# 651-4003-00L Numerical Modelling of Rock Deformation

Semester | Autumn Semester 2016 |

Lecturers | M. Frehner |

Periodicity | yearly recurring course |

Language of instruction | English |

Abstract | Introduction to the programming software Matlab. Learning and understanding the continuum mechanics equations describing rock deformation. Mathematical equations describing rock rheology: elasticity + viscosity. Introduction to the finite-element method for modeling rock deformation in 2D. A small applied project-work at the end of the semester will be tailored to the student's interest. |

Objective | At the end of this course, the students should be able to - Use Matlab for their future needs (e.g., for their MSc Thesis) - Understand the fundamental concept of the finite-element method - Apply the finite-element method to successfully work on a small project tailored to the student's interests. In addition, innovative methods will be applied to mark the performance in the course, which includes self-evaluation and peer-evaluation among the students. Therefore, some soft-skills will be required and trained as well, such as - honest self-evaluation and self-grading - providing honest feedback to a colleague in a tone that is acceptable - receiving feedback from a colleague without taking criticism personal - learning the procedure of scientific peer-evaluation |

Content | Introduction to Matlab Continuum mechanics equations necessary to describe rock deformation Rheological equations: elasticity + viscous materials Introduction to the finite-element method (in 1D) Numerical integration + isoparametric elements Going to 2D finite elements Finite-element method for 2D elasticity Stress calculation + visualization Finite-element method for 2D viscous materials Heterogeneous media Final project-based work tailored to the student's interest. A substantial part of the lecture will take place in the computer-lab, where numerical finite element codes will be applied. The used software is Matlab. Students may bring their own laptop with a pre-installed copy of Matlab. |

Lecture notes | The script is very diverse and ranges from PowerPoint-based pdf-files, to self-study tutorials. Also, the more theoretical and mathematical aspects will be explained on the black board without a proper script. All lecture-presentations, as well as the numerical codes, will be made available to the students online. |

Literature | There is no mandatory literature. The following literature is recomended: Turcotte D.L. and Schubert G., 2002: Geodynamics, Cambridge University Press, ISBN 0-521-66624-4 Pollard D.D. and Fletcher R.C., 2005: Fundamentals of Structural Geology, Cambridge University Press, ISBN 978-0-521-83927-0 Ranalli G., 1995: Rheology of the Earth, Chapman & Hall, ISBN 0-412-54670-1 Smith I.M. and Griffiths D.V., 2004: Programming the Finite Element Method, John Wiley & Sons Ltd, ISBN 978-0-470-849-70-5 Zienkiewicz O.C. and Taylor R.L., 2000: The Finite Element Method - Volume 1: The Basis, Butterworth Heinemann, ISBN 0-7506-5049-4 |

Prerequisites / Notice | A good knowledge of linear algebra is expected. The used software is Matlab. So, knowledge of Matlab is advantageous. Students may bring their own laptop with a pre-installed copy of Matlab. |