On the wellposedness of constitutive laws involving dissipation potentials

We consider a material with memory whose constitutive law is formulated in terms of internal state variables using convex potentials for the free ener gy and the dissipation. Given the stress at a material point depending on t ime, existence of a strain and a set of inner variables satisfying the cons titutive law is proved. We require strong coercivity assumptions on the pot entials, but none of the potentials need be quadratic. As a technical tool we generalize the notion of an Orlicz space to a cone " normed" by a convex functional which is not necessarily balanced. Duality a nd reflexivity in such cones are investigated.