SIAM Chapter Day
January 17th 2014, Cardiff University

Objectives

This one-day event is the second in an annual series which aims to provide a platform for discussions on current research on mathematical modelling, analysis, and simulation of problems in science and engineering.

Following the format of the very successful Cardiff SIAM Day 2013, doctoral students and postdoctoral researchers from across Cardiff University and their guests from other Universities are invited to showcase and communicate their recent results in the form of a poster accompanied by a title and a set of bullet points highlighting the core findings of their work.

Posters titles and highlights should be sent to siam@cardiff.ac.uk by January 10th, 2014.

Confirmed Guest Speakers

Prof Endre Suli (Mathematical Institute, University of Oxford) - President of UK & Republic of Ireland Section of SIAM (SIAM-UKIE) 

Talk: Adaptive Finite Element Approximation of a Variational Model of Fracture.

Abstract: The energy of the Francfort-Marigo model of brittle fracture can be approximated, in the sense of $\Gamma$-convergence, by the Ambrosio-Tortorelli functional. We formulate and analyse an adaptive finite element algorithm for the computation of its (local) minimisers. In the algorithm, we combine a Newton-type method with a residual-driven adaptive mesh refinement. We present theoretical results, which demonstrate convergence of the algorithm to local minimisers of the Ambrosio-Tortorelli functional. The talk is based on joint work with Siobhan Burke (University of Oxford)  and Christoph Ortner (University of Warwick).

Prof Andrew Fowler (University of Limerick, Ireland, and Mathematical Institute, University of Oxford)

Talk: The Origin of Drumlins.

Prof Chris Pearce (School of Engineering, University of Glasgow)


Talk: Numerical simulation of three-dimensional fracture propagation: theory, control of errors and robust implementation.

Abstract: This presentation will present a computational framework for quasi-static brittle fracture in three-dimensional solids. The presentation will focus on the theoretical basis for determining the initiation and direction of propagating cracks based on the concept of configurational mechanics, the control of numerical errors and the robust implementation of the proposed methodology within the Finite Element Method. Deformation of a cracked body is modelled within the spatial configuration, whereas evolution of the crack path is modelled within the material configuration (similar in concept to the Arbitrary Lagrangian Eulerian formulation). A particular challenge in solid mechanics is the modelling of propagating cracks by the FEM. This presentation will present a robust methodology whereby cracks are restricted to element faces and the mesh is adapted to align with the predicted crack direction. A local mesh improvement procedure is developed to maximise mesh quality in order to improve both accuracy and solution robustness and to remove the influence of the initial mesh on the direction of propagating cracks. An arc-length control technique is derived to enable the dissipative load path to be traced. A hierarchical hp-refinement strategy is implemented in order to improve both the approximation of displacements and crack geometry. The performance of this modelling approach is demonstrated on numerical examples that qualitatively illustrate its ability to predict complex crack paths. All problems are three-dimensional, including a torsion problem that results in the accurate prediction of a doubly-curved crack. The industrial context of this research will also be discussed in terms of its application to safety-critical structures.