Course syllabus
Autumn 2023
Course syllabus, Autumn 2023
Title
Finite Element Method and Constitutive Modelling
Swedish title
Finita elementmetoden och konstitutiv modellering
Course code
MT646E
Credits
15 credits
Grading scale
UA / Excellent (A), Very Good (B), Good (C), Satisfactory (D), Pass (E) or Fail (U)
Language of instruction
English
Decision-making body
Faculty of Technology and Society
Syllabus valid from
2023-08-28
Establishment date
2022-03-08
Syllabus approval date
2023-04-24
Level
Advanced level
Entry requirements
- A Bachelor’s degree in materials engineering, mechanical engineering, physics, chemistry or equivalent. The degree must be equivalent to at least 180 higher education credits.
- At least 22.5 higher education credits in mathematics
- The equivalent of English 6/English B at Swedish secondary school
- MA620E Scientific Programming, 7.5 credits or equivalent
- MA623E Numerical Methods, 7.5 credits or equivalent
Main field
Materials Science
Progression level
A1E / Second cycle, contains degree project for Master of Arts/Master of Science (60 credits)Progression level in relation to degree requirements
This course is classified under the main field of study of Materials Engineering and can be used to fulfill degree requirements for a Master’s degree (120 hp) in Materials Engineering .
Course objectives
The objective of the course is for the student to grasp basic theories of finite element methods, as well as to obtain a basic overall view of different types of constitutive laws. The student shall be able to apply this theoretical knowledge in a small project at the end of the course.
Course contents
- Weak formulation of partial differential equations
- Finite element discretisation of partial differential equations
- Common boundary value problems
- Implementation of finite element methods in a scientific programming language
- Simulation of material properties in commercial FEM software
- Isoparametric elements and Gaussian quadrature
- Commonly applied solution methods for nonlinear problems
- Convergence and stability analysis
- Linear and nonlinear elasticity
- Yield criteria and plasticity models
- Project work based on scientific articles within some area of materials science such as continuum mechanics
Learning outcomes
Knowledge and understanding
After completing the course the student shall be able to:
• Describe the basics of the finite element method
• Explain how the the finite element method applies to linear and nonlinear problems
• Identify different types of boundary value problems and explain how these are implemented
• Explain the assumptions and simplifications which are made in the mathematical description of a material model
• Define different types of constitutive models for deformable solids
Skills and abilities
After completing the course the student shall be able to:
• Formulate a weak form of a differential equation from a strong form
• Establish a finite element formulation from a weak form
• Describe the structure of a finite element programme
• Implement solution algorithms for nonlinear problems
Judgement and approach
After completing the course the student shall be able to:
• Choose suitable constitutive models for different applications
• Evaluate the suitability of a constitutive law for modeling a specific material
• Reflect upon how different problems in engineering and physics can be modelled and simulated using the same methods
• Analyse, model and simulate structures with the help of the finite element method, as well as interpret and evaluate the results
• Critically scrutinise and analyse a scientific article and understand the strengths and weaknesses of the FEM models used
Learning activities
Lectures, exercises, computer simulations, project work tutorials, presentation of project and independent study.
Assessment
Requirements for pass (grade A-E): Passed written exam (7 credits), passed assignments (2 credits), passed project report with oral presentation (6 credits).
The final grade is based on the exam.
Course literature
• Ottosen, Niels & Petersson, Hans (1992). Introduction to the Finite Element Method. Prentice Hall
• Saabye Ottosen, Niels & Ristinmaa, Matti (2005). The mechanics of constitutive modeling. 1. ed. Amsterdam: Elsevier
Course evaluation
The University provides students who are taking or have completed a course with the opportunity to share their experiences of and opinions about the course in the form of a course evaluation that is arranged by the University. The University compiles the course evaluations and notifies the results and any decisions regarding actions brought about by the course evaluations. The results shall be kept available for the students. (HF 1:14).
Interim rules
When a course is no longer given, or the contents have been radically changed, the student has the right to re-take the examination, which will be given twice during a one year period, according to the syllabus which was valid at the time of registration.
Additional information
The syllabus is a translation of a Swedish source text.