The course has the scope of providing the students with all the conceptual elements and tools necessary to understand and manage brittle and ductile collapse mechanism of structures. The brittle behaviour assessment of next-generation reinforced concrete structures (Hybrid RC, FRP-bar RC, and High-strength PC) is studied in detail. In the case of metallic structures subjected to cyclic loading, the fatigue assessment is illustrated for both resistance and subcritical crack growth.

Fundamental notions are required from the basic mathematical courses (Mathematical Analysis 1 and 2, Geometry, Rational Mechanics, Numerical Methods: Solution to ordinary and partial differential equations, eigenvalue/eigenvector problems; Statics, kinematics, and dynamics of rigid bodies) and engineering courses (Theory of Elasticity, Reinforced and prestressed concrete).

The program of the course is subdivided into the following topics: (1) Plasticity: elastic-plastic bending; plastic incremental analysis of beam systems; theorems of plastic limit analysis; proportional loads; non-proportional loads; cyclic loads and plastic adaptation (shake-down), inflected flat plates, strip method. (2) Plane elasticity: cartesian coordinates, polar coordinates (3) Plane stress and plane strain conditions: Airy stress function in cartesian and polar coordinates; Thick-walled cylinder; Circular hole in a plate subjected to tension (4) Introduction to Fracture Mechanics: Fracture energy; Griffith energy criterion (5) Stress-singularity at the crack tip: Westergaard method (complex potentials); Mixed-mode conditions; Stress-intensity factors (6) Stress-singularity at the vertex of a re-entrant corner: Williams method (series expansions); Irwin fundamental theorem (7) Extension of the plastic zone at the crack tip; Ductile-to-brittle size-scale transition; Brittleness number (8) Bridged crack model and the problem of minimum reinforcement; Applications to fibre-reinforced materials (9) Cohesive crack model and snap-back instability; Applications to plain concrete (10) Overlapping crack model and the problem of maximum reinforcement; Applications to steel-bar reinforced and to prestressed concrete (11) Applications of Fractal Geometry to strength of materials and fracture mechanics; fractal cohesive crack model; Multi-fractal scaling laws (12) Fatigue resistance and Woehler curve; Fatigue crack growth and Paris law; Fatigue limit and fatigue threshold

The theoretical classes are followed by practical exercises carried out in the Computational Laboratories. In such practical classes, numerical methods are applied for the solution of the problems already treated from an analytical point of view during the theoretical classes. Commercial finite element codes as well as software developed ad-hoc within the research activity are provided by the teacher.

Reference text books: A. Carpinteri, “Advanced Structural Mechanics”, Chaps. 11 and 12, CRC Press, New York, 2017. A. Carpinteri, “Structural Mechanics: A Unified Approach”, Chaps. 19 and 20, Chapman & Hall, London, 1997. A. Carpinteri, “Fracture and Complexity”, Springer Nature, Berlin, 2021.

Lecture slides; Text book; Video lectures (previous years);

Exam: Compulsory oral exam;

The exam consists in an oral interview, during which the student replies to scientific and technical questions related to the course topics. In this way, the level of preparation of the student is carefully assessed on both theoretical and practical aspects.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.