Course detail
Constitutive Equations for EM
FSI-RKI-A Acad. year: 2026/2027 Winter semester
Students are required to have knowledge of basic terms of theory of elasticity (stress and strain tensors, Hooke's law for multiaxial stress), as well as some basic terms of hydrodynamics (perfect, Newtonian and non-Newtonian liquids, viscosity) and thermodynamics (entropy, state equation of perfect gas, thermodynamic equilibrium). Fundamentals of FEM and basic skills in ANSYS program system are necessary.
Language of instruction
English
Number of ECTS credits
6
Supervisor
Entry knowledge
Students are required to have knowledge of basic terms of theory of elasticity (stress and strain tensors, Hooke's law for multiaxial stress), as well as some basic terms of hydrodynamics (perfect, Newtonian and non-Newtonian liquids, viscosity) and thermodynamics (entropy, state equation of perfect gas, thermodynamic equilibrium). Fundamentals of FEM and basic skills in ANSYS program system are necessary.
Rules for evaluation and completion of the course
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.
Attendance at practical training is obligatory. An apologized absence can be compensed by individual works controlled by the tutor.
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).
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.
The study programmes with the given course
Programme N-IMB-P: Engineering Mechanics and Biomechanics, Master's
specialization IME: Engineering Mechanics, compulsory
Type of course unit
Lecture
26 hours, optionally
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
13 hours, compulsory
Syllabus
- Experiment – elastomer testing
2.-3. FEM simulations of tests of elastomers
4.-5. Identification of constitutive models of elastomers
6.-7. Models of plasticity
8.-9. Models of anisotropic behaviour of elastomers and Mullins effect
10. Assessment of model parameters from experimental data
11.-12. Simulation of viscoelastic behaviour
13. Project formulation, course-unit credit.