Login to KOS for course enrollment Display time-table
Code Completion Credits Range Language
14PLA Z,ZK 3 2P+1C Czech
Vladislav Oliva (guarantor), Aleš Materna
Vladislav Oliva (guarantor), Aleš Materna
Department of Materials


Introduction to plasticity of materials and structures in terms of classical continuum mechanics. The first part contains the general incremental theory: yield criteria, strain hardening, loading criterion, flow rule and corresponding physical equations including the deformation theory. Then engineering solutions of elastic-plastic tension, bending, torsion and plastic collapse of bars, beams and pressure vessels are presented. The second part is devoted to methods and knowledge useful for material science: stress concentration and plastic deformation around notches and cracks, limit theorems and their applications to estimation of the plastic collapse, localization of plastic deformation before the fracture, differences between plasticity in plane stress and strain, elastic-plastic response to cyclic load.

Syllabus of lectures:


1. Experimental and physical knowledge about plasticity. Elastic-plastic continuum.

2. Incremental theory of plasticity. Yield criteria, strain hardening, loading surface, loading criterion, physical equations.

3. Deformation theory of plasticity.

4. Continuity of the stress and strain, Residual stress and strain.

5. Elastic-plastic bending of straight beams. Plastic hinge and fully plastic moment.

6. Plastic collapse of statically determinate and indeterminate beams, curved beam and frame.

7. Elastic-plastic torsion. Nádai's sand-hill analogy.

8. Thick-walled cylindrical pressure vessel. Autofrettage.

9. Thick-walled ball-shaped pressure vessel. Plastic zone around a ball-shaped cavity.

10. Stress concentration in the plastic zone ahead a notch. Plastic zone in front of the crack tip.

11. Principle of virtual work, limit analysis and applications - bar with a hole, notched beam, punch indentation

12. Limit analysis for structural parts.

13. Localization of plastic deformation before fracture. Bridgman’s stress.

14. Bounds of elastic-plastic analysis and a transition to the brittle fracture.

15. Gourson's model of a ductile fracture.

16. Cyclic plasticity: elastic and plastic shakedown, ratchetting, high-cycle or low-cycle fatigue.

17. Cyclic plastic deformation in front of fatigue crack

18. Alternative strain hardening models for cyclic loading.


Plastic deformation, incremental theory of plasticity, deformation theory of plasticity, pressure vessels, elastic-plastic bending, elastic-plastic torsion, elastic-plastic beams, plastic zone in front of notches and cracks, lower and upper bound theorems, plastic hinge ,plastic collapse, localization of plastic deformation, cyclic plasticity.

Syllabus of tutorials:
Study Objective:
Study materials:

Key references:

[1] Oliva, V.: Plasticity [Lecture presentations]. Praha, ČVUT-FJFI-KMAT, 2016.

[2] Dixit, P. M.; Dixit, U. S.: Plasticity: Fundamentals and Applications. CRC Press, 2015, ISBN 9781138074965

[3] Chakrabarty, J.: Theory of Plasticity, 3rd Edition, Elsevier, 2006, ISBN: 9780750666381

Recommended references:

[1] Chen, W. F.; Han, D. J.: Plasticity for Structural Engineers. J. Ross Publishing, New York, 2007,

IBSN 978-1-932159-75-2

Time-table for winter semester 2021/2022:
Time-table is not available yet
Time-table for summer semester 2021/2022:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2022-08-07
For updated information see http://bilakniha.cvut.cz/en/predmet6224306.html