Paper detail

A class of non--associated materials: n--monotone materials

Generalized Standard Materials are governed by maximal cyclically monotone operators and modeled by convex potentials. Géry de Saxcé's Implicit Standard Materials are modeled by biconvex bipotentials. We analyze the intermediate class of n-monotone materials governed by maximal n-monotone operators and modeled by Fitzpatrick's functions. Revisiting the model of elastic materials initiated by Robert Hooke, and insisting on the linearity, coaxiality and monotonicity properties of the constitutive law, we illustrate that Fitzpatrick's representation of n-monotone operators coming from convex analysis provides a constructive method to discover the best bipotential modeling a n-monotone material. Giving up the symmetry of the linear constitutive laws, we find out that n-monotonicity is a relevant criterion for the materials characterization and classification.