Course detail

Selected Chapters of Structural Mechanics 2 (K)

FAST-NDB032Acad. year: 2025/2026

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

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

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.
Students will master the subject targets, it being the knowledge about textile reinforced concrete, fiber concrete, ECC and composites characterized by a synergic combination of short fiber reinforcement with aligned (structured) reinforcement in a brittle matrix. He/she will get a basic backgroung on the 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.

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. 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 hod., 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.