Construction of bipotentials and a minimax theorem of Fan
  In Mechanics, the theory of standard materials is a well-known application of Convex Analysis. However, the so-called non-associated constitutive laws cannot be cast in the mould of the standard materials.   From the mathematical viewpoint, a non associated constitutive law is a multivalued operator which is not supposed to be monotone.   A possible way to study non-associated constitutive laws by using   Convex Analysis, proposed first in [12], consists in constructing a "bipotential" function of two variables, which physically represents the dissipation.   This is a second paper on the mathematics of the bipotentials, following math.FA/0608424 . We prove here another reconstruction theorem for a bipotential from a convex lagrangian cover, this time using a convexity notion related to a minimax theorem of Fan. 
Marius Buliga, Gery de Saxce, Claude Vallee