Course detail

Mechanics of Composite Materials

FSI-RMOAcad. year: 2017/2018

Introduction, basic terminology. Mechanical properties of the most used fibres and matrix materials. Stiffness of unidirectional fibre composites (lamina) in longitudinal and transversal direction. Critical and minimum fibre volume fraction. Short fibre composites, theory of load transport. Transport and critical fibre length. Siffness and strength. Orthotropic behaviour as a result of the fibre composite structure. Hooke's law of the anisotropic, orthotropic and transversal orthotropic material in principal material directions. Hooke's law for 2-D fibre composite (lamina) in arbitrary direction, strength conditions. Constitutive relations of the laminated thin wall and thin plate. Construction of stiffness matrix, strength analysis. Application to the thin-wall pressure vessel.

Learning outcomes of the course unit

Students will have a clear idea of the directional behaviour of composite material and of methods used in stress-strain analysis and strength control of selected structures made of composite materials.


Knowledge of basic terms of theory of elasticity (stress, principal stress, deformation, strain, general Hooke's law), membrane theory of shells. Fundamentals of FEM and basic handling of ANSYS system.


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Agarwal,B.D., Broutman,L.J.: Vláknové kompozity, SNTL, Praha, 1987
Jones,R.M.: Mechanics of composite materials. Hemisphere Publishing Corporation, New York, 1975
Krishan K. Chawla: Composite materials. Science and Engineering. Springer-Verlag, New York, Berlin, Heidelberg, 1998

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Assesment methods and criteria linked to learning outcomes

The credit conferment is based on the successful defence of the final project, dealing with computational modelling of mechanical behaviour of a defined structure made of composite material using FEM program ANSYS. The exam consists of a written review test and of an oral interview.

Language of instruction


Work placements

Not applicable.


The objective of the course is to make students familiar with basic knowledge of mechanical behaviour of composite materials, especially of fibre composites. Elastic and strength characteristics of the composite are determined from the known mechanical properties of components and from their geometrical structure. Students get acquainted with methods used in evaluation of stresses, strains and safety factor of typical structures made of composite materials.

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

Attendance at practical training is obligatory. In a justified case an absence from the seminar can be compensated by individual projects controlled by the tutor.

Classification of course in study plans

  • Programme M2A-P Master's

    branch M-IMB , 2. year of study, summer semester, 5 credits, compulsory

Type of course unit



39 hours, optionally

Teacher / Lecturer


1.Definition and basic terms. Classification of composite materials based on their structure and materials of their components.
2.Mechanical properties of typical fibres and of matrix materials. Chemical composition, way of production.
3.Unidirectional long-fibre composite. Elasticity modulus and strength in longitudinal direction.
Critical and minimal volume of fibres.
4.Unidirectional long-fibre composite. Elasticity modulus and strength in transversal direction.Shear modulus and Poisson’s ratio.
5.Failure mechanisms of long-fibre composites under longitudinal and transversal, tensional and compressive loading.
6.Short-fibre unidirectional composite. Theory of load transfer. Stress distribution in fibres. Transmission and critical length.
7.Short-fibre unidirectional composite. Elasticity modulus and strength in transversal and longitudinal directions. Strength in transversal and longitudinal directions.
8.Modelling of mechanical properties of composites within the framework of solid mechanics. 9.Principal axes of orthotropy. Hook’s law for isotropic, orthotropic and transversally isotropic materials in principal material directions.
10.Hook’s law for plane orthotropic material in general directions. Directional stiffness matrix. Balanced oriented lamina.
11.Strength conditions for a plane composite material: maximal stress, maximal strain and Tsai-Hill energetic conditions.
12.Constitutive relations for a composed laminate wall and plate.
13.Calculation of stresses and strength control of a cylindrical laminate wall.

Computer-assisted exercise

13 hours, compulsory

Teacher / Lecturer


1.FEM simulation of bending of sandwich beam.
2.FEM simulation bending of more complex geometry consisting of sandwich shells.
3.FEM simulation of tensile test of fibre composite specimen in longitudinal direction-verification of analytical equations.
4.FEM simulation of tensile test of composite specimen in transversal direction-verification of analytical equations.
5.FEM simulation of shear test of fibre composite specimen-verification of analytical equations.
6. FEM simulation of longitudinal, tranversal and shear test of fibre composite specimen with exploiting homogenization.
7.Practical demonstration of production and testing of composite materials.
8.FEM simulation of pressure cylinder made of composite materials. Using of layered version of elements.
9.FEM computation of stress concentration factor in composite materials.
10.FEM simulation of bending of fibre composite with analysis of failure states via maximal stress criterion.
11.FE analysis of fibre composite. Analysis of failure states with using TSAI-WU criterion. Effect of shear stress on a strength of fibre composite
12.FEM simulation of fibre composite layer delamination. Formulation of final projects.
13.Evaluation of final projects, credit.

E-learning texts

Vrbka, J.; Mechanika kompozitů; ÚMTMB, FSI, VUT v Brně; 2014 (cs)