A variational model of fracture for tearing brittle thin sheets

Bin Li, Daniel Millán, Alejandro Torres-Sánchez, Benoît Roman, Marino Arroyo*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


Tearing of brittle thin elastic sheets, possibly adhered to a substrate, involves a rich interplay between nonlinear elasticity, geometry, adhesion, and fracture mechanics. In addition to its intrinsic and practical interest, tearing of thin sheets has helped elucidate fundamental aspects of fracture mechanics including the mechanism of crack path selection. A wealth of experimental observations in different experimental setups is available, which has been often rationalized with insightful yet simplified theoretical models based on energetic considerations. In contrast, no computational method has addressed tearing in brittle thin elastic sheets. Here, motivated by the variational nature of simplified models that successfully explain crack paths in tearing sheets, we present a variational phase-field model of fracture coupled to a nonlinear Koiter thin shell model including stretching and bending. We show that this general yet straightforward approach is able to reproduce the observed phenomenology, including spiral or power-law crack paths in free standing films, or converging/diverging cracks in thin films adhered to negatively/positively curved surfaces, a scenario not amenable to simple models. Turning to more quantitative experiments on thin sheets adhered to planar surfaces, our simulations allow us to examine the boundaries of existing theories and suggest that homogeneous damage induced by moving folds is responsible for a systematic discrepancy between theory and experiments. Thus, our computational approach to tearing provides a new tool to understand these complex processes involving fracture, geometric nonlinearity and delamination, complementing experiments and simplified theories.

Original languageEnglish
Pages (from-to)334-348
Number of pages15
JournalJournal of the Mechanics and Physics of Solids
StatePublished - Oct 2018
Externally publishedYes


  • Fracture
  • Subdivision surface
  • Tearing
  • Thin sheets
  • Variational model


Dive into the research topics of 'A variational model of fracture for tearing brittle thin sheets'. Together they form a unique fingerprint.

Cite this