  In the classical theory of fluid mechanics a linear relationship between the
shear stress and the symmetric velocity gradient tensor is often assumed. Even
when a nonlinear relationship is assumed, it is typically formulated in terms
of an explicit relation. Implicit constitutive models provide a theoretical
framework that generalises this, allowing for general implicit constitutive
relations. Since it is generally not possible to solve explicitly for the shear
stress in the constitutive relation, a natural approach is to include the shear
stress as a fundamental unknown in the formulation of the problem. In this work
we present a mixed formulation with this feature, discuss its solvability and
approximation using mixed finite element methods, and explore the convergence
of the numerical approximations to a weak solution of the model.
