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.

Admission

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

It is not possible to sign up for this subject via the Student Web. Please contact your study programme for registration.

Prerequisites

Recommended previous knowledge

The subject should be taken after MAT1100 - Calculus,  MAT1110 - Calculus and linear algebra, MAT-INF1100 - Modelling and computations, MAT1120 - Linear algebra and MEK1100 - Vector Calculus.

Overlapping courses