Course detail

Constitutive Equations in Computational Modelling

FSI-RK0Acad. year: 2011/2012

The coarse provides a comprehensive overview od constitutive dependencies of matters, not only solid (i.e. materials in the sens of mechanical engineering) but liquid and gaseous as well, it defines the term of constitutive dependencies and their mathematical descriptions (i.e. constitutive models). It systemizes constitutive models in three cathegories: basic constitutive models represent ideal states of matter, simple ones describe an only one major property (elasticity, viscosity, plasticity), combined ones create models of a more complex constitutive behaviour by synthesis of the simple ones on the base of the so called reological models (e.g. elasto-visco-plastic matter). For each of the models described, basic constitutive equations are created and dependencies of stress vs. strain, stress vs. strain rate, strain vs. time (creep) and stress vs. time (relaxation) are evaluated.

Language of instruction

Czech

Number of ECTS credits

3

Mode of study

Not applicable.

Guarantor

prof. Ing. Jiří Burša, Ph.D.

Department

Institute of Solid Mechanics, Mechatronics and Biomechanics (ÚMTMB)

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.

Prerequisites

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.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Assesment methods and criteria linked to learning outcomes

The graded course-unit credit is awarded on condition of having actively participated in seminars, worked out an individual semester work and having passed a test of basic knowledge.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

The objective of the course is to provide students a comprehensive and systematic overview of constitutive dependencies of various types of matters and to interconnect their knowledge acquainted in various courses and fields (solid mechanics, hydromechanics, thermomechanics) and, in the same time, to make students familiar with some of the constitutive models (in FEA program system ANSYS) useful in modelling of up-to-date materials (e.g. plastics, fibre composites, elastomers).

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

Participation in seminars is required. An apologized absence can be compensed by individual works controlled by the tutor.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Lemaitre J., Chaboche J.-L.: Mechanics of Solid Materials
Holzapfel G.A.: Nonlinear Solid Mechanics
Články v odborných časopisech

Recommended reading

Janíček P.: Systémové pojetí vybraných oborů pro techniky

Classification of course in study plans

  • Programme M2A-P Master's

    branch M-IMB , 2. year of study, winter semester, elective (voluntary)

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

prof. Ing. Jiří Burša, Ph.D.

Syllabus

1. Definition of the term constitutive model. Overview of constitutive models in mechanics.
2. Basic constitutive models.
3. Simple constitutive models - overview. Linear and non-linear elastic models.
4. Revision of tensor calculus. Definitions of stress and deformation tensors under large strain conditions.
5. Hyperelastic models of isotropic hardly compressible elastomers.
6. Hyperelastic models of very compressible elastomers (foams).
7. Anisotropic hyperelastic models of elastomers with reinforcing fibres.
8. Constitutive models of Newtonian and non-Newtoniad liquids.
9. Combined models. Theories of viscoelasticity.
10. Models of linear viscoelasticity - response under static load.
11. Models of linear viscoelasticity - response under dynamic load. Complex modulus of elasticity.
12. Other combined models - basic constitutive characteristics.
13. Micropolar continuum models. Cosserat continuum.

Computer-assisted exercise

13 hours, compulsory

Teacher / Lecturer

prof. Ing. Jiří Burša, Ph.D.

Syllabus

1. Constitutive model of linear elastic material - revision. Newtonian fluid.
2. Basic constitutive models - their specifics in FE analyses.
3. Multilinear elastic model.
4. Large displacements - geometrical non-linearity.
5. Hyperelasticity - tests of elastomers and their input into the constitutive model.
6. Choice of a suitable constitutive model of hardly compressible elastomers.
7. Adaptation of the constitutive model for the required strain range.
8. Use of constitutive models of foams.
9. Linear viscoelasticity - behaviour of Voigt model.
10. Linear viscoelasticity - behaviour of Maxwell model.
11. Linear viscoelasticity - behaviour of Kelvin and generalized Maxwell models.
12. Temperature dependence of viscoelastic parameters and application in FE analyses.
13. Semester project, course-unit credit.