Existence and uniqueness theorems for boundaryvalue problems involving incrementally non linear models

Su.cient conditions for existence and uniqueness of rate boundary value problem involving an incremen! tally non!linear constitutive equation useful for geomaterials are proved[ The models considered are incrementally non!linear models not descending from a rate potential and thus are not included into the Hill theory framework[ Results are given in the framework of small strain assumption[ The main assumption is the positiveness of the second!order work[ The existence theorem is a generalisation of the Lax!Milgram theorem\ whereas uniqueness theorem is based on the well!known Hill exclusion functional