Constitutive Equations for BIO (FSI-RKB-A)

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.

1. Definition and overview of constitutive models in mechanics, constitutive models for individual states of matter, definition of deformation tensors.


2. Stress and strain tensors under large strains, hyperelasticity model neo-Hooke.


3. Mechanical tests of elastomers, polynomial hyperelastic models, predictive capability.


4. Models Ogden, Arruda Boyce - entropic elasticity.


5. Incremental modulus. Models of foams. Anisotropic hyperelasticity, pseudoinvariants.


6. Non-elastic effects (Mullins). Plasticity criteria.


7. Models of arterial wall and blood.


8. Models considering fibre arrangement, muscle contraction, poroelasticity.


9. Shape memory alloys


10. Linear viscoelasticity – introduction


11. Linear viscoelasticity – behaviour of models under static loading


12. Linear viscoelasticity - dynamic behaviour, complex modulus


13. Visco-hyperelasticity – model Bergstrom-Boyce, polar decomposition

1. 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.