  This is a first paper in convex analysis dedicated to the bipotential theory,
based on an extension of Fenchel's inequality. Introduced by the second author,
bipotentials lead to a succesful new treatment of the constitutive laws of some
dissipative materials: frictional contact, non-associated Drucker-Prager model,
or Lemaitre plastic ductile damage law. We solve here the problems of existence
and construction of a bipotential for a nonsmooth mechanics constitutive law.
