Modul Math-Ma MKMECH
Table of contents
Mathematische Elastizitätstheorie (Modul MatH-Ma MKMECH)
This course is an introduction to elasticity theory. It covers topics concerned with modeling, as well as analytical aspects that invoke ideas and methods from the theory of linear and nonlinear partial differential equations and the calculus of variations.
Elasticity theory is one of the backbones of continuum mechanics (CM). CM seeks for a systematic understanding of the motion of matter (solid or fluid) under the influence of forces and based on the (modeling) assumption that matter is continuously distributed in space. The branch of elasticity theory is concerned with solid materials - more precisely, solids that deform under the influence of forces and recover their original shape when the force is removed.
This course starts with a brief presentation of the basic elements of CM (material bodies, kinetics, forces, balance laws, constitutive relations). We then focus on the subfield of elasticity theory and examine linear, nonlinear and variational models. In particular, we discuss different existence theories for the equilibrium problem in elastostatics. For this, we explain and apply various PDE techniques (weak formulation, Sobolev spaces, Lax Milgram, implicit function theorem) and methods from the calculus of variations (direct method, polyconvexity). If time permits, we address some advanced topics, e.g. the derivation of linear elasticity from nonlinear elasticity.
Course information
- Lecturer: Prof. Dr. Stefan Neukamm
- Time and place of the lecture:
Wed. 02.50 - 04.20 pm (5th double period), WIL A221
Fri. 01.00 - 02.30 pm (4th double period), WIL A124
(tutorial is integrated) - Modul: Modul Math Ma MKMECH
- Literature:
- E. Gurtin, An introduction to continuum mechanics, Academic Press, 1981
- P. Ciarlet, Mathematical Elasticity Vol I, North-Holland
- C. Eck, H. Garcke, P. Knabner, Mathematishe Modellierung, Springer
- L.C. Evans, Partial Differential Equations, AMS Graduate Studies in Mathematics
- Language: English and/or German.
- Prerequisites: Recommended is a basic knowledge in PDE theory and in functional analysis.
Course material
- lecture notes (Feb 15th 2015)
- slides of lecture 1
- problem sheets with solution