1. Atomic bonds and microstructure of solids. Crystal lattice and its properties in metals and ceramics. Polymers, molecular and supra-molecular structure.
2. Tensors: introduction to tensors, operations with tensors, isotropic tensors, symmetric tensor of second order, quadrics, the principal values and axis of tensor.
3. Properties of second order tensors in terms of matrix theory.
4. Continuum mechanics: stress tensor, strain tensor, the generalized Hooke's law, energy of the elastic body, the emergence of discontinuities.
5. Tensor of elastic coefficients for crystalline substances, the influence of crystal symmetry.
6. Methods for calculating mechanical properties of solids. Semi-empirical models, principles of quantum-mechanical modelling.
7. Vibrations of the crystal lattice. Born - Karman boundary conditions, quasi-particles description: phonons.
8. The theoretical strength. Calculation methods for different kinds of loading, comparing with experimental data.
9. Modelling and simulation of fracture. Principles of multilevel modelling.
10. Examples of modelling of fracture: simulation of the nano-indentation test in metals, quasi-brittle fracture of ultra-high-stress steels, brittle fracture of particle reinforced composites with brittle matrix, quasi-brittle fracture of iron alloys containing phosphorus, fatigue crack closure and effective threshold in metallic materials