Higher-order discontinuous modelling of fracturing in quasi-brittle materials

Kourepinis, Dimitrios (2008) Higher-order discontinuous modelling of fracturing in quasi-brittle materials. PhD thesis, University of Glasgow.

Abstract

Quasi-brittle failure is characterised by material degradation, fracturing and potential interaction of fragmented parts. The computational description of this behaviour has presented significant challenges to the mechanics community over the past few decades, driven by the development of technology, the increasing social and economical constraints for safer and more complicated engineering designs and consequently by the increasing requirements for more accurate understanding of macro- and micro-structural processes.

Finite element methods have been pushed to their limits in an attempt to resolve strain localisation and ultimately fracturing in a unified and objective manner, while discrete methods have been utilised by artificial connection of discrete bodies which are identified a priori to act as continua. Neither of these attempts comprises a diritta via for modelling the transition from continuum to discontinuum efficiently and this has led to the investigation of alternative techniques.

Herein, the numerical modelling of quasi-brittle localisation and fracturing is investigated using the Numerical Manifold Method (NMM) as an alternative unifying framework to industry-established techniques such as the Finite Element Method (FEM) and Discrete Element Method (DEM). One of the particularly interesting aspects of NMM is with respect to its potential for modelling both continuum and discontinuum states and providing an efficient framework for modelling the entire transition between continuum to discontinuum, from a continuum point of view, without remeshing. The attractive nature of this capability advocates potential for modelling mechanics of materials such as concrete, rock and masonry, but also a more general class of quasi-brittle materials.

This work investigates and extends NMM primarily with respect to the following characteristics:

1. Discontinuities, such as cracks, are introduced naturally in a discrete manner, but in a continuum setting, without the need for remeshing
2. The approximation is improved globally or locally, for any arbitrary level, without remeshing
3. Integration is undertaken explicitly, for any arbitrary level of local improvement of the approximation

Furthermore, NMM is reformulated using a constrained variational approach for generalised three-dimensional problems. Essential boundary conditions are enforced using Lagrange multipliers and projection matrices and potential higher-order boundary issues are investigated. The developments are implemented algorithmically in MATLAB and higher-order enrichment is demonstrated with the use of adaptivity.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Keywords: Higher-order, discontinuous, fracturing, quasi-brittle, concrete, modelling, analysis, Numerical Manifold Method.
• Subjects: T Technology > TA Engineering (General). Civil engineering (General); Q Science > Q Science (General)
• Colleges/Schools: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Supervisor's Name: Pearce, Dr. Chris
• Date of Award: 2008
• Depositing User: Dr Dimitrios Kourepinis
• Unique ID: glathesis:2008-370
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 09 Sep 2008
• Last Modified: 10 Dec 2012 13:18
• URI: https://theses.gla.ac.uk/id/eprint/370