  We develop an error-in-constitutive-relation (ECR) approach toward the
full-field characterization of linear viscoelastic solids described within the
framework of standard generalized materials. To this end, we formulate the
viscoelastic behavior in terms of the (Helmholtz) free energy potential and a
dissipation potential. Assuming the availability of full-field interior
kinematic data, the constitutive mismatch between the kinematic quantities
(strains and internal thermodynamic variables) and their ``stress''
counterparts (Cauchy stress tensor and that of thermodynamic tensions),
commonly referred to as the ECR functional, is established with the aid of
Legendre-Fenchel gap functionals linking the thermodynamic potentials to their
energetic conjugates. We then proceed by introducing the modified ECR (MECR)
functional as a linear combination between its ECR parent and the kinematic
data misfit, computed for a trial set of constitutive parameters. The
affiliated stationarity conditions then yield two coupled evolution problems,
namely (i) the forward evolution problem for the (trial) displacement field
driven by the constitutive mismatch, and (ii) the backward evolution problem
for the adjoint field driven by the data mismatch. This allows us to establish
compact expressions for the MECR functional and its gradient with respect to
the viscoelastic constitutive parameters. For generality, the formulation is
established assuming both time-domain (i.e. transient) and frequency-domain
data. We illustrate the developments in a two-dimensional setting by pursuing
the multi-frequency MECR reconstruction of (i) piecewise-homogeneous standard
linear solid, and (b) smoothly-varying Jeffreys viscoelastic material.
