Browsing by Author "Van der Merwe, Carel Wagener"

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    A peridynamic model for sleeved hydraulic fracture
    (Stellenbosch : Stellenbosch University, 2014-12) Van der Merwe, Carel Wagener; Turner, Dan Z.; Strasheim, J. A. vB.; Stellenbosch University. Faculty of Engineering. Department of Civil Engineering.
    ENGLISH ABSTRACT: Current numerical methods in the eld of hydraulic fracturing are based mainly on continuum methods, such as the Finite Element Method (FEM) and the Boundary Element Method (BEM). These methods are governed by Linear Elastic Fracture Mechanics (LEFM) criteria, which su er from the inherent aw of a non-physical stress representation at the fracture tip. In response to this, a non-local method is proposed, namely the peridynamic theory, to model sleeved hydraulic fracture. A 2D implicit quasi-static ordinary state based peridynamic formulation is implemented on various benchmark problems, to verify the ability to capture constitutive behaviour in a linear elastic solid, as well as, the quanti cation of adverse e ects on the accuracy of the displacement solution, due to the nature of the non-local theory. Benchmark tests consist of a plate in tension, where convergence to the classical displacement solution, non-uniform re nement and varying cell sizes are tested, as well as, a thick walled cylinder with internal pressure, where three di erent loading techniques are tested. The most accurate loading technique is applied to the sleeved fracture model, in order to simulate fracture initiation and propagation. This model is then veri ed and validated by using the Rummel & Winter hydraulic fracturing model and experimental results, respectively. Displacement error minimisation methods are implemented and as a result, the displacement solutions for a plate in tension converges to the analytical solution, while the thick walled cylinder solutions su er from inaccuracies due to an applied load on an irregularly discretized region. The fracture initiation test captures the fracture tip behaviour of the Rummel & Winter model and the fracture propagation test show good correlation with experimental results. This research shows that the peridynamic approach to sleeved hydraulic fracture can yield a realistic representation of fracture initiation and propagation, however, further research is needed in the area of a pressure load application on a solid using the peridynamic approach.