Plasticity 1

The course is not on the list Without time-table
Code Completion Credits Range
14PLAS1 Z,ZK 3 2+0
Department of Materials

The course represents an introduction to plasticity in terms of continuum mechanics. The first part contains a general incremental theory: yield criteria, strain hardening, criterion for local loading and unloading, plastic potential, flow rule and corresponding physical equations. The second part represents a logical descent to the practical engineering solution of simple problems on elastic-plastic tension, bending, torsion and plastic collapse of bars and beams.


Elastomechanics (14EME1)

Syllabus of lectures:

Formulation of the incremental problem of plasticity. 2. Experimental knowledge about plasticity. Cyclic plasticity and a low-cycle fatigue. 3. Decomposition of the stress tenzor. Stress deviator tensor. 4. Decomposition of the strain tensor. 5. Yield criteria and the yield surface in the stress space. 6. Elastic-perfectly plastic material, isotropic and kinematic hardening. Bauschinger's effect. 7. Loading surface and a criterion for loading and unloading. 8. Plastic potential and a flow rule. 9. Physical equations for material with isotropic work-hardening. Prandtl-Reus equations. 10. Physical equations for material with kinematic hardening (Prager's, Ziegler's and Mroz's models). 11. Continuity of the stress and strain, residual stresses and strains, deformation theory of plasticity, stress relaxation and a plastic strain concentration. 12. Elastic-plastic bending of straight beams. Plastic hinge and the fully plastic moment. 13. Bending under transverse loads. Plastic collapse od statically determinate and indeterminate beams. 14. Curved beams and frames. 15. Plastic torsion. Nadai's sand-hill analogy. 15. Thick-walled cylindrical pressure vessel. Autofrettage. 16. Thick-walled ball-shaped pressure vessel.

Syllabus of tutorials:
Study Objective:

Knowledge: Basic incremental theory of plasticity - terms, assumptions, formulations, physical relations between stress and strain increments, effects of plastic deformation. Connection between the incremental theory and conventional engineering concepts of elastic-plastic bars and beams.

Skills: Standard calculations of stresses and a maximum load capacity of plastically deformed bars and beams. Understanding of formulations and methods of solution in more general model problems of plasticity.

Study materials:

Key references:

[1] Oliva, V.: Plasticita 1. [Written materials for lectures P-KMAT-806/10]. Praha, ČVUT-FJFI-KMAT 2010.

Recommended references:

[1] Plánička, F. - Kuliš, Z.: Základy teorie plasticity. [Univesrity textbook FSI]. Vydavatelství ČVUT, Praha, 2004.

[2] Servít, R. - Doležalová, E. - Crha, M.: Teorie pružnosti a plasticity I. SNTL/ALFA, Praha 1981.

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

Further information:
No time-table has been prepared for this course
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/predmet25040605.html