Soft matter at large stretch: The relationship between viscoelasticity and elasticity

Jacco Snoeijer, Anupam Pandey, Miguel Herrada, Jens Eggers

Research output: Contribution to journalArticle (Academic Journal)


Soft materials that are subjected to large deformations exhibit an extremely rich phenomenology, with properties lying in between those of simple fluids and of elastic solids. In the continuum description of these systems, one typically follows either the route of solid mechanics (Lagrangian description) or the route of fluid mechanics (Eulerian description). The purpose of this review is to highlight the relation between the theories of viscoelasticity and of elasticity, and to leverage this connection in contemporary soft matter problems. We review the principles governing models for viscoelastic liquids, for example solutions of flexible polymers. Such materials are characterised by a relaxation time λ, over which stresses relax. We recall the kinematics and elastic response of large deformations, and show which polymer models do (and which do not) correspond to a nonlinear elastic solid in the limit λ → ∞. With this insight, we split the work done by elastic stresses into reversible and dissipative parts, and establish the general form of the conservation law for the total energy. The elastic correspondence can offer an insightful tool for a broad class of problems; as an illustration, we show how the presence or absence of an elastic limit determines the fate of an elastic thread during capillary instability.
Original languageEnglish
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Publication statusSubmitted - 28 May 2020


  • elasticity
  • viscoelasticity
  • capillarity
  • gels
  • instability

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    Snoeijer, J., Pandey, A., Herrada, M., & Eggers, J. (2020). Soft matter at large stretch: The relationship between viscoelasticity and elasticity. Manuscript submitted for publication.