Course detail

Constitutive Equations for BIO

FSI-RKB-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 (state equation of a perfect gas, thermodynamic equilibrium). Fundamentals of FEM and basic skills in ANSYS program system are required as well. 

Supervisor

prof. Ing. Jiří Burša, Ph.D.

Department

Institute of Solid Mechanics, Mechatronics and Biomechanics

Learning outcomes of the course unit

Prerequisites

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 a perfect gas, thermodynamic equilibrium). Fundamentals of FEM and basic skills in ANSYS program system are necessary. Thus the course is not suitable for bachelor students.

Planned learning activities and teaching methods

Assesment methods and criteria linked to learning outcomes

Language of instruction

English

Aims

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

The study programmes with the given course

Programme N-IMB-P: Engineering Mechanics and Biomechanics, Master's
branch BIO: Biomechanics, 6 credits, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Syllabus


  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




Computer-assisted exercise

13 hours, compulsory

Syllabus


  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 and Mullins efekt


10. Assessment of model parameters from experimental data 


11.-12. Simulation of viscoelastic behaviour


13. Project formulation, course-unit credit.