Automated identification of linear viscoelastic constitutive laws with EUCLID

Enzo Marino*, Moritz Flaschel, Siddhant Kumar, Laura De Lorenzis

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)
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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.

Original languageEnglish
Article number104643
Number of pages12
JournalMechanics of Materials
Publication statusPublished - 2023

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Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project
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  • k-means clustering
  • Lasso regularization
  • Linear viscoelasticity
  • Sparse regression
  • Unsupervised learning

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