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We show a surprising connexion between a property of the inf convolution of afamily of convex lower semicontinuous functions and the fact that theintersection of maximal cyclically monotone graphs is the critical set of abipotential.  We then extend the results from arXiv:math/0608424v4 to bipotentials convexcovers, generalizing the notion of a bi-implicitly convex lagrangian cover.  As an application we prove that the bipotential related to Coulomb's frictionlaw is related to a specific bipotential convex cover with the property thatany graph of the cover is non maximal cyclically monotone.

Non maximal cyclically monotone graphs and construction of a bipotential for the Coulomb's dry friction law