Computational framework for fracture in heterogeneous materials

Edwards, Graeme (2013) Computational framework for fracture in heterogeneous materials. PhD thesis, University of Glasgow.

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There has always been an ambition from Structural Engineers to design structures which are as efficient as possible, yet meet current design requirements. In the modern era, this process has relied heavily on the use of computational packages to carry out detailed analyses. However, for the design requirements to be met, the materials being used must be accurately understood and their behaviour must be accurately captured. In materials such as concrete, this understanding can be obtained by carrying out detailed analyses of the material at the mesoscale. At this scale, capturing the behaviour of concrete can be accomplished by recognising three distinct phases. First, the heterogeneities themselves, which are stiff particles usually made of crushed rock; second, we have the cement matrix which surrounds the heterogeneities and third, we have the weak interfacial transition zone (ITZ) between the two. By accurately describing the behaviour and interaction of these three phases, the complex behaviour of concrete can be captured.

This thesis brings together several novel contributions in order to create a computational modelling framework for modelling fracture in concrete at the mesoscale in three dimensions. All cracks are discrete in nature and restricted to element interfaces. As fracture can generally be considered to be a stress driven problem, an accurate description of the stress state in the model is essential. To achieve this, hybrid-Trefftz stress elements are used for
the bulk elements in the mesh. The hybrid-Trefftz stress elements are characterised by their separate approximations of the stresses over the element domain and the displacements over the element boundary, allowing for a much higher order of approximation for the stresses to be utilised. The discrete cracks are modelled using continuous interface elements to allow the non-linear behaviour of concrete to be captured. The initiation and evolution of cracks was modelled using a plasticity model for the interface elements. This model followed the work of Winnicki and its implementation is presented in this thesis.

Unlike the conventional method of using interface elements, where they are present in the mesh from the start of the analysis, in this work, interface elements are inserted dynamically as and when the material yield criterion is violated. A crack insertion methodology is presented for the inclusion of discrete cracks along element boundaries in 3D. The procedure takes advantage of properties of the hybrid-Trefftz stress elements to aid in its implementation. In particular, due to displacement continuity being enforced in the weak sense, faces of the same tetrahedron can be considered to be independent from each other but still produce statically admissible results. Results are presented showing that this methodology works well for different topological scenarios.

To generate an accurate geometric representation of the mesostructure, a method called the Maximum Level Set method was developed. For a given geometry, this method generated
the mesostructure by placing aggregates within the domain at a maximum distance from both the boundary of the specimen and existing particles in a sequential manner. A Level Set
function is used to calculate these distances and is updated as each sequential particle was added. This procedure is compared to the standard Random Sequential Addition method,
used throughout the literature, and shows favourable results both in terms of computational cost and the suitability of the geometry for use in the creation of finite element meshes.

Finally, the application of the overall framework to realistic problems is presented. The procedure for carrying out an entire load step using a standard Newton-Rhapson procedure is outlined and the determination of the parameters used in the constitutive law is presented. Preliminary results are that demonstrated the performance of the overall framework. In these results, the softening of concrete due to fracture was captured.

Item Type: Thesis (PhD)
Qualification Level: Doctoral
Keywords: hybrid-Trefftz, fracture, concrete, mesoscale, cracking, Maximum Level Set method, non-linear analysis, computational mechanics
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Colleges/Schools: College of Science and Engineering > School of Engineering > Infrastructure and Environment
Supervisor's Name: Pearce, Professor Chris and Lukasz, Doctor Kaczmarcyzk
Date of Award: 2013
Depositing User: Mr Graeme Edwards
Unique ID: glathesis:2013-4690
Copyright: Copyright of this thesis is held by the author.
Date Deposited: 08 Nov 2013 09:36
Last Modified: 08 Jan 2014 14:49

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