Nonlinear Continuum Mechanics
Olinjär kontinuummekanik

FHL020F, 12 credits

Valid from: Spring 2024
Decided by: Gudbjörg Erlingsdottir
Date of establishment: 2023-10-10

General Information

Division: Solid Mechanics
Course type: Third-cycle course
Teaching language: English

Aim

The course objective is for the student to develop knowledge of the theoretical tools available to describe the mechanics and thermodynamics of different types of continua.

Goals

Knowledge and Understanding

For a passing grade the doctoral student must

• demonstrate the ability to describe the kinematics for deformation of solids and apply different strain and stress measurements; and
• demonstrate the ability to describe the fundamental principles for thermodynamics for deformable solids,

Competences and Skills

For a passing grade the doctoral student must

• demonstrate the ability to apply tensor expressions;
• demonstrate the ability to solve boundary value problems within finite and infinitesimal elasticity and apply mechanical principles to solve mechanical problems;
• demonstrate the ability to formulate physically reasonable constitutive laws for elastic solids;
• demonstrate the ability to describe the physical and thermodynamic assumptions behind constitutive laws;
• demonstrate the ability to evaluate the physical and thermodynamic validity of constitutive laws for deformable elastic solids; and
• be able to apply large deformation theories in modelling of materials and structures.

Judgement and Approach

For a passing grade the doctoral student must be able to critically engage with the content in literature, technical documentations, and real technical solutions to mechanical problems.

Course Contents

The course covers the following: Tensor analysis; Kinematics for deformable solids; Strain and rate of deformation tensors; Stress tensors, Conservation of mass and balance of mechanical energy; Hyperelastic materials; Thermodynamics; Variational principles – linearization; and Finite element implementations

Course Literature

Holzapfel, G.: Nonlinear Solid Mechanics – A continuum Approach for Engineering,. John Wily & Sons, Ltd, 2000. ISBN 9780471823193.

Instruction Details

Types of instruction: Lectures, project. Lectures covering the various topics, approximately 12 in total, along with individual studies. In addition to lectures, there will be two assignments and one project. The assignments will be presented at the beginning and middle of the course, and the project will be presented at the end of the course. The project will be summarized in a brief report, and the assignments will be presented through submitted code. The exam is divided into three parts, with assessment in the form of presented tasks. The assignments and the project work are presented individually.

Examination Details

Examination formats: Written exam, written assignments. Requirements for pass (G): Passed written exams (8 credits) and passed assignments (4 credits).
Grading scale: Failed, pass
Examiner:

Admission Details

Admission requirements: Basic courses in Mechanics, linear algebra and analysis.
Assumed prior knowledge: Basic courses in solid mechanics and numerical methods
Selection criteria: No limitation in the number of students.

Further Information

The course is only given if more than 5 students plan to follow it

Course Occasion Information

Contact and Other Information

Course coordinators: