Gurantor department | Department of Applied Mechanics | Credits | 4 |

Subject guarantor | doc. Ing. Radim Halama, Ph.D. | Subject version guarantor | doc. Ing. Radim Halama, Ph.D. |

Study level | undergraduate or graduate | Requirement | Choice-compulsory |

Year | 2 | Semester | winter |

Study language | Czech | ||

Year of introduction | 2015/2016 | Year of cancellation | |

Intended for the faculties | HGF, FS, USP | Intended for study types | Bachelor, Follow-up Master |

Instruction secured by | |||
---|---|---|---|

Login | Name | Tuitor | Teacher giving lectures |

PRZ031 | Ing. Jana Bartecká | ||

HAL22 | doc. Ing. Radim Halama, Ph.D. |

Extent of instruction for forms of study | ||
---|---|---|

Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 2+2 |

Combined | Credit and Examination | 8+4 |

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.

Lectures

Tutorials

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.

[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] 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

Test, example solutions

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The student prepare individual account on selected topic

Subject has no prerequisities.

Subject has no co-requisities.

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.

Task name | Type of task | Max. 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 | 16 |

Show history

Academic year | Programme | Field of study | Spec. | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|

2019/2020 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | P | Czech | Ostrava | 2 | Compulsory | study plan | |||

2019/2020 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | K | Czech | Ostrava | 2 | Compulsory | study plan | |||

2019/2020 | (B1701) Physics | (1702R001) Applied Physics | P | Czech | Ostrava | 3 | Choice-compulsory | study plan | |||

2018/2019 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | P | Czech | Ostrava | 2 | Compulsory | study plan | |||

2018/2019 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | K | Czech | Ostrava | 2 | Compulsory | study plan | |||

2018/2019 | (N2658) Computational Sciences | (2612T078) Computational Sciences | P | Czech | Ostrava | 2 | Choice-compulsory | study plan | |||

2018/2019 | (B1701) Physics | (1702R001) Applied Physics | P | Czech | Ostrava | 3 | Choice-compulsory | study plan | |||

2017/2018 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | P | Czech | Ostrava | 2 | Compulsory | study plan | |||

2017/2018 | (B1701) Physics | (1702R001) Applied Physics | P | Czech | Ostrava | 3 | Choice-compulsory | study plan | |||

2017/2018 | (N2658) Computational Sciences | (2612T078) Computational Sciences | P | Czech | Ostrava | 2 | Choice-compulsory | study plan | |||

2017/2018 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | K | Czech | Ostrava | 2 | Compulsory | study plan | |||

2016/2017 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | P | Czech | Ostrava | 2 | Compulsory | study plan | |||

2016/2017 | (N2658) Computational Sciences | (2612T078) Computational Sciences | P | Czech | Ostrava | 2 | Choice-compulsory | study plan | |||

2016/2017 | (B1701) Physics | (1702R001) Applied physics | P | Czech | Ostrava | 3 | Choice-compulsory | study plan | |||

2016/2017 | (B1701) Physics | (1702R001) Applied Physics | P | Czech | Ostrava | 3 | Choice-compulsory | study plan | |||

2015/2016 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | P | Czech | Ostrava | 2 | Compulsory | study plan |

Block name | Academic year | Form of study | Study language | Year | W | S | Type of block | Block owner |
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