Course group - TB2-CTEN
- Context and motivation of this Toolbox
Engineers are increasingly confronted with tasks of modelling multi-physical phenomena (fluid-structure interactions in the fields of transport and energy, electromagnetic - materials interactions for the characterisation of materials and in the field of microelectronics). In order to deal serenely with these questions a unique formulation of all the equations of continuum physics is necessary. The course aims to provide this formulation.
- Intended learning outcomes :
To teach students a uniform method of writing, independent of references to continuum physics (rational mechanics, electrodynamics, solid and fluid mechanics). In all these fields modern calculus codes are based on tensor writing of physics equations. The last part deals with illustrating equations of diffraction by experimental observation.
Chapter 1: Matrix and vector calculus (H. Klöcker, J. Bruchon)
1. Reminders of some notions of linear algebra
2. Physical derivative introduction operators
Chapter 2: Tensor algebra (H. Klöcker, J. Bruchon
1. Basic notions
2. Tensor algebra
Chapter 3: Differential geometry (H. Klöcker, J. Bruchon)
1. Derivatives and curvature
2. Expression of some operators
Chapter 4: Physics Equations (H. Klöcker, J. Bruchon)
1. Vector fields (O and 1st order tensor fields)
2. 2nd order tensor fields 2
3. Principle of objectivity
4. Applications to composite materials
Chapter 5: Applications to crystallography (A. Borbély)
1. Basics of crystallography
2. Diffusive and displacive transformations
3. Practical work: read a diffraction pattern; observe crystallographic structures in steel before and after thermal treatment
Tensor calculus is a basic tool for a scientific approach in all fields of theoretical and applied physics. It will help students in mechanical engineering, Materials Science (crystallography) and thermal or electrical modelling.