Math Courses

PILLAR Course: Introduction to Continuum Mechanics

→ Europe/Rome
Ex-INPS building (GSSI)

Ex-INPS building

GSSI
Description

Lecturers
Roberto Verzicco roberto.verzicco@gssi.it
Francesco Viola francesco.viola@gssi.it

Timetable and workload
Lectures: 60 hours
Calendar: available at this link
Homework assignments: 4 at 4 hours each
Final project and exam: 20 hours

Course description and outcomes
The students attending this course are expected to become familiar with the vector spaces relevant to continuum mechanics and to perform vector and tensor manipulations. They will be able to describe motion, deformation and forces in a continuum, derive equations of motion and conservation laws and use constitutive models for fluids and solids. With these tools at hand students will be able to solve simple boundary value problems for fluids and solids. As an application of a challenging problem of continuum mechanics, the final part of the course will be devoted to introduce the basics of turbulence and some related computational method.

Course requirements
T.B.A

Contents

  1. Reminders on Linear Algebra and Tensor Calculus
  2. The Continuum hypothesis: from microscopic to macroscopic
  3. Kinematics of deformable bodies
  4. Eulerian and Lagrangian descriptions of motion
  5. The balance laws of continuum mechanics: Conservation of Mass and Energy, MomentumBalance
  6. Constitutive Relations
  7. Solid mechanics: nonlinear and linearized elasticity
  8. Fluid dynamics: the Navier Stokes equations
  9. Analytical and asymptotic solutions of the Navier Stokes equations
  10. An introduction to hydrodynamic instabilities
  11. An introduction to the physics of fluid turbulence
  12. Kolmogorov theory and wall turbulence
  13. Basic concepts on computational methods for fluid dynamics and turbulence simulation

References

  • M. Gurtin, Introduction to Continuum Mechanics, Academic Press 1981
  • S. Pope, Turbulent Flows, Cambridge University Press 2000

 

Examination and grading
Each student, after having delivered a written report on the final project, will be evaluated and ranked according to the ECTS grading scale.

 

Anonymous survey link: here.