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Topics in the mechanics of soft and bio-materials

Course Type: 
PhD Course
Academic Year: 
20 h

Topics in the mechanics of soft and bio-materials

This course aims to provide an introduction to the mechanics of soft materials, of which biological materials are prominent examples. Soft materials are those that can be easily deformed by external stress, electromagnetic fields or even thermal fluctuations: in other words everything that is wet, squishy, sticky, flabby or spongy.

Elements of viscoelasticity

  • Walking on liquids and other exotic properties of viscoelastic fluids
  • Fundamental concepts of viscoelasticity
  • Maxwell and Kelvin-Voigt models
  • Time-dependent viscoelastic moduli
  • The Oldroyd-B model

Polymer mechanics

  • Basic properties of polymer chains
  • Random walks and ideal chains
  • Force-extension of an ideal chain
  • Self-avoiding chains and Flory's theory
  • Semiflexible polymers: the wormlike chain
  • Stretching DNA: the Marko-Siggia interpolation formula

Liquid Crystals

  • The zoo of liquid crystals: nematics, smectics, cholesterics, hexatics and more
  • Frank elasticity
  • Equilibrium configuration in nematics
  • Topological defects in nematics
  • Coupling to external fields and the Fredericks transition
  • Nematodynamics

Active Matter

  • Remarks on the physics of living systems
  • Collective behavior in animal groups: swarming/flocking/schooling and the Vicsek model
  • Collective behavior in robots and sperm
  • Active liquid crystals and the cell cytoskeleton
  • Spontaneous flow in active nematics
  • Active flow in proximity of topological defects
  • Cell mimicry in active droplets
  • Open problems

Mechanics of adherent cells

  • Actin cytoskeleton and cell adhesion
  • Basic concepts of cell motility
  • The Young-Laplace law and the contractile network model
  • Bending elasticity and the contractile film model

Next Lectures: 

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