School of Science

Multiscale modelling of materials

This course is part of the programme:
Materials Science

Objectives and competences

Material properties are a consequence of different phenomena on scales ranging from angstroms to meters, and only a multiscale treatment can provide a complete understanding. Materials scientists have to therefore understand fundamental concepts and techniques from different fields, and these are presented in an integral way in this course. With the help of computers we can efficiently solve a variety of problems in science and engineering of materials. The main objective of the course Multiscale modelling of materials is to present the students basic concepts, used in simulation of different materials (metals, polymers, ceramic and their composites) on different scales (continuum mechanics, phase-field, statistical mechanics, molecular and atomistic simulations, quantum mechanics) The syllabus is designed in a way to guide the students through basic concepts and train them how to apply computer programs for solving problems of material characteristics, their processing and use. They will be able to solve a standard spectrum of problems, associated with microscopic and macroscopic fluid and solid mechanics problems. They will also develop skills necessary to solve specific, more involved and non-standard problems.


Basic university knowledge of mathematics, physics chemistry, materials and numerical methods, and basic skills in using computers with one of the modern operating systems (Windows, Linux or OS X) are required.

Content (Syllabus outline)

Course in Multiscale modelling of materials provides basic understanding of phenomena and numerical approaches used in a broad field of materials simulations from electronic to macroscopic levels. The emphasis is placed on formulations and models of basic physical phenomena on each of the scales, their coupling and how to include them in a model of a specific material. Students prepare a seminary that elaborates one of the topics.

1. Introduction

  • Aims and purpose of the course
  • Syllabus presentation
  • Presentation of teaching tools, resources and course execution
  • Students’ obligations
  • Study instructions and suggestions

2. Basic terms

  • Continuum
  • Conservation equations and continuity equation
  • Conservation of momentum
  • Conservation of momentum of momentum
  • Conservation of energy
  • Transport of species
  • Entropy
  • Constitutive equations
  • Boundary and initial conditions

3. Scaling and model simplifications

  • Basic scaling analysis
  • Small parameters and boundary layers
  • Standard dimensionless groups

4. Elements of numerical algorithms

  • Weighted residual method (WRM)
  • Most popular numerical methods as special cases of WRM.
  • Methods for mesh generation
  • Methods of solving of special systems

5. Computational quantum mechanics

  • Schroedinger equation
  • Spin systems
  • Real space systems
  • Combining space and spin
  • Path integration methods

6. Molecular dynamics

  • Areas of applications and limits
  • Potentials
  • Specific molecular dynamics algorithms
  • Examples

7. Phase-field method

  • Areas of applications and limits
  • Formulation of phase-field models
  • Scpecific phase-field algorithms
  • Examples

8. Incompressible and compressible flow

  • Constitutive equations, boundary conditions.
  • Specifics of numerical solution
  • Pressure-velocity couplings

9. Newtonean and non-Newtonian flows

  • Slow Newtonian flows
  • Free surfaces and moving boundaries
  • Flows with large inertia
  • Non-Newtonian constitutive relations
  • Formulations for turbulence modelling

10. Deformation of solids

  • Microscopic and macroscipic description
  • Constitutive equations, elastic, plastic, viscoplastic behaviour
  • Numerical solution
  • Small deformations
  • Large deformations

11. Examples of simulations from molecular dynamics, phase field, solid and fluid mechanics

12. Hands-on work with simulation systems

  • Fluent
  • Deform
  • OpenFOAM
  • LVP in LSMP codes
  • Etc.

Intended learning outcomes

Students will learn the basic concepts of understanding and computer modeling of materials on different scales. They will be able to autonomously conceptually develop a computational model and use a modern simulation systems. They will be able to computationally optimize material properties and materials processing.


  • Z.X. Guo, Multiscale materials modelling, Fundamentals and applications, 1st Edition, Woodhead Publishing, London, 2007

  • E.B. Tadmor and R.E. Miller, Modeling materials: continuum, atomistic and multiscale techniques, Cambridge University Press, Cambridge, 2011.

  • E.B. Tadmor, R.E. Miller and R.S. Elliott, Continuum mechanics and thermodynamics: From fundamental concepts to governing equations, Cambridge University Press, Cambridge, 2012.

  • H. Kroemer, Quantum mechanics for engineering, materials science and applied physics, Prentice hall series in solid state physical electronics, New Jersey, 1994.

  • C. Pozrikidis, Introduction to theoretical and computational fluid dynamics, Oxford University Press, Oxford, 2011.

  • Y.C. Fung, P. Tong, Classical and computational solid mechanics, World Scientific Publishing, Singapore, 2001.

  • Fluent Computer code manual.

  • Deform computer code manual.

  • OpenFOAM manuals from training courses.

  • Meshless computer codes manuals, developed at LVP, UNG and LSMP, IMT.

  • Assessment

    Homeworks. Seminar work with discussion in order to evaluate the ability of making a numerical model of a technical problem. Written exam, which assesses knowledge of the fundamental concepts and ability of problem solving based on existing computer codes.

    Lecturer's references

    Prof. dr. Božidar Šarler is a full professor of materials science and engineering and Head of Laboratory for Multiphase Processes at the University of Nova Gorica and Head of Laboratory for Simulation of Materials and Processes at the Institute of Metals and Technologies in Ljubljana. His main research is dedicated to multiscale, multipysics and multiobjective modelling of materials and processes and development of new numerical methods, particularly for solidification problems.

    Selected bibliography:

    LIU, Qingguo, ŠARLER, Božidar. Improved non-singular method of fundamental solutions for two-dimensional isotropic elasticity problems with elastic/rigid inclusions or voids. Eng. anal. bound. elem., 2016, vol. 68, str. 24-34, [COBISS.SI-ID 1197994]

    PERNE, Matija, ŠARLER, Božidar, GABROVŠEK, Franci. Calculating transport of water from a conduit to the porous matrix by boundary distributed source method. Eng. anal. bound. elem. 2012, vol. 36, no. 11, str. 1649-1659, [COBISS.SI-ID 2412539]

    GREŠOVNIK, Igor, KODELJA, Tadej, VERTNIK, Robert, SENČIČ, Bojan, KOVAČIČ, Miha, ŠARLER, Božidar. Application of artificial neural networks in design of steel production path. Computers, materials & continua, 2012, vol. 30, no. 1, str. 19-38. [COBISS.SI-ID 2601467]

    REUTHER, K., ŠARLER, Božidar, RETTENMAYR, Markus. Solving diffusion problems on an unstructured, amorphous grid by a meshless method. Int. j. therm. sci., 2012, vol. 51, str. 16-22, d [COBISS.SI-ID 1998331]

    VERTNIK, Robert, ŠARLER, Božidar. Local collocation approach for solving turbulent combined forced and natural convection problems. Adv. appl. math. mech., 2011, vol. 3, no. 3, str. 259-279. [COBISS.SI-ID 1781243]

    YAO, Guangming, ŠARLER, Božidar, CHEN, Ching-Shyang. A comparison of three explicit local meshless methods using radial basis functions. Eng. anal. bound. elem.. [Print ed.], 2011, vol. 35, issue 3, str. 600-609, [COBISS.SI-ID 1541371]

    ISLAM, Siraj-ul-, ŠARLER, Božidar, AZIZ, Imran, HAQ, Fazal-i-. Haar wavelet collocation method for the numerical solution of boundary layer fluid flow problems. Int. j. therm. sci., 2011, vol. 50, no. 5, str. 686-697, [COBISS.SI-ID 1740027]

    University course code: 2ZMA16

    Year of study: 2

    Semester: 1

    Course principal:


    ECTS: 6


    • Lectures: 30 hours
    • Exercises: 30 hours

    Course type: elective

    Languages: slovenian / english

    Learning and teaching methods:
    teaching will consist of three parts. the first part will consist of the lectures, where the contents of the syllabus will be presented and explained. the second part will include hands-on training with simulation systems. the third part will consist of individual work where the students will be solving homeworks throughout the course and at the end write a seminar work in the form of an appropriate numerical model.