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Soft or Slender : mechanics of Nature-inspired, highly deformable bodies
« La chétive pécore, s’enfla si bien qu’elle creva ». « Je plie, et ne romps pas ». While taking inspiration from the living, La Fontaine noticed examples of organisms – frog and reed – that deform strongly, sometimes beyond unrecoverable limits.
Spectacular changes in shapes may emerge either because materials are soft enough to undergo large deformations (gels, elastomers, living tissues…) or because the structures are slender enough to allow for large displacements (filaments, membranes…). Both situations are ubiquitous among living organisms, from tendons, muscles and arterial membranes, to the pads of the gecko lizard and elongated tree branches.
Starting from the basics of elasticity, we will put emphasis on the relevant length and time scales specific to soft matter. Using examples primarily inspired from Nature, we will illustrate the relationship between some ingenious textures and structures and their mechanical performances. Our journey will confront us with those phenomena (adhesion, friction, fracture, shape conformation and morphology changes) living bodies have managed to deal with in order to perform their fundamental tasks (locomotion, nutrition, reproduction…).
Syllabus
When softness matter
Lecture 1: Be wise, linearize! [Basics of small derformation elasticity]
Lecture 2: Go Non-linear [Specificity of finite strain Elasticity, Instabilities]
When slenderness matters
Lecture 3: The shape of elastic lines [Equilibrium of rods, Euler's elastica]
Lecture 4: How rods fails [Buckling instability]
When time matters
Lecture 5: Solids that flow and ooze [Basics of visco- and poro-elasticity]
When ripples matter
Lecture 6: Plates and wrinkling [Mechanics of plates, bending versus stretching, wrinkling instability]
When Surfaces matter
Lecture 7: Sticky stuff [Basics of Adhesion]
Lecture 8: Why things hold ? How things break ? [Fracture Mechanics of Soft Solids]
When shape matters
Lecture 9: Challenging Gauss [Basics of shape-morphing]
Prerequisites
The course will start from the basics of continuum mechanics so that no prerequisites are expected beyond L-M1 basic physics.
Evaluation
The grades will be based on two components :
1/3 will be based on the oral presentation of a kitchen experiment by pairs of students.
2/3 will be on a written exam based on one or two research articles.