A nonlinear boundary value problem arising from continuum mechanics is considered. The nonlinearity of the model arises from the constitutive law which is described by means of the subdifferential of a convex constitutive map. A bipotential , related to the constitutive map and its Fenchel conjugate, is considered. Exploring the possibility to rewrite the constitutive law as a law governed by the bipotential , a two-field variational formulation involving a variable convex set is proposed. Subsequently, we obtain existence and uniqueness results. Some properties of the solution are also discussed.
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