Czech

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Institute of Structural Mechanics (STM)

Students will master the subject targets; it means the knowledge about models for inelastic deformation and failure of materials in building industry with particular attention to the theories of failure of quasi-brittle materials, e.g. concrete. The knowledge about selected failure models will be then deepened by practice with special software for analysis of concrete and reinforced concrete structures. The students will get familiar with advanced theories capturing selected phenomena occurring in the field of quasi-brittle structures, such as size effect, random distribution of strength, etc.

fundamentals of structural mechanics, analysis of structures and theory of elasticity and plasticity, fundamentals of finite element method, infinitesimal calculus, matrix algebra, fundamentals of numerical mathematics

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Requirements for successful completion of the subject are specified by guarantor’s regulation updated for every academic year.

1. Classification of structural materials according to the manner of their failure. Classification of models for mechanical behaviour (deformation and failure) of materials.
2. Viscoelasticity. Creep and compliance function. Maxwell's and Kelvin's model. Compliance function for concrete. Integration relation between strain and stress. Numerical calculation of strain for given stress development. Kelvin's and Maxwell's chain.
3. Plasticity. Physical motivation. Schmid's law. Plasticity models for uniaxial stress state. Mathematical description of plastic deformation. Isotropic and kinematical hardening.
4. Plasticity - multiaxial stress state. Basic formulation. Plastic criteria for materials with/without internal friction. Strength criteria for concrete.
5. Fracture mechanics. Fundamentals of linear elastic fracture mechanics. Stress concentration at notch tips. Inglis' stress state solution at notch of elliptical opening. Griffith's theory of brittle fracture. Energetic approach, crack stability criterion. R-curve and its application in crack stability assessment.
6. Fracture mechanics. Fundamentals of linear elastic fracture mechanics. Solution of stress state in cracked body. Modes of crack propagation. Irwin's stress approach – stress intensity factor. Fracture toughness and its determination. Crack stability assessment via stress approach. Relationship between stress and energetic approach. Size effect in linear elastic fracture mechanics.
7. Fracture mechanics. Classical nonlinear models. Nonlinear fracture behaviour of quasi-brittle materials. Formation and development of fracture process zone (FPZ). Toughening mechanism in FPZ. Modelling of nonlinear fracture behaviour. Equivalent elastic crack models. Effective fracture parameters and their determination. Resistance curves approach.
8. Fracture mechanics. Classical nonlinear models. Cohesive crack models. Determination of parameters of cohesive crack models, fracture energy, tension softening.
9. Fracture mechanics. Fracture models based on continuum mechanics. New advanced fracture models. Failure models based on physical discretization of continuum.
10. Damage mechanics. Classification of models of failure of concrete and their hierarchy.
11. Stochastic aspects of failure and deformation of structures
12. Modeling of spatial variability of material properties by random fields.
13. Interaction of progressive collapse and spatial randomness in concrete structures.

Not applicable.

Earning knowledge about models and theories utilizable for inelastic deformation and subsequent failure of materials of structures, particularly quasi-brittle silica-based composites. Getting abilities to perform nonlinear structural analysis of reinforced concrete structure using appropriate special software including evaluation of failure progress and its consequences.

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

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Bitnar, Z., Šejnoha J.: Numerical Methods in Structural Mechanics. Asce Press, Thomas Telford Pub., 1996. (EN)
Kadlčák, J., Kytýr, J.: Statika stavebních konstrukcí I. VUTIUM Brno, 2010. ISBN 978-80-214-3419-6. (CS)
Kadlčák, J., Kytýr, J.: Statika stavebních konstrukcí II. VUTIUM Brno, 2009. ISBN 978-80-214-3428-8. (CS)
Robert D. Cook: Concepts and Applications of Finite Element Analysis. John Wiley ynd Sons, Inc., 1974. (EN)
Servít, R., Doležalová, E., Crha, M.: Teorie pružnosti a plasticity I. SNTL/ALFA Praha, 1981. (CS)

Servít, R., Drahoňovský, Z., Šejnoha, J., Kufner, V.: Teorie pružnosti a plasticity II. SNTL/ALFA Praha, 1984. (CS)