  We extend EUCLID, a computational strategy for automated material model
discovery and identification, to linear viscoelasticity. For this case, we
perform a priori model selection by adopting a generalized Maxwell model
expressed by a Prony series, and deploy EUCLID for identification. The
methodology is based on four ingredients: i. full-field displacement and net
force data; ii. a very wide material model library - in our case, a very large
number of terms in the Prony series; iii. the linear momentum balance
constraint; iv. the sparsity constraint. The devised strategy comprises two
stages. Stage 1 relies on sparse regression; it enforces momentum balance on
the data and exploits sparsity-promoting regularization to drastically reduce
the number of terms in the Prony series and identify the material parameters.
Stage 2 relies on k-means clustering; starting from the reduced set of terms
from stage 1, it further reduces their number by grouping together Maxwell
elements with very close relaxation times and summing the corresponding moduli.
Automated procedures are proposed for the choice of the regularization
parameter in stage 1 and of the number of clusters in stage 2. The overall
strategy is demonstrated on artificial numerical data, both without and with
the addition of noise, and shown to efficiently and accurately identify a
linear viscoelastic model with five relaxation times across four orders of
magnitude, out of a library with several hundreds of terms spanning relaxation
times across seven orders of magnitude.
