Course detail

Constitutive Equations for IME

FSI-RKI-AAcad. year: 2021/2022

The course provides a comprehensive overview od constitutive dependencies and constitutive models of matters, not only of solids (i.e. structural materials) but also of liquids and gases. It deals also with time dependence of stress-strain response of materials and describes it using different viscoelastic models. It applies the theory of finite strains of solids in description of non-linear elastic as well as non-elastic behaviour of elastomers and composites with elastomer matrix and of plastic behaviour of metals including their ductile fracture. It presents specific ways of material testing needed for identification of their models. For each of the presented models basic constitutive equations are formulated on the basis of which the response of the material under load is derived using both analytical and numerical (FEM) methods, including applications of the models in ANSYS software.

Language of instruction

English

Number of ECTS credits

6

Mode of study

Not applicable.

Guarantor

prof. Ing. Jiří Burša, Ph.D.

Department

Institute of Solid Mechanics, Mechatronics and Biomechanics (ÚMTMB)

Offered to foreign students

Of all faculties

Learning outcomes of the course unit

Students get an overview of mechanical properties and behaviour of matters and of possibilities of their mathematical description and modelling, especially of their time dependent as well as large strain behaviour. They will have a clear idea of their sophisticated application in design of machines and structures. Within the framework of capabilities of the used FE programme systems, they will be made familiar with the practical use of some of the more complex constitutive models (hyperelastic and non-elastic, isotropic and anisotropic) 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 required as well.

Co-requisites

Not applicable.

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 application of topics presented in lectures using ANSYS software.

Assesment methods and criteria linked to learning outcomes

The course-unit credit is awarded on condition of having actively participated in seminars and submitted an individual semester project. The exam is based on a written test of basic knowledge and defense of the individual semester project.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

The objective of the course is to provide students a comprehensive overview of constitutive dependencies of various types of matters, to interconnect their knowledge acquainted in various courses and fields (solid mechanics, hydromechanics, thermomechanics) and to make students familiar with practical applications of some of the constitutive models (in finite element program system ANSYS) useful in modelling of up-to-date materials (e.g. elastomers, plastics, composites with elastomer matrix, metals above the yield limit).

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

Attendance at practical training is obligatory. 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

Články v odborných časopisech
Holzapfel G.A.: Nonlinear Solid Mechanics. Wiley, 2001.
Lemaitre J., Chaboche J.-L.: Mechanics of Solid Materials. Cambridge University Press, 1994.

Recommended reading

Němec I. a kol. Nelineární mechanika. VUTIUM, Brno, 2018

Elearning

eLearning: currently opened course

Classification of course in study plans

  • Programme N-IMB-P Master's

    specialization IME , 2 year of study, winter semester, compulsory

  • Programme N-ENG-Z Master's 1 year of study, winter semester, recommended course
    2 year of study, winter semester, recommended course

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

prof. Ing. Jiří Burša, Ph.D.

Syllabus

1. Definition of the term constitutive model. Overview of constitutive models in mechanics, constitutive models for individual states of matter.
2. Hooke's law and Newton's law of viscosity in general tensor notation. Introduction to linear theory of viscoelasticity.
3. Models of linear viscoelasticity - response under static and dynamic loads.
4. Complex modulus of elasticity, relaxation and creep functions.
5. Stress and deformation tensors under large strain conditions. Basic tensor operations. Definition of hyperelasticity.
6. Hyperelastic polynomial models of isotropic hardly compressible elastomers. Decomposition of deformation tensor and its invariants.
7. Mechanical tests of hyperelastic materials. Predictiive capability of constitutive models.
8. Structure based hyperelastic models, models of very compressible elastomers (foams).
9. Models describing inelastic effects of elastomers, large strain viscoelasticity.
10. Models of shape memory alloys.
11. Anisotropic hyperelastic models of elastomers with reinforcing fibers. Pseudoinvariants of deformation tensor.
12. Models of elastic-plastic behaviour of materials. Criteria of plasticity.
13. Models of plastic flow and plastic failure. General criteria of failure.

Computer-assisted exercise

13 hod., compulsory

Teacher / Lecturer

prof. Ing. Jiří Burša, Ph.D.

Syllabus

1.-2. Revision of applications of linear elastic constitutive model. Matrix and tensor forms of Hooke’s law and Newton's law of viscosity.
3.-4. Linear viskoelasticity - behaviour of simple rheological mdoels.
5.-6. Introducing experimental data into FE models of viscosleasticity and temperature dependence of viscoelastic parameters.
7.-8. Hyperelastic models in ANSYS - testing of elastomers and their input into the constitutive model.
9.-10. Choice of a suitable constitutive model of a hardly compressible elastomer, predictive capability of the model.
11.-12. Anisotropic hyperelastic models, models of non-elastic behaviour.
13. Semester project, course-unit credit.

Elearning

eLearning: currently opened course