330-0542/01 – Theory of Plasticity (TP)

Gurantor departmentDepartment of Applied MechanicsCredits4
Subject guarantorprof. Ing. Radim Halama, Ph.D.Subject version guarantorprof. Ing. Radim Halama, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semestersummer
Study languageCzech
Year of introduction2021/2022Year of cancellation
Intended for the facultiesFSIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
HAL22 prof. Ing. Radim Halama, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Part-time Credit and Examination 16+0

Subject aims expressed by acquired skills and competences

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.

Teaching methods

Lectures
Tutorials

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.

Compulsory literature:

[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.

Recommended literature:

[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

Way of continuous check of knowledge in the course of semester

Test, example solutions, combined exam.

E-learning

ne

Other requirements

The student prepare individual account on selected topic

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

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.

Conditions for subject completion

Part-time form (validity from: 2021/2022 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 35  20
        Examination Examination 65  25
Mandatory attendence parzicipation: Zápočet a zkouška

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2023/2024 (N0715A270033) Applied Mechanics MPT P Czech Ostrava 1 Compulsory study plan
2023/2024 (N0715A270033) Applied Mechanics MPT K Czech Ostrava 1 Compulsory study plan
2022/2023 (N0715A270033) Applied Mechanics MPT K Czech Ostrava 1 Compulsory study plan
2022/2023 (N0715A270033) Applied Mechanics MPT P Czech Ostrava 1 Compulsory study plan
2021/2022 (N0715A270033) Applied Mechanics MPT P Czech Ostrava 1 Compulsory study plan
2021/2022 (N0715A270033) Applied Mechanics MPT K Czech Ostrava 1 Compulsory study plan
2020/2021 (N0715A270033) Applied Mechanics MPT P Czech Ostrava 1 Compulsory study plan
2020/2021 (N0715A270033) Applied Mechanics MPT K Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner