Student will become familiar with the dependence of deformations and fracture of material to the structure of solids. A multi-level approach is applied from the nano view (atoms and electronic structure) to the macro view (continuum).

1. Microstructure of solids, crystalline structure and bonds. Crystal lattice and its properties. Polymers, molecular and supramolecular structure.
2. Tensors: Introduction to tensors, tensor calculus, isotropic tensors, symmetrical tensor of second order, quadrics, principal axes and principal values of tensor.
3. Properties of second order tensors from the point of view of matrix theory.
4. Continuum mechanics: Stress tensor, strain tensor, generalized Hooke's law, energy of elastic body, creation of discontinuities.
5. Tensors of elastic coefficients for crystalline solids; influence of symmetry.
6. Methods of calculation of mechanical properties of solids. Semi-empirical models, principles of quantum mechanical modelling.
7. Oscillations of crystal lattice. Born-Kármán boundary conditions, quasi-particle description: phonons.
8. Theoretical strength. Methods of calculation for different stress types, comparison with experimental data.
9. Modelling and simulation of fracture processes. Principles of multilevel modelling.
10. Examples of failure models: simulation of nano-indentation test in metals, quasi-brittle fracture of ultra high strength steels, brittle fracture in particle reinforced composites with brittle matrix, quasi-brittle fracture of phosphorus doped ferrous alloy, fatigue crack closure and the effective threshold in metallic materials.