Mechanical design of solid deformable media 1

The aim of the course is to establish the various concepts of the mechanics of deformable solids. The first part of the course introduces tensor calculus, then defines strain and stress tensors for small deformations.

No special prerequisites

Chapter I- Elements of tensor calculus

Einstein's notations, tensors, principal values and directions, differential operators, curvilinear coordinate systems

Chapter II- Infinitesimal deformations

Definitions of kinematics, deformation, extension, slip, state of deformation at a point, physical meaning of the components of the deformation tensor.

Chapter III- Stresses

Definition of stress vector, stress tensor, physical meaning, normal and shear stresses, Mohr's circle.

Physics

"Mécanique des solides déformables", C. Bacon and J. Pouyet
"Introduction à la mécanique des milieux continus", P. Germain and P. Muller
"Ondes élastiques dans les solides 1", D. Royer, E. Masson, 1996.
" Mécanique des solides déformables", P. Lac (course handout)
" Mécanique des milieux continus - élasticité linéaire", E. Ringot
course handout - Université de Toulouse III - Paul Sabatier
"Mécanique des milieux continus et discrets", N. Moës (course handout - ECN)
" Nonlinear continuum mechanics for finite element analysis", J. Bonet and R.D. Wood. Cambridge University Press, 1997.