Summer School
12 – 16 July 2021
Teacher Victor Eremeyev
Summer School
12 – 16 July 2021
Teacher Victor Eremeyev
The Summer School will be held both in presence and online.
Enter the online classroom
The course, of about 28 hours, aims to provide a short but comprehensive introduction into direct (index-free) tensor calculus together with a few applications in Continuum Mechanics.
Timetable
Monday 12 July – Thursday 15 July session 9:00-13:00, session 15:00-17:00
Friday 16 July session 9:00-13:00
Tentative program
1. Vectors and Transformations
1.1 Change of basis and the reciprocal basis
1.2 The cross product and other operation
2. Tensors and Tensor Fields
2.1 Dyadic quantities
2.2 Second-order tensors
2.3 Third- and higher-order tensors
2.4 Isotropic tensors
2.5 Tensor-valued functions of tensor arguments
2.6 Differentiation of tensorial functions
2.7 Tensor fields, differential operations.
2.8 Pseudovectors, pseudoscalars, and pseudotensors
2.9 Invariants of tensors and vectors
3. Elements of Differential Geometry – Curves, Surfaces, etc.
4. Continuum Mechanics
4.1 Kinematics: motion, gradient of deformations, strains.
4.2. Stress tensors
4.3. Notion of constitutive relations: some basic principles (objectivity, locality,
equipresence, etc.)
4.4. Linear elasticity. Hooke’s law. Stiffness tensor and its symmetries.
4.5. Elements of nonlinear elasticity.
4.6. Fluids.
4.7. “A few words” on generalized models.
4.8. Elements of shells theory.
Contact and registration
For information and registration contact:
Victor A. Eremeyev victor.eremeev@unica.it
Maria Cristina Porcu mcporcu@unica.it
Emanuele Reccia emanuele.reccia@unica.it
Recommended literature
- B. Wilson, Vector Analysis, Founded upon the Lectures of G. W. Gibbs. Yale University Press, New Haven, 1901.
- G. Simmonds, A Brief on Tensor Analysis, 2nd Edition, Springer, New York, 1994.
- P. Lebedev, M.J. Cloud, V.A. Eremeyev, Tensor Analysis with Applications in Mechanics, World Scientific, New Jersey, 2010.
- A. Eremeyev, M.J. Cloud, L.P. Lebedev, Applications of Tensor Analysis in Continuum Mechanics. World Scientific, New Jersey, 2018.