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.

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.