  We discuss the Hu-Washizu (HW) variational principle from a geometric
standpoint. The mainstay of the present approach is to treat quantities defined
on the co-tangent bundles of reference and deformed configurations as primal.
Such a treatment invites compatibility equations so that the base space
(configurations of the solid body) could be realised as a subset of an
Euclidean space. Cartan's method of moving frames and the associated structure
equations establish this compatibility. Moreover, they permit us to write the
metric and connection using 1-forms. With the mathematical machinery provided
by differentiable manifolds, we rewrite the deformation gradient and
Cauchy-Green deformation tensor in terms of frame and co-frame fields. The
geometric understanding of stress as a co-vector valued 2-form fits squarely
within our overall program. We also show that for a hyperelastic solid, an
equation similar to the Doyle-Erciksen formula may be written for the co-vector
part of the stress 2-form. Using this kinetic and kinematic understanding, we
rewrite the HW functional in terms of frames and differential forms. Finally,
we show that the compatibility of deformation, constitutive rules and equations
of equilibrium are obtainable as Euler-Lagrange equations of the HW functional
when varied with respect to traction 1-forms, deformation 1-forms and the
deformation. This new perspective that involves the notion of kinematic closure
precisely explicates the necessary geometrical restrictions on the variational
principle, without which the deformed body may not be realized as a subset of
the Euclidean space. It also provides a pointer to how these restrictions could
be adjusted within a non-Euclidean setting.
