# MEK4020 – Viscous liquids and elastic materials

## Course content

MEK4020 gives an introduction to continuum mechanics and the mathematical description of forces, stresses and deformations in viscous fluids and elastic materials. The course focuses on the stress tensor, Cauchy’s stress-strain relations, deformations and strain. We study Hooke’s law for elastic matter, Newton’s law of friction in fluids, as well as simple viscoelastic models (stress-strain relations). We consider the derivation of fundamental equations of motion and conservation equations.

## Learning outcome

After completing this course you will:

• master vectors and tensors, index notation, stress tensors for fluids and liquids, Cauchy stress rate, the principal stresses and principal stress directions;
• have knowledge of deformation (strain) and strain rates, deformation tensors, Hooke's law for elastic materials, Newton's friction law for liquids, simple viscoelastic models (stress-strain relations), Navier-Stokes equation and motion of isotropic elastic materials;
• have knowledge of explicit solutions of the equations of elastic materials: Stress distribution due to gravity, axial stretch, torsion of cylindrical rod, longitudinal and transversal (p- and s-) waves, reflection of waves;
• have knowledge of explicit solutions of equations for viscous fluids: Couette flow, laminar pipe flow, flow on inclined planes, boundary layers;
• have knowledge of the energy equation, energy dissipation, heat transfer equation, heat conduction, Fourier's law, thermally driven flow, creep flow.;
• have knowledge of scaling and principles of modeling.

To take this course you must have been enrolled in the following study programme:

## Prerequisites

### Recommended previous knowledge

The subject should be taken after MAT1100 - Calculus,  MAT1110 - Calculus and linear algebraMAT-INF1100 - Modelling and computationsMAT1120 - Linear algebra and MEK1100 - Vector Calculus.

## Teaching

Self study under supervision.

## Examination

mandatory assignments, and in addition 1 larger project assignment with written report that must be approved before one can take the exam.

The oral hearing of the project assignment is included as part of the final oral exam.

Final oral examination.

### Language of examination

You may write your examination paper in Norwegian, Swedish, Danish or English.

### Resit an examination

Students who can document a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.

Re-scheduled examinations are not offered to students who withdraw during, or did not pass the original examination.

### Withdrawal from an examination

It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.

### Special examination arrangements

Application form, deadline and requirements for special examination arrangements.

10

Master

Every autumn

Every autumn

### Teaching language

Norwegian (English on request)