Course detail

Fracture Mechanics

FAST-NDB031Acad. year: 2025/2026

Linear elastic fracture mechanics, fracture parameters of material – fracture toughness, fracture energy, characteristic length –, methods for determination of fracture parameters, function of geometry, two-parameters fracture mechanics, T-stress, biaxiality factor, non-linear fracture behaviour, approximate non-linear models, resistance curves and surfaces, toughening processes, brittleness, fractal dimension of crack and fracture surfaces, size effect theory, modelling of failure of concrete structures using FE method, constitutive laws for quasi-brittle materials, strain localization problems, crack band model, non-local continuum mechanics, fictitious crack model, ATENA – FEM software, application – modelling of experiments/structures.

Language of instruction

Czech

Number of ECTS credits

Mode of study

Not applicable.

Guarantor

prof. Ing. Zbyněk Keršner, CSc.

Department

Institute of Structural Mechanics (STM)

Entry knowledge

Structural mechanics, meaning of quantities stress and strain, modelling, finite element method.

Rules for evaluation and completion of the course

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Aims

Aim of the course is introduction to mechanics of material, theory of materials failures and linear/nonlinear fracture mechanics. Students will be acquainted with fracture parameters of materials (e.g. fracture toughness, fracture energy, characteristic length) and with methods for determination of these parameters. Students will be orientating in size effect models. They will be able to model of failure of concrete structures using FE method using ATENA.
Student handle design of constructions, fundamentals in thermal evaluation of buildings. Design of building constructions with respect of thermal insulation requirements. Evaluation of thermal comfort and energy efficiency of buildings. Summary of basic requirements for buildings and their constructions from thermal, acoustic and visual comfort point of view. Introduction to solving basic equation of stress analysis and introduction to basics of fracture mechanics with respect to typical structural materials.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme NPC-SIK Master's 2 year of study, winter semester, compulsory-optional

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

prof. Ing. Zbyněk Keršner, CSc.

Syllabus

  • 1. Introduction to mechanics of material, theory of materials failures and fracture mechanics. Linear elastic fracture mechanics – energy/stress approach.
  • 2. Fracture parameters of material, fracture toughness, fracture energy, characteristic length. Methods for determination of fracture parameters, function of geometry.
  • 3. Two-parameters fracture mechanics. Non-linear fracture behaviour, approximate non-linear models, resistance curves and surfaces.
  • 4. Toughening processes quantification. Determination of brittleness number. Size effect theory.
  • 5. Fractal dimension of crack and fracture surfaces.
  • 6. Modelling of failure of concrete structures using finite element method. Constitutive equations for concrete and other quasi-brittle materials.
  • 7.–8. Strain localization problems. Crack band model, non-local continuum mechanics. Fictitious crack model. Models of fixed/rotated crack.
  • 9.–10. Software; application – modelling of experiments/structures.

Exercise

13 hod., compulsory

Teacher / Lecturer

prof. Ing. Zbyněk Keršner, CSc.

Syllabus

  • 1. Introduction to fracture mechanics, information sources. Theoretical study of fracture experiment.
  • 2. Fracture test – three-point bending of beam with central edge notch.
  • 3. Test evaluation – determination of effective fracture toughness, critical crack opening displacement, specific fracture energy.
  • 4. Wedge splitting fracture test (WST).
  • 5. WST evaluation – determination of fracture toughness, critical crack opening displacement, specific fracture energy.
  • 6. Resistance curves of selected fracture parameters. Quantification of toughening processes. Brittleness number determination.
  • 7.–8. Numerical simulation – data preparation. Software, simulation of fracture experiment.
  • 9.–10. Using parameters obtained in modelling of structural response. Credit.