The teaching unit is optional
The teaching unit is taught in English.

Team

Coord. Bastien Durand (bastien.durand@ens-paris-saclay.fr, ENS Paris-Saclay)

 

Pedagogical team:

DURAND, Bastien, Assistant Professor, CNU 60, ENS Paris-Saclay
bastien.durand@ens-paris-saclay.fr

 

Pedagogical objectives:

The course deals with the mechanical behavior of engineering materials (metals and foams) under dynamic loading conditions. The mechanical wave propagation study is the key of this field.

 

Content:

The course first gives the theoritical background necessary to understand wave propagation (characteristic method in Lagrange Diagram, Rankine & Hugoniot relations). This knowledge is relevant for future engineers and researchers working on problems that involve the dynamic loading of structures and materials.

The course also gives experimental (Hopkinson bars) and numerical (ABAQUS) abilities.

Concerned fields: energy absorption in vehicles, military applications, high-speed machining...

 

Prerequisites:

MAGIS core courses

 

References:

Kolsky, H., 1963, Stress Waves in Solids, Clarendon Press, Oxford.

Meyers, M.A., 1994, Dynamic behavior of materials, John Wiley & Son Inc.

Zhao, H., 2004, Cellular materials under impact loading, Amas-edition, Warsaw.

 

Procedure and organization:

ELASTIC WAVES:

• Simple tensile and compressive waves;
• Hydrostatic and deviatory waves in a 3D medium;
• Confined tensile and compressive waves;
• Torsion waves;
• Bending waves;
• Tensile and compressive waves in plates;
• Theoretical study of the compression Hopkinson bar technique;
• Wave dispersion in a bar due to lateral inertia.

ELASTIC PLASTIC WAVES:

• Piece by piece linearity;
• Lagrange diagrams.

RANKINE & HUGONIOT EQUATIONS AND COMMON EQUATIONS OF STATE:

• Conservation equations;
• Application to elasticity;
• Waves in polytropic gases and in highly compressed solid materials (shock front theory, Rayleigh line);
• Application to non-compressive fluid mechanics (Bernoulli relation);
• Foam dynamic behavior.

VISCO-ELASTIC WAVES

EXPERIMENTAL WORK:

• Dynamic shear test on a glue joint using tensile Hopkinson bars;
• Strain gauge measurement processing to determine forces and velocities;
• Digital Image Correlation to determine local displacements.

NUMERICAL WORK:

• Use of a finite element software (ABAQUS-CAE);
• Numerical study of elastic-plastic waves in solid materials and in foams;
• Numerical study of wave dispersion.