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Abstract
Introduction to statistical mechanics applied to elasticity for engineers. Treatment of polymers and crystalline solids, notions of ensembles, phase spaces, partitions functions, derivation of constitutive relations, polymer chain statistics, polymer networks, harmonic and quasi-harmonic crystalline solids, limitations of classical methods and quantum mechanical influences.
Objective
To provide a modern introduction to the application of statistical mechanics to the determination of constitutive relations for elastic solids.
Content
Topics and Description 1 Overview of thermo-elasticity from the continuum viewpoint. 2 Concepts of state functions in thermo-mechanics. 3 Introduction to Hamiltonian mechanics. 4 Statistics in statistical mechanics, Phase functions and time av- erages. 5 Phase space dynamics of isolated systems, weakly interacting systems. 6 Canonical distributions. 7 Concepts of temperature, local equilibrium processes, phase functions for generalized forces. 8 First and second laws of thermodynamics. 9 Partition function relations, continuum formulations of nonuni- form processes. 10 Equipartition and alternative definitions of entropy, applications to gases. 11 Crystal elasticity, Bravais lattices, harmonic and quasi-harmonic approximations to crystals. 12 Rubber elasticity of single chains and networks. 13 Quantum mechanical influences on elasticity.
Resources
Literature
Statistical Mechanics of Elasticity, J.H. Weiner, Dover press, 2002 (or wiley Press 1983)
General Information
- Language
- English (lecture), German (exercise)
- Levels
- MSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- oral 30 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture |
Statistical Mechanics of Elasticity
Does not take place this semester.
|
No time listed | 2 h weekly |
| exercise |
Statistical Mechanics of Elasticity
Does not take place this semester.
|
No time listed | 1 h weekly |
Offered In
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Application Area (only necessary for the Master degree in Applied Mathematics)
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