  The endochronic theory, developed in the early 70s, allows the plastic
behavior of materials to be represented by introducing the notion of intrinsic
time. With different viewpoints, several authors discussed the relationship
between this theory and the classical theory of plasticity. Two major
differences are the presence of plastic strains during unloading phases and the
absence of an elastic domain. Later, the endochronic plasticity theory was
modified in order to introduce the effect of damage. In the present paper, a
basic endochronic model with isotropic damage is formulated starting from the
postulate of strain equivalence. Unlike the previous similar analyses, in this
presentation the formal tools chosen to formulate the model are those of convex
analysis, often used in classical plasticity: namely pseudopotentials,
indicator functions, subdifferentials, etc. As a result, the notion of loading
surface for an endochronic model of plasticity with damage is investigated and
an insightful comparison with classical models is made possible. A damage
pseudopotential definition allowing a very general damage evolution is given.
