Course detail

Selected Chapters of Structural Mechanics 2 (K)

FAST-NDB032Acad. year: 2026/2027

Textile reinforced concrete, fiber concrete, ECC and composites characterized by a synergetic combination of short fiber reinforcement with aligned (structured) reinforcement in a brittle matrix. Consideration of the natural heterogeneity and randomness of composites. Modeling of the mechanical response of composites to tensile test. Modeling of the mechanical response of multifilament yarns under tension. Statistical characterization of the sources of randomness in yarns. Probabilistic distribution of strength of yarns and composites.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

prof. Ing. Miroslav Vořechovský, Ph.D.

Department

Institute of Structural Mechanics (STM)

Entry knowledge

fundamentals of the structure mechanics and the theory of elasticity and plasticity, fundamentals of the finite element method, infinitesimal calculus, matrix algebra, fundamentals of numerical mathematics, nonlinear mechanics

Rules for evaluation and completion of the course

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

Aims

Professional Knowledge

The student will acquire knowledge of textile-reinforced concrete, engineered cementitious composites (ECC), fibre-reinforced concrete, and other composites characterized by a synergistic combination of short fibre reinforcement and structured reinforcement embedded in a brittle matrix. The student will become familiar with the influence of the inherent heterogeneity and randomness of these materials on their mechanical response. They will gain knowledge of modelling the tensile response of composites and fibre bundles, the statistical characterization of sources of randomness, and the probability distributions of the strength of fibres, fibre bundles, and composites.

Professional Skills

The student will be able to formulate and apply models of the tensile response of fibre-reinforced composites and fibre bundles. They will be able to identify and statistically characterize the principal sources of randomness affecting the mechanical properties of composites. The student will be able to evaluate the strength distributions of fibres, fibre bundles, and the resulting composite, and to assess the influence of material heterogeneity on tensile behaviour.

Professional Competencies

The student will be able to independently apply the acquired knowledge to the analysis and modelling of the mechanical response of fibre-reinforced and hybrid-reinforced composites with a brittle matrix. They will be able to select an appropriate model and statistical approach for describing the tensile behaviour of the material, interpret the results with respect to inherent heterogeneity and randomness, and critically assess the influence of the individual composite constituents on its strength and failure behaviour.

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 hours, optionally

Teacher / Lecturer

prof. Ing. Miroslav Vořechovský, Ph.D.

Syllabus

  • 1. Introduction to fiber reinforced composites. Application sphere, comparison with steel-reinforced concrete and other traditional materials. Characterization of the main features influencing the mechanical response. Insight into the mechanisms of energy dissipation and mechanisms of stress redistristribution during progressive failure. Connections to fracture mechanics.
  • 2. Characterization of various fiber types and materials for fiber production (such as steel, glass, carbon, aramid, polyester etc.). Characterization of yarn type, yarn production and yarn testing.
  • 3. Classical model of yarn based on the FEM. Model of the mechanical response based on sorting algorithms.
  • 4. Probabilistic model of the yarn response. Definition , explanation of the paradigm, revision of the main ingredients and basic transformations of the model.
  • 5. Study of the influence of basic sources of heterogeneity and randomness on random yarn response. Comparison of all the studied models.
  • 6. Distribution of strength of multifilament yarns. Daniels’ theorem. Transition of the strength tail to the distribution core. Recursive formulas. Asymptotic strength.
  • 7. Extension to the strength of composites with chained crack bridges. Theory of extreme values and the associated weakest-link model.
  • 8. Advances questions in the theory of composites, revision.

Exercise

13 hours, compulsory

Teacher / Lecturer

prof. Ing. Jan Eliáš, Ph.D.

Syllabus

  • 1. Submission of individual problems to be solved on computer.
  • 2.–9. Work on the tasks with the help of the teacher.
  • 10. Presentation of the results, credits.