# 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 having finished this course:

• you master vectors and tensors, index notation, stress tensors for fluids and liquids, Cauchy stress rate, the principal stresses and principal stress directions.
• you 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.
• you 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.
• you have knowledge of explicit solutions of equations for viscous fluids: Couette flow, laminar pipe flow, flow on inclined planes, boundary layers.
• you have knowledge of the energy equation, energy dissipation, heat transfer equation, heat conduction, Fourier's law, thermally driven flow, creep flow.
• you have knowledge of scaling and principles of modeling.

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

• Master progamme in Mechanics (from 2018)
• Master programme Computational Science and Engineering, field of study Mechanics

## 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 with dedicated teacher.

## Examination

Two compulsory assignments and one larger project with written report and oral examination, need to be passed within given deadlines to be allowed to take the final exam. Final mark based on oral examination at the end of the semester.

Rules for compulsory assignments at the Department of Mathematics.

### 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)