Course detail
Constitutive Equations for IME
FSI-RKI-AAcad. year: 2024/2025
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
Number of ECTS credits
Mode of study
Guarantor
Offered to foreign students
Entry knowledge
Rules for evaluation and completion of the course
Attendance at practical training is obligatory. An apologized absence can be compensed by individual works controlled by the tutor.
Aims
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.
Study aids
Prerequisites and corequisites
Basic literature
Holzapfel G.A.: Nonlinear Solid Mechanics. Wiley, 2001.
Lemaitre J., Chaboche J.-L.: Mechanics of Solid Materials. Cambridge University Press, 1994.
Recommended reading
Elearning
Classification of course in study plans
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
- Definition and overview of constitutive models in mechanics, constitutive models for individual states of matter, definition of deformation tensors.
- Stress and strain tensors under large strains, hyperelasticity model neo-Hooke.
- Mechanical tests of elastomers, polynomial hyperelastic models, predictive capability.
- Models Ogden, Arruda Boyce - entropic elasticity.
- Incremental modulus. Models of foams. Anisotropic hyperelasticity, pseudoinvariants.
- Non-elastic effects (Mullins). Plasticity criteria.
- Models of plastic flow, triaxiality factor, Lode parameter.
- Models of ductile fracture.
- Shape memory alloys
- Linear viscoelasticity – introduction
- Linear viscoelasticity – behaviour of models under static loading
- Linear viscoelasticity - dynamic behaviour, complex modulus
- Visco-hyperelasticity – model Bergstrom-Boyce, polar decomposition
Computer-assisted exercise
Teacher / Lecturer
Syllabus
- Experiment – elastomer testing
2.-3. FEM simulations of tests of elstomers
4.-5. Identification of constitutive models of elastomers
6.-7. Models of plasticity
8.-9. Models of anisotropic behaviour of elastomers
10. Model of Mullinsova efektu
11.-12. Simulation of viscoelastic behaviour
13. Project formulation, course-unit credit.
Elearning