Course detail
Materials Modelling II
FSI-WMQ Acad. year: 2025/2026 Winter semester
Supervisor
Learning outcomes of the course unit
Prerequisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Language of instruction
Czech
Aims
Specification of controlled education, way of implementation and compensation for absences
The study programmes with the given course
Programme N-MTI-P: Materials Engineering, Master's
branch ---: no specialisation, 6 credits, compulsory
Programme N-IMB-P: Engineering Mechanics and Biomechanics, Master's
branch BIO: Biomechanics, 6 credits, compulsory-optional
Programme C-AKR-P: , Lifelong learning
branch CZS: , 6 credits, elective
Programme N-IMB-P: Engineering Mechanics and Biomechanics, Master's
branch IME: Engineering Mechanics, 6 credits, compulsory-optional
Type of course unit
Lecture
26 hours, optionally
Teacher / Lecturer
Syllabus
1. Modelling of relationships between microstructure and physical properties, history and presence.
2. Equilibrium statistical mechanics, spin models and their mean field solutions.
3. Phase space, phase trajectory, ergodic theorem, entropy.
4. Numerical methods for the minimizations of functions of N variables.
5. Crystallography and symmetry in the real and reciprocal spaces.
6. Molecular statics, atomic-level forces, energies and stresses in many-body systems.
7. Molecular dynamics, stability of numerically integrated equations of motions, thermostats, barostats.
8. More advanced interaction potentials and their physical origins.
9. Mesoscopic phase field models.
10. Phase field crystal model.
11. Methods for finding the minimum energy paths of systems.
12. Finite Element Method, shape functions and elasticity.
13. Modern trends in computational studies of materials.
Computer-assisted exercise
26 hours, compulsory
Teacher / Lecturer
Syllabus
1. Investigation of the Fermi-Pasta-Ulam problem.
2. Monte Carlo studies of the 1D-3D Ising models and calculations of their phase diagrams.
3. Calculation of the density of states of the 2D Ising model using the Wang-Landau method.
4. Implementation of numerical methods for the minimizations of functions of N variables.
5. Construction of an arbitrary Bravais lattice and introduction to visualizations.
6. Ground state of crystalline argon in 2D a 3D using the Lennard-Jones potential.
7. Crystallization of inert gas in the Lennard-Jones potential.
8. Calculation of the energies of point defects and surfaces in an fcc material.
9. Study of twinning in ferroelastic materials.
10. Evolution of microstructure in the phase field crystal model.
11. Obtaining the transition pathway of a model system using the Nudged Elastic Band method.
12. Distribution of stresses and strains in a deformed elastic body using the Finite Element Method.
13. Discussions on the assigned problems.