Continuum Mechanics (SoSe 2023)
- Lecturers
- Prof. Dr. Klaus Hackl
- Course id, hours/week, CP
- 126502, 4 h/week, 6 CP
- Frequency of occurrence
- every summerterm
- Study programmes
- MSc-CE, MSc-MB
- Time/place
- Tue 08:00 - 10:00 h, IC 04-410
Thu 14:00 - 16:00 h, IC 03-112
- For the first time
- Tue, 04.04.2023
- Examinations
- Written exam, 120 minutes
- Next exam date:
- Please note the announcement of the examination office
Content
The course starts with an introduction to the advanced analytical techniques of linear elasticity theory, then moves on to the continuum-mechanical concepts of the nonlinear elasticity and ends with the discussion of material instabilities and microstructures. Numerous examples and applications will be given.
- Advanced Linear Elasticity
- Beltrami equation
- Navier equation
- stress-functions
- scalar- and vector potentials
- Galerkin-vector
- Love-function
- solution of Papkovich - Neuber
- Nonlinear Deformation
- Strain tensor
- Polar descomposition
- stress-tensors
- equilibrium
- strain-rates
- Nonlinear Elastic Materials
- Covariance and isotropy
- Hyperelastic materials
- constrained materials
- Hypoelastic materials
- objective rates
- material stability
- microstructures
References and reading assignments
Non-Linear Elastic Deformations

R.W. Ogden
Paperback - 544 pages (June 1997)
Dover Publications, Inc.;
ISBN: 0486696480
Mathematical foundations of elasticity

J.E. Marsden, T.J.R. Hughes,
Dover,
ISBN 0-486-67865-2
Nonlinear solid mechanics

G.A. Holzapfel
ISBN 0-471-82319-8
Elasticity

Pei Chi Chou, Nicholas J. Pagano,
Paperback - 290 pages - Reprint (20 June 1997)
Dover Publications, Inc.;
ISBN: 0486669580
External Links:
p>From MathWorld--A Wolfram Web Resource:
http://mathworld.wolfram.com/LegendrePolynomial.html
http://mathworld.wolfram.com/SphericalHarmonic.html
http://mathworld.wolfram.com/BesselFunctionoftheFirstKind.html
http://mathworld.wolfram.com/BesselFunctionoftheSecondKind.html
http://mathworld.wolfram.com/HankelFunction.html