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Nonlinear finite element analysis of quasi-brittle materials

Alnaas, Waled 2016. Nonlinear finite element analysis of quasi-brittle materials. PhD Thesis, Cardiff University.
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Abstract

The development of robust solution schemes for the nonlinear finite element analysis of quasi-brittle materials has been a challenging undertaking, due mainly to the stability and convergence difficulties associated with strain-softening materials. The work described in this thesis addresses this issue by proposing a new method for improving the robustness and convergence characteristics of a finite element damage model. In this method, a smooth unloading-reloading function is employed to compute an approximate tangent matrix in an incremental iterative Newton type solution procedure. The new method is named ‘the smooth unloading-reloading’ (SUR) method. A range of examples, based on a set of idealised quasi-brittle specimens, are used to assess the performance of the SUR method. The results from these example analyses show that the proposed approach is numerically robust, effective and results in considerable savings relative to solutions obtained with a reference secant model. Three acceleration approaches are also proposed in this thesis to further improve the convergence properties of the new SUR method. The first acceleration approach, named ‘the predictive-SUR method’, predicts a converged value of a damage evolution variable using an extrapolation in semi-log space. The second proposed method is designated ‘the fixing approach’, in which a damage evolution parameter is updated from the last converged step in Stage-1 iterations and then fixed in Stage-2 iterations. The third acceleration technique employs ‘a slack tolerance’ at key stages in a computation. The improvement of the convergence properties of the SUR method, when the proposed acceleration approaches are introduced, is illustrated using a series of example computations based on the analysis of a range of plain and reinforced concrete structural elements. In addition, a new element with an embedded strong discontinuity is proposed for simulating cracks in quasi-brittle structures. The new formulation is applied to quadrilateral elements and exploited to simulate mode-I, mode-II and mixed mode fracture. The interface element approach and the smeared crack approach are used as reference methods. The results from a series of examples show that the new proposed embedded strong discontinuity approach is both effective and accurate.

Item Type: Thesis (PhD)
Date Type: Publication
Status: Unpublished
Schools: Engineering
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Uncontrolled Keywords: Damage; Non-linear Finite Element Analysis; Quasi-Brittle Materials; Constitutive Model; Strong Discontinuity; Concrete.
Date of First Compliant Deposit: 3 August 2016
Last Modified: 05 Jun 2017 05:38
URI: http://orca-mwe.cf.ac.uk/id/eprint/93465

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