phase field and material point parameters on induced crack path is also examined. Validation based on experimental observations is also performed.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Triantafyllou, Savvas
Keywords: Dynamic fracture, Brittle fracture, Frictional contact, Anisotropy, Phase field, Material Point Method, Rocking
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Faculties/Schools: UK Campuses > Faculty of Engineering
Item ID: 56500
Depositing User: Kakouris, Emmanouil
Date Deposited: 22 Jul 2019 13:16
Last Modified: 06 May 2020 12:33
URI: http://eprints.nottingham.ac.uk/id/eprint/56500

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