A CLASS OF NON-ASSOCIATED MATERIALS:n-MONOTONE MATERIALS

Generalized Standard Materials are governed by maximal cycli- cally monotone operators and modeled by convex potentials. Gery de Saxce's Implicit Standard Materials are modeled by biconvex bipotentials. We ana- lyze 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 insisti ng on the linearity, coaxiality and monotonicity properties of the constitutiv e law, we illustrate that Fitzpatrick's representation of n-monotone operators coming from convex anal- ysis 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 cha rac- terization and classification.