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We extend EUCLID, a computational strategy for automated material modeldiscovery and identification, to linear viscoelasticity. For this case, weperform a priori model selection by adopting a generalized Maxwell modelexpressed by a Prony series, and deploy EUCLID for identification. Themethodology is based on four ingredients: i. full-field displacement and netforce data; ii. a very wide material model library - in our case, a very largenumber of terms in the Prony series; iii. the linear momentum balanceconstraint; iv. the sparsity constraint. The devised strategy comprises twostages. Stage 1 relies on sparse regression; it enforces momentum balance onthe data and exploits sparsity-promoting regularization to drastically reducethe 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 termsfrom stage 1, it further reduces their number by grouping together Maxwellelements with very close relaxation times and summing the corresponding moduli.Automated procedures are proposed for the choice of the regularizationparameter in stage 1 and of the number of clusters in stage 2. The overallstrategy is demonstrated on artificial numerical data, both without and withthe addition of noise, and shown to efficiently and accurately identify alinear viscoelastic model with five relaxation times across four orders ofmagnitude, out of a library with several hundreds of terms spanning relaxationtimes across seven orders of magnitude.

Automated identification of linear viscoelastic constitutive laws with EUCLID