Course detail

Nonlinear Mechanics and FEM

FSI-9NMTAcad. year: 2023/2024

The course is a follow-up to basic lectures in solid mechanics, which are traditionally limited to linear problems, and introduces the basic nonlinearities. Material nonlinearity is represented by several models of plastic behaviour, viscoelasticity and hyperelasticity.
Next, contact problems, stability, large displacement and large strain problems are presented. Although some classical solutions to selected nonlinear problems are mentioned (Hertz contact, deformation theory of plasticity),
attention is given to numerical solution. Above all, the relation between stability and convergence of numerical solution and physical interpretation of the analysed problem is thoroughly inspected. In the second part, students work on individual projects under the guidance of tutor.

Language of instruction


Number of ECTS credits


Mode of study

Not applicable.

Entry knowledge

Mathematics: linear algebra, matrix notation, functions of one and more variables, calculus, ordinary and partial differential equations.
Others: basic theory of elasticity, theory and practical knowledge of the FEM.

Rules for evaluation and completion of the course

Final evaluation is based on the ability of active work with a selected FEM system, which is proved by individual preparation and presentation of a semestral project.
Active participation in the course is controlled individually according to the progression of the semestral project.


The aim of the course is to provide students with advanced knowledge and experience with the solution of nonlinear problems of solid mechanics, connected with the topic of PhD dissertation.
Students learn how to solve basic types of nonlinear behaviour in solid mechanics. They can prepare numerical computational model, solve it using some of the commercial FE systems and make a rational analysis of typical problems connected to the PhD dissertation topic.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

T.Belytschko, T.Liu, K.Moran: Nonlinear Finite Elements for Continua and Structures. J.Wiley, New York, 2000 (EN)
G.A.Holzapfel: Nonlinear Solid Mechanics, Wiley, 2000 (EN)
M.A.Crisfield: Non-linear Finite Element Analysis of Solids and Structures 1-2, Wiley, 1991-97 (EN)

Recommended reading

M.Okrouhlík, editor: Mechanika poddajných těles, numerická matematika a superpočítače. Ústav termomechaniky AV ČR, Praha, 1997
C.Höschl_: Kontaktní úlohy a lisované spoje. Dům techniky ČSVTS Praha, 1985


Classification of course in study plans

  • Programme D-APM-K Doctoral, 1. year of study, summer semester, recommended
  • Programme D-APM-P Doctoral, 1. year of study, summer semester, recommended
  • Programme D-IME-K Doctoral, 1. year of study, summer semester, recommended
  • Programme D-IME-P Doctoral, 1. year of study, summer semester, recommended

Type of course unit



20 hours, optionally

Teacher / Lecturer


1. Introduction to numerical solution of nonlinear problems of solid mechanics
2. Material nonlinearity
3. Stability of structures, bifurcation, buckling
4. Large deformation
5. Contact problems
6. Simulation of material damage, ductile fracture, fracture mechanics
7. Explicit solvers, solution stability, mesh-dependent solutions
8.-12. Solution of individual projects, consultations
13. Presentation of individual projects