Course detail

Selected Topics of Structural Mechanics I

FAST-BD53Acad. year: 2020/2021

Theories of deformation and failure of materials of civil engineering structures.
Viscoelasticity - creep and relaxation. Basic rheology models and their coupling. Compliance function for concrete.
Plasticity models for both uni- and multi-axial stress state. Mathematical description of plastic deformation. Plasticity criteria for material with/without internal friction.
Stress concentration around notches. Fundamentals of linear elastic fracture mechanics. Griffith theory of brittle fracture. Energy balance in cracked body, crack stability criterion. Stress state solution in cracked body, modes of crack propagation. Stress intensity factor, fracture toughness. Size effect predicted by linear fracture mechanics. Classical nonlinear fracture models. Nonlinear fracture behaviour, fracture process zone, toughening mechanisms. Models of equivalent elastic crack, effective fracture parameters, resistance curves. Cohesive crack models and their parameters, fracture energy, tension softening.
Damage mechanics,
Stochastic aspects of failure of quasi-brittle materials/structures.

Language of instruction

Czech

Number of ECTS credits

4

Department

Institute of Structural Mechanics (STM)

Learning outcomes of the course unit

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.

Prerequisites

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

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. 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 and Kelvin model. Compliance function for concrete. Integration relation between strain and stress. Numerical calculation of strain for given stress development. Kelvin and Maxwell chain.
3. Plasticity. Physical motivation. Schmid 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 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 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.

Work placements

Not applicable.

Aims

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.

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

Servít, R., Doležalová, E., Crha, M.: Teorie pružnosti a plasticity I. SNTL/ALFA Praha, 1981. (CS)
Kadlčák, J.: Statics of Suspension Cable Roofs. A. A. Balkema, 1995. (EN)
Bittnar, Z., Šejnoha, J.: Numerical Methods in Structural Mechanics. Published by ASCE Press, 1996. (EN)
Kolář, V., Němec, I., Kanický, V.: FEM Principy a praxe metody konečných prvků. Computer Press, 1997. (CS)

Recommended reading

Not applicable.

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

Syllabus

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 and Kelvin model. Compliance function for concrete. Integration relation between strain and stress. Numerical calculation of strain for given stress development. Kelvin and Maxwell chain. 3. Plasticity. Physical motivation. Schmid 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 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 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.

Exercise

26 hours, compulsory

Teacher / Lecturer

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.