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Mechanics of Materials and of Biological Systems

  • Nonlinear solid mechanics: finite elasticity and elasto-plasticity
  • Soft matter elasticity: polymers, liquid crystals, granular materials
  • Electro-magneto-mechanically coupled systems
  • Variational methods fracture mechanics
  • Scientific computing
  • Mechanics of biological systems
  • Stokes Equations

Mathematical Theory of Elasticity

  • Nonlinear elasticity: derivation of the equilibrium equations.
  • Existence theory via the implicit function theorem (Korn inequality, existence theory for linearized elasticity) and by variational methods (polyconvexity, weak continuity of minors, Ball's Theorem).
  • Properties of solutions: global invertibility, singularities (cavitations).
  • Rigorous relation between nonlinear and linearized elasticity in terms of Gamma-convergence.
  • If time permits, lower dimensional models.

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