Course detail
Constitutive Equations for BIO
FSI-RKB-A Acad. year: 2024/2025 Winter semester
The course provides a comprehensive overview od constitutive dependencies and constitutive models of matters, not only of solids (i.e. strructural 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 introduces the theory of finite strains and applies it in description of non-linear elastic as well as poroelastic and non-elastic behavour of soft biological tissues, also with taking their anisotropy caused by their fibrous structure into consideration. Models accounting for waviness and directional dispersion of collagen fibres in the tissues are adressed and also models non-Newtonean behaviour of blood. Also other specific properties of biological tissues absent at technical materials are presented, including their impact on procedures of mechanical testing and ways how to take them into consideration in constitutive models of soft tissues. For each of the presented models basic constitutive equations are formulated, on the basis of which the response of the tissue 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
Supervisor
Entry knowledge
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.
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 and systematic overview of constitutive dependencies of various types of matters, to interconnect their knowledge acquainted in various courses and fields (solid mechanics, hydromechanics, thermomechanics) and, at the same time, to make students familiar with practical applications of some of the constitutive models (in FE program system ANSYS) useful in modelling of soft tissues.
Students get an overview of mechanical properties and behaviour of matters and of possibilities of their modelling, especially under large strains. They will have a clear idea of sophisticated application of computational modelling in biomechanical problems with soft tissues. 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 BIO: Biomechanics, compulsory
Programme C-AKR-P: , Lifelong learning
specialization CZS: , elective
Type of course unit
Lecture
26 hours, optionally
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 arterial wall and blood.
- Models considering fibre arrangement, muscle contraction, poroelasticity.
- 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
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 arterial wall
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.