Course detail

Computational Models of Non-linear Material Behaviour

FSI-9VMMAcad. year: 2020/2021

The coarse provides an overview od constitutive dependencies of matters, especially of solids, but liquid and gaseous matters as well, and their computational models. It deals in detail with materials showing large strains, non-linear elastic as well as non-elastic, isotropic as well as anisotropic. For each of the presented models the basic constitutive equations are formulated allowing description of the mechanical response of the material using both analytical and numerical (FEM) methods. Mechanical testing of materials is dealt with as well, together with application of the experimental data in identification of the constitutive models. The course deals in detail with the models applicable in solution of the doctoral topic.

Learning outcomes of the course unit

Students get an overview of mechanical properties and behaviour of matters and of possibilities of their modelling. They will have a clear idea of their sophisticated application in design of machines and structures. Within the framework of abilities of the used FE programme systems, they will be made familiar with the practical use of some of the more complex constitutive models in stress-strain analyses.


Students are expected to have knowledge of basic terms of theory of elasticity (stress, strain, general Hooke's law), as well as some basic terms of hydrodynamics (ideal, Newtonian and non-Newtonian liquids) and thermodynamics (state equation of ideal gas, thermodynamic equilibrium). Fundamentals of FEM and basic skills in ANSYS program system are recommended.


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Lemaitre J., Chaboche J.-L.: Mechanics of Solid Materials, (EN)
Němec I. a kol. Nelineární mechanika. VUTIUM, Brno, 2018 (CS)
Holzapfel G.A.: Nonlinear Solid Mechanics (EN)
Články v odborných časopisech (EN)
J.D.Humphrey: Cardiovascular Solid Mechanics. Springer, 2002 (EN)

Planned learning activities and teaching methods

The course is taught as regular lectures aiming and theoretical fundamental and applications of the computational models and additionally as individual studies of the recommended literature.

Assesment methods and criteria linked to learning outcomes

The exam consists of oral test of basic knowledge and defence of an individual project related to the doctoral topic.

Language of instruction

Czech, English

Work placements

Not applicable.


The objective of the course is to provide students with broader and deeper knowledge on constitutive dependencies of various types of matters and to make them familiar with some constitutive models useful in modelling of up-to-date materials (e.g. elastomers, plastics, composites with elastomer matrix). Some of them require interconnecting of knowledge acquainted in various courses and branches (solid mechanics, hydromechanics, thermomechanics).

Specification of controlled education, way of implementation and compensation for absences

Specific items are checked in individual consultations in intervals corresponding to the difficulty of the items.

Classification of course in study plans

  • Programme D-IME-P Doctoral, 1. year of study, winter semester, 0 credits, recommended

Type of course unit



20 hours, optionally

Teacher / Lecturer


1. Definition of the term constitutive model. Overview of constitutive models in mechanics, basic constitutive models for individual states of matter.
2. Introduction to tensor calculus, notation and properties of tensors, basic tensor operations. 3. Stress and deformation tensors under large strain conditions, their invariants and decomposition into spherical and deviatoric parts.
4. Hyperelastic models for isotropic hardly compressible elastomers on the polynomial basis.
5. Other hyperelastic models, models for very compressible elastomers (foams), poroelastic models.
6. Anisotropic hyperelastic models of elastomers with reinforcing fibers. Pseudoinvariants of deformation tensor.
7. Models describing inelastic effects of elastomers.
8. Combined models. Introduction in the theory of viscoelasticity.
9. Models of linear viscoelasticity - response under static and dynamic load.
10. Complex modulus of elasticity, relaxation and creep functions, non-linear viscoelasticity.