Continuum Mechanics - 8EC

Prerequisites

Prerequisites include a basic knowledge of linear algebra, multivariate calculus, and differential equations. The course is self-contained and the overlap with similar master courses in TU Delft and TU Eindhoven is minimal.

Aim

The aim of this course is to teach mathematics students the basic idea, concepts, and philosophy of modelling in the continuum world.
Description

Continuum mechanics revolves around the combination of balance laws on one side and constitutive laws on the other. At the end of the course, the student will be well versed in the classical balance laws for mass, momentum, and energy, and the accompanying concepts of work and power; the student will be familiar with the constitutive laws for elastic, viscous, and visco-elastic materials. Many examples will be discussed, and the student will be able to apply these concepts in the modelling of an actual situation.

Describing the motion of a system: geometry and kinematics. The concept of mass and fundamental laws of dynamics. The Cauchy stress tensor and the Piola-Kirchhoff tensor. Real and virtual powers. Deformation tensor, deformation rate tensor. Energy equations and shock equations. General properties of Newtonian fluids. Inviscid flows. Viscous flows. Coupled systems (thermohydraulics, chemotaxis, combustion). Equations of the atmosphere and the ocean. General equations of linear elasticity. Classical problems of elastostatics. Wave propagation in mechanical systems. The lectures will intensively rely on chapters form [2]. We recommend [1] as additional reading material.

Rules about Homework / Exam

The final grade is determined by an oral examnination

    Lecture Notes / Literature

    [1] M.H. Sadd. Elasticity: Theory, Applications, and Numerics. Elsevier, New York, Amsterdam 2005.

    [2] R.M. Temam and A.M. Miranville. Mathematical Modeling in Continuum Mechanics. Cambridge University Press, Cambridge, 2000.

    Lecturers

    M. Peletier (Tue) & J. Dubbeldam (TUD)