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151-0560-00L 4 Credits MSC D-MAVT

Advanced Finite Element Formulations

Lecturers & Examiners: Prof. Dr. Mahmood Jabareen
VVZ CR n/a

Last Updated: 2026-06-03 00:14:36

Abstract

This course explores advanced topics in the finite element method, with an emphasis on formulations for modeling solids and structures undergoing large deformations. It explores a range of material models, from hyperelasticity to plasticity, and introduces various strategies for solving the resulting nonlinear equations.

Objective

After taking this class, students will be able to: 1) Explain the mathematical principles underlying advanced finite element formulations for nonlinear solid and structural mechanics; 2) Distinguish between geometric, material, and contact nonlinearities and describe how they are incorporated into finite elements method; 3) Derive and implement different element formulations and assess their applicability and limitations; 4) Model a range of material behaviors, including hyperelasticity and plasticity; 5) Apply and compare numerical strategies for solving nonlinear finite element systems.

Content

1. Introduction: Review of nonlinear continuum mechanics 2. Different finite element formulation: Bubnov Galerkin, three-field mixed finite element formulation, reduced integration with hourglass control, enhanced strain method, Cosserat point element, solid shell element 3. Different material models: hyperelasticity, plasticity 4. Different numerical strategies for solving nonlinear system of equations: Newton–Raphson, modified Newton-Raphson, arc-length

Resources

Lecture Notes

Lecture notes will be provided, however, students are also encouraged to take their own notes.

Literature

Relevant references will be provided.

General Information

Language
English
Levels
MSC

Examination

Type
end-of-semester examination
Mode
written 120 minutes
Aids
One double-sided hand-written page of notes/formulae is allowed. No further material is allowed.
The written final exam (taking place on May 20th, 2026) covers all contents of this course, including lectures, exercises, and programming assignments. It counts 55% towards the final grade. Additionally, there will be nine compulsory homework. Each of the nine homework assignments must be submitted one week after assignment. Collectively, they count 45% (5% each). The homework, which are integrated with the lectures require the student to understand and apply the course material and involve coding.

Course Components

Type Title Time & Place Hours
lecture Advanced Finite Element Formulations
  • Wed 12:15-14:00 (HG E 33.1)
2 h weekly
exercise Advanced Finite Element Formulations
  • Wed 14:15-15:00 (HG E 33.1)
1 h weekly

Offered In

  • Mechanical Engineering Master
    • Core Courses (The Core Courses in the Master’s program Mechanical Engineering listed below are indicative and include courses designed by the Department at the Master's level. With the approval of the tutor, students may also select Master's-level courses offered by other departments at ETH. These courses will be marked as non-regular in the LAG, but their categorization as Core Courses is possible if included in the approved LAG.)