Please note! Course description is confirmed for two academic years (1.8.2018-31.7.2020), which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.


On this course, participants learn to read publications written in
tensor notations. By the end the course, the student will be able produce his
or her own text in tensor notations. Students will be familiar with the laws of
nature of continuum mechanics and the general principles derived from these.
The students will understand how continuum thermodynamics extends the view of
continuum mechanics to cover material models. During the course, student will
study how to test material models by the theory of internal variables. Upon
completing the course, the student will be able to use the Levenberg-Marquardt
method in determining the values of the material parameters from the
experimental data. He or she will also understand the foundations of mechanics
of materials, be able to implement a material model in the Abaqus finite
element program, and be capable of determining the values of the material

Credits: 5

Schedule: 11.01.2021 - 25.02.2021

Teacher in charge (valid 01.08.2020-31.07.2022): Kari Santaoja

Teacher in charge (applies in this implementation): Kari Santaoja

Contact information for the course (applies in this implementation):

CEFR level (applies in this implementation):

Language of instruction and studies (valid 01.08.2020-31.07.2022):

Teaching language: English

Languages of study attainment: English


  • Valid 01.08.2020-31.07.2022:

    The beginning of the course covers the application of tensor notation
    and the derivation of tensor equations. The basic laws and axioms of continuum
    mechanics and of continuum thermodynamics are evaluated. The local forms of these
    basic laws and axioms are derived from their global forms. Description of the
    material models by continuum thermodynamics is practised with several
    constitutive equations. The Levenberg-Marquardt method is used for determining
    the values of material parameters from the experimental data. At the end of the
    course the implementation of material models in the Abaqus program is examined
    with the use of examples.

Assessment Methods and Criteria
  • Valid 01.08.2020-31.07.2022:

    Weekly homework assignments and examination.

  • Valid 01.08.2020-31.07.2022:

    Lectures 24 h / 20 %

    Exercise 10 h / 8 %

    Independent work 86 h / 72 %


Study Material
  • Valid 01.08.2020-31.07.2022:

    Santaoja, Kari. Lecture Notes on Continuum Thermodynamics, Taras

    Santaoja, Kari. Determination of the Values of the Material Parameters
    by Extended Levenberg-Marquardt Method, Sasata

    Santaoja, Kari. Implementation of material models in the Abaqus UMAT and
    VUMAT subroutines.

    Solutions for the home assignments will be delivered to the students.

Substitutes for Courses
  • Valid 01.08.2020-31.07.2022:

    Kul-49.4501 Continuum Mechanics and Material Modelling P

  • Valid 01.08.2020-31.07.2022:

    Good knowledge of material mechanics, mechanics, structural mechanics or thermodynamics. The course material covers all the information needed to pass the course. Therefore, a some previous knowledge of the topics mentioned above is adequate for passing this course with excellent marks.

SDG: Sustainable Development Goals

    5 Gender Equality



Registration and further information