Variational approximation methods for long-range force transmission in biopolymer gels

Haiqin Wang, Xinpeng Xu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The variational principle of minimum free energy (MFEVP) has been widely used in research of soft matter statics. The MFEVP can be used not only to derive equilibrium equations (including both bulk equations and boundary conditions), but also to develop direct variational methods (such as Ritz method) to find approximate solutions to these equilibrium equations. We apply these variational methods to study long-range force transmission in nonlinear elastic biopolymer gels. It is shown that the slow decay of cell-induced displacements measured experimentally for fibroblast spheroids in three-dimensional fibrin gels can be well explained by variational approximations based on the three-chain model of biopolymer gels.
Original languageEnglish
JournalChinese Physics B
StateE-pub ahead of print - 1 Sep 2022


  • biopolymer gels
  • cell-cell communications
  • force transmission
  • variational methods


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