Course detail

Selected Chapters of Structural Mechanics 2 (S)

FAST-CD051Acad. year: 2022/2023

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)

Learning outcomes of the course unit

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.

Prerequisites

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

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Course curriculum

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.
2. Insight into the mechanisms of energy dissipation and mechanisms of stress redistristribution during progressive failure. Connections to fracture mechanics.
3. Characterization of various fiber types and materials for fiber production (such as steel, glass, carbon, aramid, polyester etc.).
4. Characterization of fiber types and of yarn types, yarn production and yarn testing. Influence of strain rate and amount of twist.
5. Classical model of yarn based on the FEM. Model of the mechanical response based on sorting algorithms.
6. Probabilistic model of the yarn response. Definition , explanation of the paradigm, revision of the main ingredients and basic transformations of the model.
7. Study of the influence of basic sources of heterogeneity and randomness on random yarn response.
8. Modeling approaches exploiting the theory of random fields. Comparison of all the studied models.
9. Distribution of strength of multifilament yarns. Daniels' theorem.
Transition of the strength tail to the distribution core. Recursive formulas.
10. Asymptotic strength.
11. Extension to the strength of composites with chained crack bridges.
Theory of extreme values and the associated weakest-link model.
12. Advances questions in the theory of composites.
13. Extreme value theory and its application to statistical strength of materials and structures. Revision.

Work placements

Not applicable.

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.

Specification of controlled education, way of implementation and compensation for absences

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

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme N-P-C-SI Master's

    branch S , 1 year of study, summer semester, compulsory-optional

  • Programme N-K-C-SI Master's

    branch S , 1 year of study, summer semester, compulsory-optional

  • Programme N-P-E-SI Master's

    branch S , 1 year of study, summer 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. 2. Insight into the mechanisms of energy dissipation and mechanisms of stress redistristribution during progressive failure. Connections to fracture mechanics. 3. Characterization of various fiber types and materials for fiber production (such as steel, glass, carbon, aramid, polyester etc.). 4. Characterization of fiber types and of yarn types, yarn production and yarn testing. Influence of strain rate and amount of twist. 5. Classical model of yarn based on the FEM. Model of the mechanical response based on sorting algorithms. 6. Probabilistic model of the yarn response. Definition , explanation of the paradigm, revision of the main ingredients and basic transformations of the model. 7. Study of the influence of basic sources of heterogeneity and randomness on random yarn response. 8. Modeling approaches exploiting the theory of random fields. Comparison of all the studied models. 9. Distribution of strength of multifilament yarns. Daniels' theorem. Transition of the strength tail to the distribution core. Recursive formulas. 10. Asymptotic strength. 11. Extension to the strength of composites with chained crack bridges. Theory of extreme values and the associated weakest-link model. 12. Advances questions in the theory of composites. 13. Extreme value theory and its application to statistical strength of materials and structures. Revision.

Exercise

26 hod., compulsory

Teacher / Lecturer

prof. Ing. Miroslav Vořechovský, Ph.D.

Syllabus

1. Submission of individual problems to be solved on computer. 2. - 12. Work on the tasks with the help of the teacher. 13. Presentation of the results, credits.