Elasticité non-linéaire des structures  élancées

Informations pratiques

Discipline :


Niveau :

Master 2

Semestre :


Crédits ECTS :


Volume Horaire :

18h Cours

Responsable :

Arezki Boudaoud

Mokhtar Adda-Bedia

CNRS, Université Paris 6 and École Polytechnique

Intervenants :


Arezki Boudaoud


Mokhtar Adda-Bedia


Pattern formation and energy focussing can be easily experienced when crumpling a sheet of paper or when tearing it. Indeed, nonlinear behaviours arise out of geometry, even when the material is described with a linearly elastic constitutive law. The main objective of this course is to demonstrate how geometrical constraints yield ordered and disordered patterns in elastic media under mechanical loading. The course will cover a whole spectrum from theoretical descriptions and approaches to applications such as micro-fabrication, biological growth, foldable structures, fragmentation, geophysical patterns, earthquakes, or contact between solids.




I.- Introduction to elasticity of continuous media

II.- Thin elastic plates

II.1.- Introduction: differential geometry of a surface, equations

II.2.- Buckling: roll-like patterns, growth-induced patterns

II.3.- Singularities: focussing of energy around points (developable cones) and lines (stretching ridges)

II.4.- Patterns from singularities and foldable structures

III.- Fracture and related problems

III.1.- Introduction to brittle fracture mechanics

III.2.- Quasi-static crack propagation: instabilities and crack-induced patterns

III.3.- Fast fracture: dynamics, instabilities, and fractography

III.4.- Friction: from fracture to earthquakes

III.5.- Adhesion and contact mechanics



Undergraduate course on continuum mechanics and elastic media


Presentation of a research article