Analytical continuum mechanics \`a la Hamilton-Piola: least action principle for second gradient continua and capillary fluids

Understand

In this paper a stationary action principle is proven to hold for capillary fluids, i.e.

• fluids for which the deformation energy has the form suggested, starting from molecular arguments, for instance by Cahn and Hilliard.
• Remark that these fluids are sometimes also called Korteweg-de Vries or Cahn-Allen.
• In general continua whose deformation energy depend on the second gradient of placement are called second gradient (or Piola-Toupin or Mindlin or Green-Rivlin or Germain or second gradient) continua.