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Mechanics of Materials

Credits 4
Hours per week 2 / 1 / 0
Examination Ex
Study Language English
Level Master subject
Guarantor prof. Dr. Dipl. Min. Willi Pabst


This course provides a self-contained and consistent overview of the mechanical and thermomechanical properties of materials, based on the theory of rational mechanics and thermomechanics. The presentation of the topics is based on the exact theory of continua and requires from the student the ability to follow tensor formalism. Apart from standard topics this course contains recent developments in the field of materials mechanics, and tries to correct some of the errors and misconceptions in the common textbook literature. The course is appropriate for students of all subjects.


1. Introduction: balance equations of mechanics and thermomechanics, tensors, principal values, invariants, Cayley-Hamilton theorem
2. Constitutive theory: constitutive principles, deformation function, deformation gradient, deformation and strain tensors, stress tensors
3. Linear elasticity of anisotropic solids, nonlinear elasticity of isotropic solids, viscosity of non-Newtonian fluids
4. Linear elasticity of isotropic solids (uniaxial tension, simple shear, isotropic deformation), definition of elastic constants, auxetic materials
5. Linear thermoelasticity of solids and fluids (stress, heat flux, energy, entropy), isothermal and adiabatic elastic constants
6. Equations of state, principles of atomistic modeling of elastic and thermoelastic properties; property values for metals, ceramics, glasses and polymers
7. Effective elastic, thermoelastic and thermal properties of dense polycrystalline materials; measurement of elastic, thermoelastic and thermal properties
8. Temperature dependence of elastic, thermoelastic and thermal properties; high-temperature behavior of materials
9. Basic fracture mechanics: plane elasticity, stress intensity factor, fracture criteria, plastic zone, fatigue, lifetime, elastoplastic behavior
10. Testing of mechanical properties: strength, Weibull statistics, hardness, fracture toughness; temperature and grain size dependence of properties
11. Effective properties of heterogeneous materials I: Rigorous micromechanical bounds
12. Effective properties of heterogeneous materials II: Model relations for composites
13. Effective properties of heterogeneous materials III: Model relations for porous materials
14. Rheology: Viscous, viscoplastic and viscoelastic material behavior, damping


R - Haupt P.: Continuum Mechanics and Theory of Materials. Springer, Berlin 2000. (ISBN 3-540-66114-X).
R - Billington E. W., Tate A.: The Physics of Deformation and Flow. McGraw Hill, New York 1981. (ISBN 0-07-005285-9).
R - Green D.J.: An Introduction to the Mechanical Properties of Ceramics. Cambridge University Press , Cambridge 1998. (ISBN 0-521-59913-X).
R - Menčík J.: Pevnost a lom skla a keramiky. SNTL, Praha 1990. (ISBN 80-03-00205-2).
R - Pabst W., Gregorová E.: Effective elastic moduli of alumina, zirconia and alumina-zirconia composite ceramics, pp. 31-100 in Caruta B.M. (ed.): Ceramics and Composite Materials � New Research. Nova Science, New York 2006. (ISBN 1-59454-370-4).
A - Torquato S.: Random Heterogeneous Materials - Microstructure and Macrosopic Properties. Springer, New York 2002.
A - Menčík J.: Strength and Fracture of Glass and Ceramics. Elsevier, Amsterdam 1992. (ISBN 0-444-98685-5).
A - Pabst W., Gregorová E.: Effective thermal and thermoelastic properties of alumina, zirconia and alumina-zirconia composite ceramics, pp. 77-138 in Caruta B.M. (ed.): New Developments in Materials Science Research. Nova Science, New York 2007. (ISBN 1-59454-854-4).

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