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Theory of Plasticity

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Course Unit Code330-0504/01
Number of ECTS Credits Allocated4 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *Second Cycle
Year of Study *Second Year
Semester when the Course Unit is deliveredWinter Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
HAL22prof. Ing. Radim Halama, Ph.D.
Summary
Plasticity theory is focused to theory and practice using of material loading beyond yield limit. Plasticity theory summarized basic knowledge of physics of materials, testing of materials, testing devices etc.
Learning Outcomes of the Course Unit
To teach students the basic procedures for solving some technical problems of the continuum mechanics. To ensure understanding of such teaching problems. To learn our students to apply of theoretical knowledge in praxis.
Course Contents
Plasticity theory is focused to theory and practice using of material loading beyond yeld limit. Plasticity theory summarized basic knowledge of physics of materials, testing of materials, testing devices etc.

Outline:
1 – Tensile test, axial strain, axial stress, true stress and true strain calculation. Additivity of logarithmic strain. Evaluation of tensile test. Proof yield stress, ductility, Poisson’s ratio.
2 – Approximation of static stress/strain curve for analytical calculations. Ideally plastic material, Ramberg – Osgood equation, bilinear material model. Application of least square method for constant determination in constitutive relations.
3 – Analytical solution: Truss structures loaded in plastic domain. Solution of beams in plastic domain. Plastic bending modulus for rectangular cross-section. Plastic hinge.
4 – Incremental theory of plasticity - additive rule, Hooke’s law for elastic strain under uniaxial and multiaxial loading. Incremental theory of plasticity – yield condition under uniaxial and multiaxial loading for ideally plastic material.
5 – Incremental theory of plasticity – isotropic hardening rule, kinematic hardening rule, loading criteria.
6 – Nonlinear isotropic hardening rule according to Voce and its combination with linear isotropic hardening rule in ANSYS. Bilinear kinematic hardening rule according to Prager and Ziegler.
7 – Nonlinear kinematic hardening rule according to Armstrong and Frederic.
8 – Nonlinear kinematic hardening rule according to Chaboche.
9 – Calibration of Armstrong-Frederic-type model based on data from static stress-strain curve. Stress-strain behaviour of ductile materials under cyclic loading. Calibration of Armstrong-Frederic-type model based on data from cyclic stress-strain curve and from a large uniaxial hysteresis loop.
10 – Algorithms for stress integration in elastoplasticity – explanation on uniaxial loading case, explicit and implicit methods.
11 – Algorithms for stress integration in elastoplasticity – radial return method for ideally plastic material under uniaxial loading case and under multiaxial loading case.
12 – Algorithms for stress integration in elastoplasticity – radial return method for material with mixed hardening,
Koabyashi-Ohno algorithm under uniaxial loading case.
13 – Algorithms for stress integration in elastoplasticity – radial return method for material with mixed hardening,
Koabyashi-Ohno algorithm under multiaxial loading case.
14 – Newton-Raphson method and its modifications. Tangent stiffness modulus influence on the convergence of the N-R method. Consistent tangent modulus.
Recommended or Required Reading
Required Reading:
[1] Ottosen, N.S., Ristinmaa, M. The mechanics of Constitutive Modeling. Elsevier Amsterdam – Oxford – New York – Tokyo 2005, p.745. ISBN 0-080-44606-X.
[2] Chakrabarty, J. Applied Plasticity. Second Edition. Springer New York 2010, p.755. ISBN 978-0-387-77673-6.
[1] Pešina, E. Základy užité teorie plasticity, SNTL / SVTL Praha, 1966.
[2] Kuliš, Z. Plasticita a creep, skriptum ČVUT FS Praha, 1986.
[3] Veles, P. Mechanické vlastnosti kovov a ich skúšanie, ALFA, 1979.
[4] Halama, R. Teorie plasticity – sylabus katedry aplikované mechaniky, VŠB-TU Ostrava.
Recommended Reading:
[1] COTTRELL, A.H.: The Mechanical Properties of Materials. John Wiley and Sons, New York, 1964, 423p.
[2] SZCZEPAŃSKI, W.: Experimental Methods in Mechanics of Solids. Elsevier Amsterdam – Oxford – New York – Tokyo, 1990, ISBN 83-01-08259-3
[1] Němec, J., Dvořák, J., Hoschl, C. Pružnost a pevnost ve strojírenství,
Technický průvodce 69, SNTL Praha, 1989
[2] Kratochvíl, P., Lukáč, P., Sprušil, B. Úvod do fyziky kovů I, SNTL / ALFA Praha 1984
[3] Fuxa, J. Teorie plasticity – sylabus katedry pružnosti a pevnosti, VŠB-TU Ostrava
Planned learning activities and teaching methods
Lectures, Tutorials
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Credit and ExaminationCredit and Examination100 (100)51
        CreditCredit35 20
        ExaminationExamination65 16