Jan Burczak: Continuum Mechanics

  • Lecturer: Jan Burczak
  • Date: Wednesday 9:15 - 10:45 and Friday 9:15 - 10:45
  • Room: Leipzig University, Augusteum, room A-314
  • Language: English
  • Target audience: MSc students, PhD students, Postdocs
  • Prerequisites: Only general acquaintance with basic notions of linear algebra and calculus will be needed to follow the lecture, and they will be recalled and systemised at the beginning. The course is in English. The requirements to pass will not go much beyond solving a few exercises or presenting a small piece of theory.
  • Reading list: see MPI MiS owncloud

Abstract

Continuum mechanics models behaviour of continuous materials: fluids (water, air) and solids, when forces (or displacements) act upon them. This course presents basics of mathematical theory of mechanics of continua, with a slight bias towards fluid mechanics in the second part of the semester. Depending on the lecture's pace and interests of the audience, we may take a few excursions into continuum thermodynamics or turbulence theory (marked by (*) in the outline below).
The course will be provided as 3 lectures per 1 tutorial (3+1) approximately.

Outline

Part I: General Theory

  1. Preliminaries: Vector and tensor algebra and analysis.
  2. Kinematics: Continuous body, reference con guration, deformation, displacement, motion, trajectories. Strain and stress. Rate quantities. Lagrange criterion and Reynolds theorem.
  3. First mechanical and thermodynamical principles: balance laws, frame indifference, stresses and (*) entropy. Nonsmooth case.
  4. Case-specification: constitutive relations.

Part II: Examples of specific theories

  1. (*) Rigid heat conductors: Coleman-Noll Procedure. Fourier's Law.
  2. Elastic solids: Linear elasticity, Hooke's Law.
  3. Compressible and incompressible ows: Navier-Stokes and Euler equations.

Part III: Turbulence in fluids

Regular Lectures (Summer 2019)

07.05.2019, 09:16